A Peer-Tree Based Location Lookup Service in Mobile Wireless Networks

2.1. Locationing Techniques for Mobile Stations in Wireless Networks

Most of the localization technologies in the wireless networks are landmark based. In landmark-based localizations, a number of fixed access points (APs) periodically broadcast their accurate positions. A mobile host could determine its current location through geometric computations using the estimated distances between a mobile station (MS) and the fixed APs. The distances are estimated through various measurements obtained from radio frequency signals that are transmitted between the MS and the fixed APs. The measurements can be categorized into the received signal strength-based metrics and the time delay-based metrics.

The received signal strength (RSS) [4] exploits the relation between power loss of the signals and the distance [5]. RSS is defined as the voltage measured by a receiver's received signal strength indicator (RSSI) circuit [6]. RSS measurements are relatively inexpensive and simple to implement in hardware, though they are easily affected by two sources of error: multipath signals and shadowing [6].

Time delay-based metrics form the finer resolution distance measurements by estimating the propagation time of the line-of-sight (LOS) signals. The time delay-based metrics include time of arrival (TOA), time difference of arrival (TDOA), and round-trip time of arrival (RTOA). An TOA measurement is defined as the time of transmission plus a propagation-induced time delay [7]. TOA measurements require a common time reference between wireless stations, whereas TDOA and RTOA measurements can be obtained in an asynchronous environment. Time delay-based signal metrics are susceptible to two sources of error: additive noise and multipath signals.

The angle of arrival (AOA) measurements [8] are defined as the direction to neighboring sensors (rather than the distance to neighboring sensors). The AOA measurements require each wireless station to be equipped with two (or more) directional antennas that point in different directions. The AOA measurements can be incurred in two approaches. The most common method is to use an array of wireless stations which adopt the array signal processing techniques. AOA is estimated from the differences in arrival times for a transmitted signal at each wireless station in the array. The second approach is to estimate the RSS ratio between two (or more) directional antennas that are located on a wireless station. An AOA measurement is estimated from the ratio of the individual RSS values at two directional antennas.

2.2. Traditional Location-Ignorant Routing Protocols

Traditional ad hoc routing protocols maintain routing tables in order to determine the paths for forwarding packets [9]. Each host proactively maintains its routing table to reflect its current view of the network topology. Each wireless host propagates the content of its routing table to others either periodically or upon content changes. A wireless host updates its own routing table based on the content of a routing table that is propagated by another host, such as the Destination-Sequenced Distance-Vector (DSDV) routing protocol [10]. Route maintenance is performed by each host even when there is no pending data transmissions.

2.3. Location-Aided Routing Protocols

In order to restrict the overhead in maintaining routing tables, some ad hoc routing protocols have been proposed to eliminate or restrict the use of routing tables. Landmark-based routing protocols [11] only make limited use of routing tables. A landmark hierarchy is established in a landmark-based routing protocol. A network is divided into scopes. Each scope maintains one landmark, typically a router, which maintains routing information within the scope. The landmarks in different scopes interconnect themselves. Any packet sent between different scopes goes through the corresponding pair of landmark hosts. Landmarks exchange routing information among themselves. Other landmark-based routing protocols include the LANMAR routing protocol [12] and the Location-Aided Routing (LAR) protocol [13].

Geographically forwarding packets is generally used in location-based routing protocols, such as the GPSR protocol [1]. Geographic forwarding is also used in content delivery networks. The scalable Content-Addressable Network (CAN) [14] also makes use of the geographic forwarding. The key of a content is used as the storage location of the content. Queries to a content are geographically forwarded to the corresponding storage location whose address is the key of the content.

2.4. Indexing Structures

Decentralized index structures have been used in many application scenarios. In the Logarithmic Dictionary Tree (LDT) [15], each entity maintains its own view of an entire distributed tree. An operation is accomplished through the collaboration of a set of entities by forwarding it among these entities. The Chord protocol [16] is a content retrieval service by the content keys. An indexing structure is used in Chord and is organized into a balanced binary search tree. Both content lookups and updates to content only involves a small number of hosts. Tapestry [17] is a peer-to-peer overlay routing infrastructure for sending requests to nearby servers. A decentralized indexing structure provides good scalability because no atomic operation is required across multiple entities.

Other decentralized indexing structures include PGrid [18], Chord [16], and peer-tree [2]. PGrid is a distributed and balanced binary search tree that is used for retrieving data objects. Each host only maintains a small portion of the whole set of data objects, and a retrieval about a data object is served through a collaboration among a small set of hosts with regard to the total number of data objects. Chord is a balanced binary search tree. A content lookup or a content update only involve a small number of hosts. peer-tree is constructed as a distributed complete binary search tree. The peer-tree structure aims to limit the number of times that a service packet is forwarded by defining the cooperative relations among entities.

