A Comparison of Protocols for Updating Location Information

A Comparison of Protocols for Updating Location Information
                                      Alexander Leonhardi and Kurt Rothermel
                                          Institute of Parallel and Distributed
                                           High-Performance Systems (IPVR)
                                                 University of Stuttgart
                                                  Breitwiesenstr. 20-22
                                                70565 Stuttgart, Germany

                                               Technical Report 2000/05
                                            Department of Computer Science
                                                University of Stuttgart
                                                      March 2000

                         Abstract                                    example a printer. The location information for these ob-
                                                                     jects may have been acquired by di erent types of sensor
    The detailed location information of mobile objects, for         systems and therefore has di erent degrees of accuracy.
example that of a user with a mobile computer or phone,                  If the location information is acquired on the mobile ob-
is an important input for many location-aware applications.          ject itself (e.g., via GPS), it has to be transmitted from the
However, constantly updating the location information for            mobile object to a location server using wireless communi-
thousands of mobile objects is not feasible. Update protocols        cation. In case of a distributed service, where the location
for location information therefore use the special properties        information is cached or replicated on a number of servers,
of this information to transmit it as eciently as possible,         the information also has to be transmitted between location
that is requiring only few update messages, while still be-          servers. To control the transmission of location informa-
ing e ective in returning the location information with the          tion, di erent update protocols with varying properties can
desired accuracy. Di erent classes of such update protocols          be used. In case of a querying protocol the information is
are described in this paper and a new combined protocol              pulled by the receiver, while with a reporting protocol it is
is proposed. To be able to compare their e ectiveness and            pushed by the sender. A combined protocol is also possible,
eciency, we present an analysis for the minimum and av-             where an optimal ratio between the number of updates and
erage resulting accuracy of the location information on the          the number of queries has to be found.
receiver and the number of messages transmitted between                  In this paper we will discuss the characteristics of these
them. We also present some simulation results, which we              classes of update protocols and their subclasses as well as
have performed to back up our analysis.                              their strengths and weaknesses according to di erent areas
                                                                     of application. To be able to guarantee the receiver a cer-
1 Introduction                                                       tain accuracy of the returned location information, it usually
                                                                     has to be transmitted rather frequently. If the location in-
As detailed information about the location of a mobile de-           formation is transmitted from a mobile device to a location
vice or user has become widely available, mainly through             server, a wireless channel has to be used, where bandwidth
the satellite positioning system GPS, more and more appli-           is low and expensive. It is therefore important to use an
cations are using this information. Examples are car naviga-         update protocol that works eciently, that is requires as
tion or eet management systems, as well as location-aware            few messages as possible, and e ectively, that is achieves a
information services for cellular phones (which today use the        desired accuracy of the location information on the server.
less accurate information of the communication cell a mobile         In this paper we discuss the eciency of the basic types of
phone is currently located in). Most of these applications           update protocols by means of an analysis of the number of
only consider the location of a single user. Further function-       transmitted messages and their e ectiveness by analyzing
ality, like determining all mobile objects inside a given area       the resulting minimum and average accuracy of the location
or generating an event whenever a mobile object enters a             information at the receiver. Although this work has been
room, requires a special location service, which collects and        performed in the context of updating the location informa-
manages the location information for all of these objects. A         tion on a location service, its results are applicable wherever
universal global location service has been proposed for ex-          location information is transmitted from a sender to a re-
ample by [Leo98] and [Maa97]. Such a location service has to         ceiver.
deal with all sorts of mobile objects with various movement              The remainder of this paper is structured as follows: In
characteristics, for example objects that move continuously          Section 2 we look at related work and in Section 3 we de-
for a longer period of time, like cars and trucks, or objects        scribe the background for this paper as well as its technical
that only move seldomly, like pieces of oce equipment, for          environment. The di erent classes of update protocols and

their properties are discussed in Section 4, while Section 5,            In the DOMINO project a database for the tracking of
besides de ning a data-model for the location information            mobile objects is being developed (see [WSCY99]). One in-
and its accuracy, compares their eciency and e ectiveness           tended area of application is eet management for the trucks
by means of an analysis. In Section 6 we present some sim-           of a transportation company. To reduce the number of up-
ulation results, to support the outcome of our analysis. Fi-         dates, it is assumed that the route, on which the mobile
nally, Section 7 contains our conclusion, as well as the plans       object is traveling, is known to the database in advance and
for future work.                                                     that the object informs the database when it changes its
                                                                     route. Di erent dead-reckoning strategies are proposed and
2 Related Work                                                       compared, where the database estimates the current loca-
                                                                     tion of a mobile object on this route based on its speed
Architectures for a location service have been discussed in          and the object sends an update of its location when it dif-
the area of location-aware applications as an important com-         fers from this estimation by more than a certain threshold.
ponent of such systems. However, di erent update proto-              The di erent strategies have di erent ways for determining
cols for the transmission of the location information have           this threshold or for adapting it dynamically. These dead-
not been compared in detail. Early location services were            reckoning protocols have been designed on the assumption
usually developed for a particular positioning system, like          that the route of the mobile objects is known beforehand. In
the location service for the Active Badge system, which is           this paper we examine update protocols from a more general
described in [HH94]. For a similar positioning system, the           point of view, where we assume no knowledge of the mobile
ParcTab system developed at Xerox Parc, a location ser-              objects' future movements.
vice has been created, where the location information of
a mobile object or user is protected by a dedicated Home             3 Background
Agent, which controls access to it [ST94]. In this context
the problem of disseminating the location information to a           This section gives an overview of the technical environment
large number of clients has been discussed in [ST94]. Clients        our work is based on, namely the sensor systems the location
with similar queries receive the location information over dy-       information is acquired from and the network environment
namically created multicast groups in which the responses            it is transmitted over. Finally, we describe the architecture
to these queries are grouped. In his PhD-thesis, Leonhardt           for a universal distributed location service, which is being
([Leo98]) proposes a universal location service, which is in-        developed at our Institute and where we plan to apply the
dependent from the types of applications accessing it and the        results of this work.
types of positioning systems it gets the location information
from. A detailed location model is presented that integrates         3.1 Positioning Sensors
di erent types of location information. Another main con-
cern of this work is privacy and security. For this purpose it       The location information for a mobile object can be deter-
de nes requirements and policies for access control of a loca-       mined through various types of positioning systems. A basic
tion service. The thesis also contains some thoughts about           distinction can be made between tracking systems, where a
the design of a global, general-purpose location service but         system of stationary sensors determines the location of a
does not propose or evaluate a speci c architecture.                 mobile object, and positioning systems, where the location
    The management of the location information of their mo-          information is determined by a sensor on the mobile object
bile phones is a very important issue in the area of mobile          itself. A typical tracking-system is the Active Badge system
communication networks. When a call has to be forwarded              (see [WHFG92]), where an Active Badge carried by a user
to a mobile phone, a mobile communication network sends              or attached to an oce device periodically emits an infrared
a paging message to all the cells the mobile phone may be            beacon, which is detected by an infrared sensor placed in
in, whereupon the corresponding mobile phone answers to              each room of a building. The widely used global positioning
accept the call. The mobile phone on the other hand pe-              system (GPS) is a positioning system, where a sensor deter-
riodically reports its current cell, which is updated in the         mines its own position by taking a bearing on four of a whole
Visitor Location Register and Home Location Register. Var-           of twenty-four special satellites (see [HWLC97]). Di erent
ious update strategies have been discussed with the goal of          types of positioning systems return the location informa-
minimizing the overall number of paging and update mes-              tion with varying formats and degrees of accuracy. It can
sages. In [BNKS95] a distance-based, a movement-based                be symbolic (i.e., the identi er of a region, like a room or
and a time-based protocol are compared. In this special              communication cell) or geometric, where it is described by a
application area the location information is a discrete iden-        global geodetic coordinate system like WGS84 (see [IA97]).
ti er, describing a certain cell of the communication net-           The classi cations in this paragraph have been taken from
work. Today, these cells have a size of about 1 to 10 miles          [Leo98].
but are expected to become smaller with the introduction                 Because no positioning system o ers a global coverage
of future technologies. Update policies for location manage-         (e.g., GPS works only outdoors) a universal location service
ment have been optimized for these special requirements. In          has to be able to integrate the location information acquired
[BD99] the LeZi-update approach is described, which uses             by all types of positioning systems.
the cell names as an alphabet for minimizing the updates
by an mechanism similar to the Lempel-Ziv compression. In            3.2 Network Environment
our work we have assumed that the location information is
much more accurate, acquired for example by a GPS sensor,            In our work, we have assumed the following network environ-
and that the location information can have di erent levels           ment: Location servers and stationary clients, which query
of accuracy. The location service, these update protocols            the location information, communicate over a xed network.
are intended to be used for, also allows di erent types of           Mobile devices need to be connected to this network by a
queries (e.g., range queries), which are not supported by the        wireless link. They have to be able to communicate and to
location management components of mobile communication               be contacted independently from their geographical location
networks.                                                            (e.g., using a mechanism like Mobile IP [Pe96]), because the

device has to transmit location information to a server via                  We have proposed an architecture for such a location
the wireless link or is queried by the location server through           service, which is shown in Figure 1. Its components and
it, if the information is determined locally. Mobile devices             their functionality are described next:
may also act as a client of the location service by posting                   Clients and sensor systems: Clients of the location ser-
queries over the wireless link. The wireless network can ei-                   vice are location-aware applications, which run either
ther be a wireless WAN, like GSM [MP92], a MAN, like the                       on a mobile or on a stationary computer and query the
Metricom Ricochet network, or a LAN, for example accord-                       location servers using the interface mentioned earlier
ing to the IEEE 802.11 standard [Com97].                                       in this subsection. A client on a mobile device is usu-
    A common characteristic of these wireless networks is                      ally also equipped with a positioning sensor or is being
that a connection can be temporarily lost while the device is                  tracked by one. Sensor systems, which, depending on
at an unfavorable location (e.g., inside of a tunnel), a state                 their type, determine the location information for one
which is called a disconnection. In most cases a wireless                      or more mobile objects, are associated with a certain
network can also not o er as good a bandwidth and latency                      location server and update the location information for
as a xed networks (see [Sat96]).                                               these objects.
3.3 A Universal Location Service                                              Location server: Each location server is responsible
                                                                               for a certain geographical area and stores the location
This comparison of update protocols has been done as part                      information for all mobile objects that are currently
of our e orts to design and develop a universal distributed                    inside of this area. If a mobile object leaves the area,
location service (see [LK99]). As mentioned before, this ser-                  a hand-over has to be performed with the server, into
vice will have to collect and integrate the location infor-                    whose area the object has moved. A location server
mation from various sensor systems. Furthermore, it will                       answers the clients' queries concerning the mobile ob-
provide a general interface through which di erent types of                    jects it is responsible for and forwards other queries to
applications can access the location information in a general                  the appropriate server(s). This is done by accessing
way. For reasons of scalability and to achieve short response                  one of the two following registers:
times as well as high update rates, the information will be
distributed between a number of location servers.                             Object register: The data, which belongs to a single
    The location service shall provide the following function-                 mobile object, is stored in the object register. It can
ality: It will support range queries, that is nding all mobile                 contain general information about the object or infor-
objects inside a given area, as well as position queries, which                mation that is determined by the location service, like
request the current location of a certain mobile object. A                     the maximum speed of the object. The object regis-
more specialized query is, for example, the search for the                     ter also stores the addresses of the location servers the
nearest object to a certain location. It is intended, that the                 location information for this object is currently stored
location service will additionally support an event mecha-                     on. It can easily be distributed, so that each register
nism, where the client can de ne a certain predicate and                       server is responsible for a certain set of objects.
is noti ed by the service whenever this predicate becomes                     Location register: The location register stores the as-
true. A client program may for example be noti ed, when-                       sociation between the location servers and the area
ever a mobile object enters or leaves a given area or when                     they are responsible for. It is used to nd the appro-
a mobile object meets another one, that is comes within a                      priate location servers for a range query. If necessary,
certain distance from it.                                                      the location register can be distributed across di erent
                                                                               servers, which are organized in a tree structure similar
                                                                               to the Domain Name System (DNS) of the Internet.
                                                                         Because of privacy concerns, security and access control for
              client                        sensor                       such a location service are very important issues. A user
              programs                      systems
                                                                         should be able to control in detail who and to what degree
                                                                         has access to his location information. Some solutions for
          results,            queries,                   object          this problem have been presented in [Leo98]. In this paper
          notifications       events                     sightings
                                                                         we do not discuss privacy any further, but will address the
                                                                         issue in future work.
                service API                                              4 Update Protocols
                                                                         In this section the di erent classes of update protocols are
                                                                         introduced and their main properties are discussed. The
                     lookups                        lookups              protocols are used to update a remote secondary copy of the
                                                                         location information for a certain mobile object based on
                                                                         the contents of a primary copy. The goal is to guarantee a
                          updates         updates                        given accuracy of the location information in the secondary
                                                                         copy. The information of the primary copy is either deter-
             location                         object                     mined directly by a positioning system or is the information
             register                         register
                                                                         stored on another location server. We call the component
                                                                         which manages the primary copy the source of the location
                                                                         information. The secondary copy is usually stored on a spe-
                                                                         cial or general location server, which is queried by local or
Figure 1: Main components of a universal distributed loca-               remote applications. Figure 2 shows the components which
tion service                                                             are involved in the transmission of the location information.