2.5. Comparison of the PTLS Location Lookup Service with Other Location Lookup Services

The PTLS service has two prominent properties. First, PTLS restrains the bandwidth consumption. This is achieved by making one forwarding hop at the protocol level to correspond to one hop of forwarding in the underlying physical network. Second, PTLS forwards location updates and queries along multiple paths. Multi-path forwarding serves to achieve both the high rates of successfully answering location queries and the robustness to changes of network topology.

The Grid Location Service (GLS) [19] is a location lookup service based on geographically forwarding location updates and queries. Each mobile host distributes its up-to-date location information to a number of location servers across a geographic area. A location query about a target host is served through being geographically forwarded to a location server which holds an answer. Heavy overhead on forwarding packets has been a problem in GLS. One hop of packet forwarding at the protocol level may correspond to multiple hops in the underlying physical network. Without taking into account the connectivity in an underlying network, a large amount of network bandwidth can be consumed in forwarding packets. In the topology-aware Content-Addressable Networks [20], a routing mesh is made to match the underlying network-level connectivity by clustering geographically proximate hosts.

Multi-path forwarding has also been adopted in the wireless ad hoc routing protocols. In the DSR protocol [21], a source host can maintain multiple routes to a destination under highly dynamic network connectivity. The Geocast routing protocol [22] forwards a packet through multiple routes in order to enhance the chances of reaching a destination under dynamic network connectivity. The service-restorable bandwidth-guaranteed routing [23] maintains two routing paths. One is the main path, and the other one is the backup path. Efficient path selection algorithms are desired constrain the computational overhead in arranging the multipath routes. The peer-tree structure adopted in the PTLS service facilitates the computationally efficient selection of paths.

3.1. The Friendship Relations

Sharing common suffixes of various lengths reveals the degrees of friendship among hosts. Two hosts are closer friends if they share a longer common suffix between their identifiers. The friendship determines a cooperative relation among hosts. The friendship of different degrees can be expressed as the equivalence classes using the modulo operations. For a common suffix with its length of , an equivalent class of hosts is defined as , where denotes the host identifiers. The equivalent classes can be represented as the internal tree node in a complete binary search tree. The tree levels of such a search tree are incremented as it moves toward the leaf level with the root level being denoted as level . The leaf level is denoted as level which corresponds to the height of the tree. The value of is equivalent to the total number of bits of the identifiers. The depth of an intermediate tree level is denoted by . When each internal tree node at tree level is labeled by , a node represents an equivalence class: . A pair of hosts are the closest friends (a.k.a. peers) to each other if their identifiers share the longest suffix, that is, their identifiers only differs in the most significant bit, for example, two hosts with their identifiers and are peers if .

The peer-tree indexing structure can serve as a guideline for forwarding location updates and queries. When a target host represents a host whose location is under query or is being updated, a location query or update is always forwarded to the closer friends of the target host. A closer friend of the target host should qualify two conditions. First, the closer friend is one of the neighbors surrounding the host which currently holds a location update or query. Second, the identifier of the closer friend must share the longest suffix with the identifier of the target host. The selection of a closer friend can be imagined as searching in the peer-tree. The search starts at the root and moves toward the leaf node representing the identifier of the target host. The height of a peer-tree represents the maximum number of times that a location update or query can be forwarded.

Although the peer-tree structure seemingly shares similarity with PGrid [18], they have significant differences. First, each entity in PGrid is only responsible for a particular set of data. In peer-tree, a host can hold location information for any of its friends on a dynamic basis. Second, the forwarding chain in PGrid is fixed. In peer-tree, the forwarding chain is jointly determined by the peer-tree structure and the dynamic network connectivity. Third, the main concern of PGrid is load balancing. Thus, a query may have to be forwarded to a particular host for a service. Moreover, the forwarding path cannot be flexibly determined under the dynamic network connectivity. In peer-tree, the main concern is to enhance the success rates of answering location queries while restricting the bandwidth consumption. Due to the opportunistic communications among hosts, it is ideal that a location update or query can be flexibly serviced by multiple hosts. Since PGrid does not provide such flexibility, it is not suitable for being used to form an indexing structure for aiding the forwarding of queries or updates in wireless networks with mobile hosts. The peer-tree indexing structure allows a flexibility based on a well-defined cooperative relation among hosts. The actual forwarding path is jointly determined by the set of eligible next-hop hosts and the dynamic network connectivity.

3.2. Determination of Paths for Forwarding Updates and Queries

The host that currently holds a location update or a location query is called the current host. A current host first locates the smallest equivalent class that includes its own identifier and the identifier of the target host. Then, a next-hop host is selected within this equivalent class based on two criteria:

Criterion 1

The identifier of the next-hop host should share the longest suffix with the identifier of the target host among the candidates included in the same equivalent class.