time of the server is also comparatively large, as the server
                                                 secondary                                  has to contact the source for each query. On the other hand,
                       copy                      copy                                       this protocol has to be used, if because of privacy concerns
    sensor                                                                                  the user does not allow his/her location information to be
    system         mobile            update
                                                                                            stored on any location server other than on his/her personal
                   device or
                                                                                            device. In this case, the personal device has to be accessed
                                     fixed                                                  for each query to check for access rights. An example for
                                     network or                                             this is the location service presented in [ST93], where a spe-
                                     communication                                          cial program, a so-called User Agent, stores and protects
                                                                                            the location information of a certain user. Here, we use this
                                                                                            protocol mainly for comparison.
Figure 2: Components involved in the updating of location                                   Cached: The cached querying protocol is an optimization of
information.                                                                                the simple protocol, where the server stores a cached copy
                                                                                            of the last transmitted location information. When the lo-
4.1 Classi cation                                                                           cation information for this mobile object is queried by an
                                                                                            application, the server estimates the accuracy of the cached
The update protocols can be divided into three main classes,                                copy and returns it, if it is considered to be accurate enough.
namely querying, reporting and combined protocols, where                                    Otherwise, the server has to send a request to the source like
each class has a number of typical variants. Each of these                                  in the simple protocol. A pessimistic cached querying pro-
protocols has its characteristic properties and is suitable for                             tocol uses the distance, a mobile object may have traveled
a given environment or for certain requirements. Some of                                    at its maximum speed, for the estimation of the accuracy.
the reporting protocols are similar to the paging/update                                    If the maximum speed of the mobile object is much higher
schemes that are used for Location Management in the re-                                    than its average speed, the cached copy is often unnecessar-
search area of Personal Communication Service (PCS) net-                                    ily considered not accurate enough. An optimistic cached
works and are summarized, for example, in [BNKS95]. The                                     querying approach could use the average speed of the mo-
classes of update protocols and their relationships are shown                               bile object instead of the maximum one. However, with any
in more detail in Figure 3.                                                                 optimistic estimation for the accuracy of the location infor-
                                                                                            mation, the actual location of the mobile object can in the
                                                                                            worst case di er from the reported location by more than
                                                                                            the requested accuracy. With a cached querying protocol
                                           update protocols                                 the response time of the server is varying and depends on
                                                                                            whether the server can use the cached copy or has to contact
                                                                                            the source.
                                                reporting                                   Periodic: If the server queries the location information peri-
                                                                                            odically from the source with a certain time interval D, the
              querying                                                     combined

                                                                                            protocol is called a periodic querying protocol. Although
                                                                                            here the initiative is reversed, this protocol has the same
  simple     caching      periodic      simple distance-      time-      dead-              properties as the time-based variant of the reporting proto-
                                               based          based      reckoning
                                                                                            cols described next.
Figure 3: Classi cation of update protocols for the trans-                                  4.1.2 Reporting Protocols
mission of location information.                                                            In case of a reporting protocol the initiative is on the side of
                                                                                            the source. It remembers which location information it has
                                                                                            sent last to the server and therefore knows which location
4.1.1 Querying Protocols                                                                    is stored there. An update of the location information is
A protocol is called a querying protocol, if the server decides                             sent, whenever a comparison to the current position of the
when to request the location information from the source.                                   mobile object exceeds a certain distance or time threshold.
In this case, the source can be very simple, as it does not                                 The server can therefore conclude the maximum uncertainty
need to keep extensive information about its state or realize                               of its copy from the value of this threshold. With an un-
a complicated logic. This may be important for small mo-                                    modi ed reporting protocol the server always answers the
bile devices. The simple and the cached querying protocols                                  queries of the applications by directly returning the infor-
transmit the location information on-demand, that is only                                   mation currently stored in its copy. It can therefore only
when it is queried by an application. If the location infor-                                return the location information with an accuracy speci ed
mation is queried only seldomly, these protocols are more                                   by the value of the threshold, even if a more accurate in-
ecient than the reporting protocols described in 4.1.2, be-                                formation is queried by an application. The response time
cause the information is not transmitted unnecessarily (see                                 of the server on the other hand is shorter, as it does not
Section 5).                                                                                 have to contact the source. A reporting protocol is usually
                                                                                            more ecient for a given maximum accuracy than a query-
Simple: In the most simple form the server requests the lo-                                 ing protocol, if the location information is queried often (see
cation information from the source each time it is queried                                  Section 5) or if the server has to check periodically for the
by an application and therefore does not need a secondary                                   occurrence of events.
copy at all. This leads to the highest possible accuracy of                                 Simple: The most simple reporting protocol sends the lo-
the location information, but also to a large number of mes-                                cation information each time the value of the primary copy
sages, if the information is queried very often. The response

Message rate is Message                       Upper       bound Allows applica- Can detect dis-
                        adjusted to mo- rate is adjusted to           for spatial uncer- tions to specify a connections.
                        bility of object. query rate and re-          tainty of returned desired accuracy.
                                          quested accuracy.           information.
     simple                                                                ()                                      
     cached                                                                ()                                      
     simple                                                                 ()                                      ()
     dead reckoning                                                         
   combined                                                                                                      ()
                                Table 1: Summary of properties for di erent update protocols.

changes, for example because a sensor system has deter-                4.1.3 Combined Protocol
mined a new location sighting. In this case the number of              While a plain querying protocol can not be adjusted to dif-
messages depends on the update rate of the sensor system               ferent mobility characteristics of the mobile objects, a re-
and can be rather high. Depending on the type of sensor                porting protocol does not consider the query rate and the
system, the simple reporting protocol also falls into one of           accuracy requested by the applications. With a combined
the two following categories. We therefore do not consider             protocol, which integrates the distance-based reporting pro-
it any further.                                                        tocol and the cached querying protocol, both of these fea-
Time-based: With a time-based protocol the location infor-             tures can be achieved. Similar to the distance-based report-
mation is transmitted periodically, after a certain interval of        ing protocol, the source may update a secondary copy on
time T has elapsed. The update rate is xed and does not                the server to achieve a given spatial accuracy D. If the
depend on the behavior of the mobile object, which guaran-             location information stored in the secondary copy is not ac-
tees a certain temporal but not a spatial uncertainty of the           curate enough for a certain query, the server requests the
information. If the object moves slowly or not at all, there is        information from the source as in a querying protocol. To
little or no di erence in the location information transmit-           minimize the total number of messages consisting of updates
ted by the messages to the server. If the object moves fast,           and queries, it has to be decided whether to update a sec-
not enough messages are sent to achieve a high accuracy.               ondary copy at all and what distance threshold D has to
                                                                       be used, depending on the mobility properties of the mobile
Distance-based: The distance-based protocol sends an up-
                                                                       object and on the queries by the applications (see Section
date of the location information whenever the geographic               5). If the source monitors the mobility properties and the
distance between the current location of the mobile object             server those of the queries, they can adapt the properties of
and the last reported location becomes greater than a given            the protocol dynamically by increasing/decreasing the dis-
threshold D. As this protocol sends more messages if the               tance threshold D or by starting/stopping the updating of
mobile object is moving fast and less messages if it is slower         the secondary copy altogether. With the combined protocol,
or stationary, it is often more ecient for objects that per-          the response time is again varying and depends on whether
form sporadic movements between periods of immobility.                 the secondary copy on the server is accurate enough or if
This is, for example, typical for users in an oce environ-            the server has to contact the source.
ment or for all sorts of oce equipment. It is also possible
to integrate the time-based and the distance-based protocol            4.2 Behavior in Case of Disconnection
to combine their properties.                                           A problem that frequently occurs with mobile devices and
                                                                       wireless data transmission is a temporal disconnection of the
Dead-reckoning: Dead-reckoning is an optimization of the               communication link. A protocol which is intended to trans-
distance-based protocol. Here, the server estimates the cur-           mit location information from a mobile device to a server
rent location of the mobile object based on its old location,          via a wireless communication link has therefore to be able
its speed and the direction of its movement or on informa-             to deal with such disconnections. In the following para-
tion about the route of the object. The source also calculates         graphs we discuss the properties of the basic protocols with
this estimated location and sends an update when it di ers             regard to disconnections, namely how long it takes to detect
from the actual location by more than a certain distance               a disconnection and the maximum uncertainty of the loca-
threshold. A dead-reckoning approach performs very well,               tion information returned during that time. If the server has
if the object is moving with constant speed in a given di-             detected a disconnection it can, according to the preferences
rection for some time or if the route of the mobile object             of its users, either return an error message when queried for
is known in advance. In the second case the update costs               the location information or return the last known position
can, according to [WSCY99], be reduced by 85% compared                 together with an indication that it is obsolete. Where neces-
to other reporting protocols.                                          sary we sketch appropriate modi cations to these protocols
                                                                       that enable them to deal with disconnections.
                                                                       Querying protocols: In case of a querying protocol, the dis-
                                                                       connection is detected as soon as the server receives a query

and requests the location information from the source (and,           these protocols, based on the results of the analysis. Only
in case of a cached querying protocol, also can not answer            the updates and queries for the location information of a
the query from its cached copy). Therefore, the server does           single mobile object are considered, as the results can be
not at any time return less accurate information than in the          easily applied to several objects. For reasons of simplicity
normal case.                                                          we also do not consider the delays for the transmission of
                                                                      the messages, which would lead to a further (temporal) un-
Time-based reporting protocol: When using a time-based                certainty of the location information. Because it is added
protocol a disconnection can be detected if no update mes-            uniformly to all messages, the delay does not substantially
sages have arrived after the time threshold T has elapsed             a ect the comparison of the protocols.
since the last update. Again the server only returns loca-                The eciency of an update protocol is here considered
tion information with the speci ed accuracy.                          to be the average number of messages m that is transmitted
                                                                      per second between the source and the server. Messages can
Distance-based reporting protocol: With the basic distance-           be location updates generated by the source as well as loca-
based protocol the server is not able to detect a disconnec-          tion requests from the server. The accuracy of the location
tion. Instead, it assumes that the mobile object has not              information on the server, which describes the e ectiveness
moved by more than the distance threshold D and returns               of a protocol, is de ned by the maximum and average de-
the old location information as being up-to-date. To be able          viation between the information returned as a result of a
to detect disconnections, the distance-based protocol can be          query and the actual position of the mobile object. Up to
combined with a time-based one, by having it sent a location          now, we have assumed that applications are only interested
update at least every time interval Tmax . A suitable value           in the maximum uncertainty of the location information, for
for Tmax has to be found by considering the message over-             example if they want to be able to determine which room of
head versus the maximum uncertainty, the user is willing to           a building a certain user is in. However, other types of appli-
tolerate in case of an error.                                         cations may be more concerned with the average accuracy
                                                                      of the information. An example for this could be a map,
Dead-reckoning reporting protocol: A basic dead-reckoning             where the current locations of a number of mobile objects is
protocol has the same problems with disconnections as the             shown. In our analysis we have therefore considered both,
distance-based protocol and the same mechanism can be                 the maximum and the average accuracy, dmax and davg .
used to deal with them. In [WSCY99] another technique                     The calculations for m, dmax and davg are based on
for detecting disconnections has been introduced, were the            the behavior of the mobile object, de ned by its average
distance threshold D is being continuously decreased until            and maximum speed, vavg and vmax , and on the uncer-
the source is forced to send an update message or it has be-          tainty up with which the location information is available
come increasingly likely that a disconnection has occurred.           at the source. Moreover, the calculations depend on how
                                                                      frequently and to what accuracy the location information is
Combined protocol: How the combined protocol reacts to                queried by the applications, which is described by the av-
disconnections depends on how accurate a secondary copy               erage number of queries per second q and the average of
is kept on the server. A disconnection is detected as soon as         the requested uncertainty uq . The calculations are also af-
the server has to request the location information from the           fected by characteristic parameters of the di erent protocols,
source. If this is not the case, the combined protocol behaves        namely the maximum uncertainty required of the secondary
like the distance-based protocol and can return inaccurate            copy us , the speed that is assumed for the mobile object by
location information. Again, a maximum time interval Tmax             the cached querying protocol vasd, and the time threshold T
between update messages should be speci ed.                           for a time-based or the distance threshold D for a distance-
                                                                      based reporting protocol. Table 2 shows a summary of these
    A summary of the properties for the di erent update               variables.
protocols discussed in this section is contained in Table 1.              Some important restrictions between these variables are
It shows, whether the message rate of a protocol depends              as follows: Because the information transmitted to the server
on the mobility characteristics of the mobile objects and             can not be more accurate than the information of the source,
whether it depends on the queries of the applications. It             the uncertainty of the secondary copy is always equal to or
also indicates, whether the protocol can guarantee an upper           greater than the uncertainty of the primary copy, us  up .
bound for the returned location information and if it allows          Also, it is not practical for an application to request more
the applications to request a certain accuracy of the infor-          accurate location information than the one available at the
mation. The nal column shows, whether the protocol is                 source. Hence, we also assume that uq  up . For the calcu-
able to deal with disconnections.                                     lation of the average deviation we assume that the average
                                                                      uncertainty of the location information on the source is half
                                                                      of the maximum uncertainty. This may not be true for all
5 Analytical Comparison of the Protocols                              sensor-systems (e.g., the average uncertainty is less than half
                                                                      of the maximum if the source is a GPS sensor), but does not
In this section, the e ectiveness and eciency of the update          have much in uence on the outcome of the analysis. The re-
protocols are compared in more detail, by means of an analy-          strictions described here apply to all formulas in this section
sis. First, the variables that appear in the following analysis       and are not explicitly stated again.
are described and a general data model for the location in-
formation and its accuracy is de ned. The analysis considers          5.1 Location and Uncertainty Model
the number of messages required for updating the location
information on the server as opposed to the minimum and               For the following analysis we use a uniform model of the
average accuracy of the location information returned to an           location information returned by the di erent positioning
application. Corresponding formulas are shown rst for the             systems and of its accuracy.
querying and reporting protocols, then for a combined pro-               The location information is supposed to be given by
tocol. Finally, we discuss the characteristic properties of           global geodetic coordinates, for example of the WGS84 stan-

vmax Maximum speed of mobile object.                                                            u(t)
        vavg Average speed of mobile object.
        q    Average number of times per sec-
             ond, the location information of the                                       vmax (t - tl)
             mobile object is queried.
        uq   Average of requested accuracy for                                                                 up
             this location information.
        uq  Accuracy requested in one certain                                                     up
        up   Uncertainty of primary copy.
        Tp   Update interval of primary copy.
        tl   Time at which a certain location                                                                       location sighting
             sighting l has been acquired.                                                                          uncertainty
        us   Uncertainty of secondary copy.
        vasd Speed that is assumed for estimat-
             ing the accuracy of the location                        Figure 4: Uncertainty of location information depending on
             information.                                            the accuracy of the sensor system and the elapsed time.
        T    Time threshold of the time-based
             reporting protocol.
        D    Distance threshold of the distance-                     of a person to 36 km/h. By evaluating the history of the
             based reporting protocol.                               location sightings of a mobile object, it is also possible to
        m    Average number of messages trans-                       determine a maximum velocity separately for each object.
             mitted per second between source                            In many cases, however, the location sighting will be
             and server.                                             more accurate than the uncertainty given by this equation,
        dmax Maximum deviation between the lo-                       as the mobile object will not be moving at its maximum
             cation information the server re-                       speed or not in a straight line. A person in an oce will usu-
             turns as result of a query and the                      ally remain relatively stationary at a certain location (e.g.,
             actual position of the mobile object.                   his oce or a conference room) for a longer interval of time,
        davg Average deviation.                                      while moving at a comparatively high speed between these
                                                                     locations. If the uncertainty does not need to be limited by
                                                                     an upper bound or the maximum velocity is not known, an
          Table 2: Variables used in the analysis.                   assumed velocity vasd (e.g., the average velocity vavg of the
                                                                     mobile object) can be used to predict the uncertainty instead
                                                                     of the maximum velocity vmax . In some cases this will lead
dard, where the distance between two locations can easily            to an actual deviation, which is greater than the predicted
be calculated. Symbolic location information (e.g., the name         one. This error will be worse for the sporadic movement of a
of a room) returned by some of the positioning systems can           person in an oce, compared to the more steady movement
easily be converted to geometric coordinates. The geomet-            of a traveling car.
ric coordinate for a region described by a certain symbolic
name is given by the center of the region, while the spatial         5.2 Basic Protocols
accuracy is the distance from the center to the farthest point
in the region.                                                       The equations for an approximate calculation of the number
    A location sighting can have a temporal as well as a             of transmitted messages as well as for the maximum and av-
spatial accuracy. The temporal accuracy is given by the              erage uncertainty of the location information are shown next
time that has elapsed since the location sighting has been           for the basic querying and reporting protocols. We have
acquired, while the spatial accuracy is de ned by the max-           not yet performed the analysis for the dead-reckoning pro-
imum distance between the position reported by the sight-            tocol, because it depends to a great extent on the movement
ing and the actual position of the mobile object. For many           characteristics of the mobile object and we did not want to
location-aware applications the spatial accuracy of a sighting       assume prior knowledge about the route of the object. In
is more important, because the applications are concerned            general the dead-reckoning protocol can be expected to be-
with the spatial relationship between (mobile) objects. The          have similar to the distance-based reporting protocol.
uncertainty ul (t) of a certain location sighting l describes
the spatial accuracy at a given time t  tl .                        Simple querying protocol: In the simple querying protocol,
    At the time of the sighting the uncertainty is determined        which is presented here only for reasons of comparison, the
by the accuracy up of the sensor system. The uncertainty at          number of exchanged messages is equal to the number of
a later time t can be estimated by the distance the mobile           queries as every query is forwarded to the source.
object may have traveled during the time t ; tl . If a maxi-
mum bound for the velocity of the mobile object (vmax ) ex-                                      m=q                          (2)
ists, the maximum uncertainty of the location sighting can
be calculated by adding the distance the object can have             If we do not consider the communication delay, the loca-
traveled to the uncertainty of the sensor system (see Figure         tion information presented to the applications has the same
4). This is described by the following equation:                     accuracy as the location information of the source.
                  ul (t) = up + vmax (t ; tl )             (1)                              dmax = up                         (3)
                                                                                            davg = 2 p                        (4)
    For example, the maximum velocity of a car can be set to
300 km/h (to be on the safe side) and the maximum velocity

Distance-based reporting protocol: The number of messages
Cached querying protocol: The cached querying protocol              transmitted with the distance-based protocol is also inde-
uses Formula 1 to estimate the uncertainty of the location          pendent of the number of queries. To guarantee a given
information stored on the server and if accurate enough re-         uncertainty us of the location information on the server, the
turns it without contacting the source. For the speed of the        distance threshold D is set to us ; up . The average num-
mobile object used in this formula it can take a pessimistic        ber of messages per second can then be calculated by the
approach with vmax (as shown in Formula 1), or an opti-             time interval that the mobile object requires to cover this
mistic approach with vavg instead of vmax . In the following        distance at average speed.
considerations we represent the assumed speed of the mobile
object by vasd, which is then replaced by the speed used in                                   m = u v;
                                                                                                       u                       (11)
a concrete version of the protocol. Compared to the sim-                                               s     p
ple protocol, the caching approach eliminates all messages          If no messages are lost due to problems with the network
where the query falls into the period of time in which the          connection (compare Section 4), the distance-based proto-
cached copy of the location information is considered accu-         col achieves the requested maximum uncertainty us for the
rate enough, t = (uq ; up )=vasd (derived from Formula 1).         secondary copy on the server. On average the uncertainty
The number of messages transmitted between source and               is half of it.
server is therefore the total number of queries, multiplied
by the fraction of queries that can not be answered from the                               dmax = us                     (12)
cache, which is approximately 1=(q(uq ; up )=vasd + 1).                                    davg = u2s                    (13)
                     m=           q                      (5)
                                ;up + 1
                           q uvqasd                                 5.3 Combined Protocol
The maximum uncertainty of the returned location informa-           The combined protocol comprises elements of the distance-
tion is given by the time t the cached copy is considered          based reporting protocol and the pessimistic cached query-
accurate, multiplied with the maximum speed of the mo-              ing protocol, described in the previously. Therefore, it also
bile object. To this the initial uncertainty of the location        combines elements of their behavior. The transmitted mes-
information of the primary copy has to be added. The av-            sages are the updates sent to keep the secondary copy up-
erage uncertainty can be approximated by the uncertainty            to-date as well as the requests for the location information
of the sensor system, if the location information has to be         on the source sent by the server, if the secondary copy is
requested from the source. Otherwise, the average uncer-            not accurate enough. The number of updates can be cal-
tainty is half the distance that the mobile object can have         culated similar to the number of messages in the distance-
traveled at average speed during the time in which a cached         based reporting protocol. The number of requests is the
copy is considered valid. The corresponding Formula 7 is            number of messages in the cached querying protocol, where
shown in a simpli ed form.                                          the query rate is reduced by the probability that the un-
                                                                    certainty demanded in a query is lower than the accuracy
              dmax = uqv; up vmax + up                   (6)        of the location information already stored in the secondary
                                                                    copy, P (uq < us). The probability distribution depends
                     uq ;up  vavg                                  on how the location information is queried and used by the
              davg = vasd          up                               applications.
                        vasd + 1 + 2                     (7)

                     (uq ;up )q

                                                                              m = u vavg    +      P (uq < us )  q          (14)
If the assumed speed vasd of the mobile object is set to its                                                     ;up + 1
                                                                                     s ; up P (uq < us )  q uvqmax
maximum speed vmax , the uncertainty of the location infor-
mation presented to the querying application is limited by          Because the combined protocol queries the source whenever
uq (substituting the variables in Formula 6). The protocol          the location information stored in the server is less accurate
can therefore in this case guarantee the accuracy requested         than the accuracy demanded in a query, it can always return
by the applications.                                                the desired accuracy similar to a cached querying protocol.
                                                                    The maximum uncertainty returned is therefore the uncer-
Time-based reporting protocol: As the time-based protocol           tainty demanded in the queries. The average uncertainty is
sends a location update periodically, the number of messages        again a combination of the average accuracy of the reporting
depends only on the time threshold T . To achieve a given           protocol, in case the accuracy requested in a query can be
uncertainty us for the secondary copy, T has to be set to the       met by the secondary copy, and of the average accuracy of
time, the mobile object needs to cover the distance given by        the querying protocol, otherwise.
us minus the uncertainty of the primary copy at maximum
speed, T = (us ; up )=vmax .                                                                 dmax = uq                        (15)
                           m= 1 T                         (8)              davg = P (uq  us )  u2s +
The maximum deviation can be calculated by adding the                                                      uq ;up  vavg     !
distance that the object may have traveled during time T                              P (u < us )         vmax         u p
                                                                                                             vmax + 1 + 2      (16)
to the uncertainty of the location information at the source.                                              (uq ;up )q
For the average deviation the average speed is used, instead
of the maximum one.                                                 The behavior of the combined protocol can be controlled
                                                                    through the uncertainty of the secondary copy. If it is set to
                 dmax = T  vmax + up                     (9)       a low value, the protocol behaves like the distance-based re-
                         T   v avg  u p                            porting protocol, if it is set to in nity, the combined protocol
                 davg = 2 + 2                            (10)       can be made to behave like a cached querying protocol.

5.4 Discussion                                                                                 The other aspect of the update protocols, which is dis-
To compare the properties of the protocols, we rst look                                    cussed in this paper, is their e ectiveness, that is to what
at their eciency, that is the number of messages that are                                 degree the server can ful ll the accuracy demanded in a
transmitted between source and server. These are shown in                                  query. The maximum and average uncertainty (dmax and
Figure 5 for the querying and reporting protocols depending                                davg ) of the location information returned by the server is
on the number of queries per second. For the other param-                                  shown separately for the two cached querying and the two
eters we have assumed values taken from GPS traces that                                    reporting protocols in Figure 6. The uncertainty is shown
we have obtained from a Di erential GPS sensor during a                                    depending on the speed ratio between the average and the
car ride and which are described in more detail in the next                                maximum speed of the mobile object (vavg =vmax ), which
section. The average and maximum speed for the mobile                                      gives a good indication of its mobility characteristics. A
object is vavg = 12 m/s and vmax = 40 m/s. The uncer-                                      mobile object with a low ratio moves sporadic, an object
tainty of the primary copy up is that of the sensor system                                 with a ratio approaching 1 moves steadily. For the graphs
and is set to 5 m. For the queries we have assumed a xed                                   we have assumed a query rate q of 0:1 queries per second.
demanded uncertainty of uq = 100 m.                                                            The pessimistic cached querying approach can meet the
                                                                                           required accuracy independently from the mobility of the
                                                                                           object. For a low speed ratio it also has a very low average
                                                                                           uncertainty. In comparison, the optimistic cached querying
                                                                                           protocol, which is much more ecient, results in an almost
                        100                                     simple querying
                                                   pessimistic cached querying
                                                    optimistic cached querying
                                                                                           constant average uncertainty, a little below the uncertainty
                                                                                           requested by the client. However, for a low speed ratio the
                                                           time-based reporting
                         10                           distance-based reporting
                                                                                           maximum uncertainty can be much higher than the one de-
 messages per second

                                                                                           manded by the client. This protocol is therefore not suitable
                                                                                           for objects with sporadic movement, if the querying appli-
                                                                                           cation can not tolerate variations in the uncertainty.
                                                                                               Both reporting protocols can meet a xed uncertainty
                                                                                           demanded by the client. The time-based protocol has a low
                                                                                           average uncertainty for a small speed ratio, compared to
                        0.01                                                               the distance-based protocol, which o ers a constant average
                                                                                           uncertainty for all types of mobile objects. As the former
                                                                                           requires more messages, the later is to be preferred. The
                       0.001                                                               reporting protocols, however, can only return the location
                           0.001   0.01            0.1             1              10
                                                                                           information with the accuracy currently stored on the server.
                                                                                           They can not meet the demand of applications which        query
                                            queries per second

Figure 5: Analytical results: A comparison of the number                                   the information with a lower requested accuracy, uq < us .
of messages transmitted with the querying and reporting                                        From the viewpoint of their e ectiveness, the distance-
protocols for a given query rate.                                                          based reporting protocol is equal to the cached querying
                                                                                           protocol if only a xed requested accuracy is considered (al-
    Generally, a distance-based reporting protocol performs                                though, the later has a better average uncertainty, especially
better than the time-based one and the optimistic cached                                   for a low speed rate). The reporting protocols are not suit-
querying protocol better than the pessimistic one. While                                   able, if the location server allows the client to exibly specify
the properties of the reporting protocols are independent                                  the requested accuracy and it is important to meet these re-
from the query rate, the number of messages increases with                                 quirements.
a querying protocol with the number of queries. If the query                                   As mentioned before, the performance of the combined
rate is low, a querying protocol is therefore better than a re-                            protocol depends on the uncertainty with which the sec-
porting protocol. For very low query rates a simple protocol                               ondary copy is updated as well as on the query rate. In
is sucient. If the query rate is higher, the distance-based                               Figure 7, the number of transmitted messages is shown for
reporting protocol requires fewer messages than the pes-                                   the combined protocol depending on the uncertainty of the
simistic cached querying protocol, which is in many cases to                               secondary copy and the query rate. For the uncertainty de-
be preferred to the optimistic protocol as it can guarantee a                              manded in the queries we have assumed a Gaussian distri-
maximum uncertainty of the returned location information.                                  bution with an expected value of uq = 100 m and a standard
The query rate at which the performance of the reporting                                   deviation of 20 m. All other parameters have the same val-
protocol becomes better than that of the querying protocol                                 ues as before.
is given by the following inequation:                                                          Figure 7 indicates an optimal value for the uncertainty
                                                                                           of the secondary copy for higher query rates, whereas for
                                 1                                                         lower query rates the number of messages is lowest, if the
                     q>                   us ;up          (17)
                                                         ;up                               uncertainty is set to in nity. It is therefore possible to use
                                           vavg     ; uvqmax                               Formula 14 to decide, whether it is useful to update a sec-
                                                                                           ondary copy at all and to nd an optimal uncertainty value
    If vavg is low compared to vmax , which is the case for                                for it. The uncertainty value can either be calculated with
mobile objects with sporadic movements, the limit for the                                  the necessary parameters set to the average values deter-
query rate in Formula 17 approaches 0. For such objects,                                   mined for a certain environment, the protocol is going to
the distance-based reporting protocol is always better than                                be used in. Or it can be adjusted dynamically according to
the cached querying one. If vavg approaches vmax , the limit                               changes in the environment.
for the query rate approaches in nity. In this case, the                                       For comparison with the other protocols, Figure 8 shows
cached querying protocol always performs better. However,                                  the number of messages transmitted with the combined pro-
the number of messages for high query rates is only a little                               tocol depending on the query rate. Optimal values for the
higher with the reporting than with the querying protocol.                                 uncertainty of the secondary copy have been taken from Fig-

pessimistic cached querying                                                                                                                                                                  optimistic cached querying
   uncertainty of returned location information in meters

                                                                                                                                                                                               uncertainty of returned location information in meters
                                                                                                                                                     maximum uncertainty                                                                                                                                                                         maximum uncertainty
                                                                                                                                                      average uncertainty                                                                                                                                                                         average uncertainty

                                                                                                   1000                                                                                                                                                                                        1000

                                                                                                       100                                                                                                                                                                                         100

                                                                                                       10                                                                                                                                                                                          10

                                                                                                        1                                                                                                                                                                                           1
                                                                                                             0       0.1     0.2   0.3   0.4    0.5  0.6   0.7    0.8     0.9    1                                                                                                                       0       0.1     0.2   0.3   0.4    0.5  0.6   0.7    0.8     0.9    1
                                                                                                                     ratio between average and maximum speed of mobile object                                                                                                                                    ratio between average and maximum speed of mobile object

                                                                                                                                         time-based reporting                                                                                                                                                                      distance-based reporting
                                              uncertainty of returned location information in meters

                                                                                                                                                                                                                                          uncertainty of returned location information in meters
                                                                                                                                                      maximum uncertainty                                                                                                                                                                         maximum uncertainty
                                                                                                                                                       average uncertainty                                                                                                                                                                         average uncertainty

                                                                                                       1000                                                                                                                                                                                        1000

                                                                                                        100                                                                                                                                                                                         100

                                                                                                         10                                                                                                                                                                                          10

                                                                                                             1                                                                                                                                                                                           1
                                                                                                                 0    0.1     0.2   0.3   0.4    0.5  0.6   0.7    0.8     0.9       1                                                                                                                       0    0.1     0.2   0.3   0.4    0.5  0.6   0.7    0.8     0.9       1
                                                                                                                      ratio between average and maximum speed of mobile object                                                                                                                                    ratio between average and maximum speed of mobile object

Figure 6: Analytical results: Maximum and average uncertainty of the location information on the server for the optimistic
and pessimistic cached querying protocols and the time-based and distance-based reporting protocols.

ure 7.                                                                                                                                                                                        and a location service with a secondary copy for the loca-
    The combined protocol integrates the positive features                                                                                                                                    tion information of one mobile object. The information on
of the more simple querying and reporting protocols. Al-                                                                                                                                      the source is updated from the GPS trace, while the server
though, for a higher query rate it is less ecient than the                                                                                                                                   receives randomly created location queries with an exponen-
distance-based reporting protocol, it requires much less mes-                                                                                                                                 tially distributed time interval and a xed or, in case of the
sages for a low query rate, similar to the querying protocols.                                                                                                                                combined protocol, a Gaussian distributed accuracy. The
Unlike the reporting protocols, it is also able to meet an ar-                                                                                                                                mean value for the exponential distribution of the time in-
bitrary requested accuracy. Its disadvantages are that it is                                                                                                                                  terval between queries is the inverse of the query rate q.
more complicated to implement, because an optimal value                                                                                                                                       The xed accuracy requested in the queries is 100 m for the
for the uncertainty of the secondary has to be found, and                                                                                                                                     basic protocols. The Gaussian distributed accuracy for the
that communication errors are more dicult to handle.                                                                                                                                         combined protocol has a mean value of 100 m and a stan-
    In summary, the combined protocol is suitable for most                                                                                                                                    dard deviation of 20 m. Into this simulation environment
cases, especially if a protocol is needed that performs equally                                                                                                                               di erent update protocols can be inserted that specify, how
well in di erent environments or even can adapt to them. Of                                                                                                                                   the source and server react to incoming updates or queries
the querying and reporting protocols the pessimistic cached                                                                                                                                   and how the location information is transmitted. As in the
querying protocol and the distance-based protocol are to                                                                                                                                      analysis, the delays for transmitting the messages are not
be preferred, because they combine an upper bound for the                                                                                                                                     considered.
spatial accuracy of the returned location information with a                                                                                                                                      The ten GPS traces used in our simulations have been ac-
good eciency. Of these two, the former is decidedly better                                                                                                                                   quired on a typical car ride in the commuting trac around
for objects with sporadic movements and for higher query                                                                                                                                      the city of Stuttgart. These traces have an average length
rates, but does not allow the accuracy of the location infor-                                                                                                                                 of about 28 minutes and an average speed of 44.68 km/h. A
mation to be requested on application-level.                                                                                                                                                  Di erential GPS sensor with an accuracy between 2 and 5
                                                                                                                                                                                              meters has been used to determine the location information,
6 Simulation Results                                                                                                                                                                          which is written to a le every second.
                                                                                                                                                                                                  For each trace we have performed various simulation
For the update protocols discussed in Section 5, we have                                                                                                                                      runs, where the number of transmitted messages has been
performed various simulation runs based on ten actual GPS                                                                                                                                     calculated depending on a given query rate. Figure 9 shows
traces. To this end we have developed a simple simulator,                                                                                                                                     the results of these simulation runs as the mean values of 100
which implements a location source with a primary copy                                                                                                                                        separate simulations. The parameter values for the proto-
                                                                                                                                                                                              cols (e.g., the average and maximum speed) have been taken

speed ratio pessimistic                        optimistic                    distance-based                          time-based      combined
                           cached querying                    cached querying               reporting                               reporting
                            max.       avg.                    max.      avg.                max. avg.                                max.     avg.  max. avg.
                    0.260 74.167 5.922                        335.798 22.725                99.817 49.664                            99.998 16.971 99.926 6.131
                    0.291 88.299 6.507                        287.795 23.286                99.964 49.005                            88.299 17.067 99.506 6.604
                    0.302 56.288 6.138                        294.754 19.696                99.982 50.597                           100.078 13.096 101.970 6.208
                    0.352 104.133 6.761                       253.763 20.917                99.899 49.091                           100.233 19.121 88.127 7.034
                    0.354 73.911 6.998                        263.790 21.720                99.887 45.730                            75.895 17.598 104.243 7.238
   Table 3: Simulation results: Maximum and average accuracy of the location information for the di erent update protocols.

                                                                                                                         100                                           combined
                                                       combined protocol

messages per second

                                                                                                  messages per second
             0.3                                                           10
                                                                     4 queries per second                                0.01
                   20   40                                        1
                             60  80 100 120 140
                                                    160 180 200
                    uncertainty of secondary copy in meters                                                                 0.001      0.01        0.1             1              10
                                                                                                                                              queries per second

  Figure 7: Analytical results: Number of messages transmit-                                     Figure 8: Analytical results: Number of messages transmit-
  ted with the combined protocol depending on the number                                         ted with the combined protocol depending on the number
  of queries and the uncertainty of the secondary copy on the                                    of queries. For the uncertainty of the secondary query the
  server.                                                                                        optimal values taken from Figure 7 are used.
  from the respective trace.                                                                     of a certain trace. Because we have averaged the maximum
      In general, these simulation results con rm the assump-                                    speed over 5 seconds, the apparent speed of two neighbor-
  tions we have made for the analysis. The number of mes-                                        ing entries in the trace may be higher than the one we have
  sages for the cached querying protocols is a little higher than                                assumed for the parameters of our protocols. This can lead
  in the analysis. One reason for this is that the location infor-                               to a maximum accuracy that is greater than the requested
  mation queried at the source is not determined exactly when                                    one (100 m), when using a cached querying or the combined
  queried, as we have assumed there. Instead, it has already                                     protocol.
  an average age of Tp =2 where Tp is the update interval of the
  sensor system, in our case 1 second. Therefore, the location
  information on the server has to be updated a little sooner                                    7 Conclusion and Future Work
  than calculated. Also, the maximum velocity of the mobile
  object is sometimes dicult to obtain from the GPS traces,                                     In this paper, we have described di erent protocols for trans-
  because the uncertainty of the positioning systems can have                                    mitting location information and have compared them ac-
  a great in uence on the distance of two neighboring entries.                                   cording to their e ectiveness and eciency. These protocols
  We therefore take the average of 5 seconds to determine the                                    may be used, wherever location information is queried or
  maximum speed. It happens a number of times that the the                                       updated continuously. With the help of the analysis a suit-
    ow of location information from the DGPS sensor is inter-                                    able protocol can be found for a given environment. Fur-
  rupted for a short time, which may also lead to variances in                                   thermore, the analysis gives an estimation for the expected
  the behavior of the protocols.                                                                 network load and the average uncertainty of the transmit-
      For the combined protocol, we have again determined the                                    ted location information, as well as an upper bound for its
  message count depending on the uncertainty value for the                                       maximum uncertainty. Based on the querying and report-
  secondary copy as well as on the query rate. The results of                                    ing protocols, we have proposed a combined protocol that
  this simulation are shown in Figure 10. Although the results                                   integrates most of the advantageous properties of the basic
  are again a little higher than the values determined in our                                    protocols. Here, the analysis can give optimal parameter
  analysis, the analysis re ects their characteristics nicely.                                   settings for a certain environment.
      For ve GPS traces with di erent speed ratios ranging                                           For our future work, we plan to run further simulations
  from 0.26 to 0.354 the maximum and average resulting ac-                                       with di erent types of mobile objects, for example a per-
  curacies are depicted in Table 3. The query rate has been                                      son while window-shopping in a city or riding a bicycle, to
  set to 0.1, as the results tend to vary more for higher rates,                                 look at various movement characteristics. The results will
  while the other parameters have the same values as before.                                     then be used, to further improve the analysis, where nec-
  For the accuracies, as compared to the number of transmit-                                     essary. We also plan to extend the combined protocol by
  ted messages, the results depend more on the characteristics                                   adding a mechanism that allows it to adapt to changes in

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