Criterion 2

The next-hop host has to be among the neighborhood of the current host.

The procedure of selecting a next-hop host is shown in Algorithm 1. The selection of a next-hop host corresponds to moving downward in the peer-tree. The traversal always starts at the root of the tree and ends at the smallest equivalent class which includes both the next-hop host and the target host. For example, the paths of forwarding location updates and queries made by host are shown in Figure 2. Based on Algorithm 1, the operations of propagating location update and forwarding location query are defined as follows.

  a target host.

1. (1)

   Propagating Location Updates. When a host updates its location, it first sends the update to one of its friends that are in its current neighborhood. Then, this update can be further forwarded to the closer friends of the host which has initiated this update. At each forwarding, a location update is only unicasted to the next-hop host. The location information of the host whose location is being updated is memorized by each host along the forwarding path of a location update. Therefore, a location query about a target host could be answered by any of the friend hosts of this target host. Moreover, a host can hold location replicas for any of its friend hosts. The procedure of forwarding a location update is illustrated in Algorithm 2. For example, the updates of the location about host can be replicated at hosts , , and (ref. Figure 2(b)).

    
2. (2)

   Forwarding Location Queries. When the location of a target host with its identifier is being queried, the location query is gradually forwarded to the closer friends of the target host. Assuming that a location query is currently in the hand of a host with its identifier , but host cannot answer this query. Host has to forward this query to a next-hop host. Again, host searches for a closest friend of the target host among its current neighbors. The procedure of searching a next-hop host for forwarding a location query can be illustrated in Algorithm 3. For example, the paths of forwarding location updates and queries made by host are shown in Figure 2(a).

    

4.1. Relationship to the Location-Aided Routing Protocols and the Localization Subsystem

It is noteworthy that the PTLS service only facilitates the location-aided routing protocols, rather than acting as a routing protocol. The functions of the PTLS service is not dependent on an underlying routing protocol. The forwarding of PTLS-specific packets is jointly determined by the peer-tree indexing structure and the direct connectivity in the neighborhood.

The PTLS service runs on top of an underlying localization subsystem and disseminates the estimated locations of mobile hosts. A mobile host is assumed to possess the ability of estimating its current location. The accuracy of the localization is orthogonal to the functions of the PTLS service, though inaccurate location estimations are disseminated by the PTLS service under inaccurate locationing. The functions of the PTLS service make no specific requirement on the format of locations. For simplicity, the format of locations used in this paper is assumed to be either a pair in a 2-D geometric setting, or a tuple in a 3D geometric setting with representing the altitude.

4.2. Detecting the Temporary Single-Hop Connectivity

Each wireless host detects the temporary single-hop connectivity between itself and its neighbors by listening to the packets received from the wireless channel. Each host declares its existence by periodically broadcasting Hello packets. Due to the fast decay of the signal strength, a Hello packet can only be received by the hosts which are within the coverage of the sender. The following information is specified in a Hello packet: the broadcaster's identifier and current location, as well as a timeout value. A timeout value signifies the duration during which a single-hop connectivity is valid between the broadcaster and the receiver of a Hello packet. A timeout value is set as twice the interval between two consecutive broadcasting of Hello packets. A Hello packet is broadcasted once every seconds of silence.

4.3. Updating Locations

The frequency of updating the location is dependent on the speed of the movement of a mobile host. A mobile host updates its location once a certain distance has been traversed. The distance is related to the coverage of the signal strength of a mobile host. For example, a distance of meters is appropriate for a coverage with a -meter radius.

The location information is gradually propagated to other hosts through forwarding Location Update packets. The host which initiates a location update is called an issuer. An issuer sends each Location Update packet to its peer (whose identifier shares a longest suffix with the issuer). An issuer host only unicasts a Location Update packet to a next-hop host in its current neighborhood. A Location Update packet can be further forwarded until no next-hop host can be found. The selection of a next-hop host follows Algorithm 1. Each host maintains a table for memorizing the locations of other hosts. Upon receiving a Location Update packet, a host updates its location table with the location information carried in the packet.

4.4. Answering Location Queries

A target host is the host whose location is under query. A responder host is the host which can answer the query about the location of a target host. A host looks up the location of a target host by sending a Location Query packet which includes the identifier of the target host and the last time when the location of the target host was updated. The last update time is used as the qualification criterion for selecting an up-to-date location from the copies of locations that are stored at different hosts. A host responds to the issuer of a Location Query by a Location Response packet which includes either the location of the target host, or a "not found" message when no answer can be found. A Location Query is failed to be answered when it cannot be further forwarded before an answer is found.

Upon receiving a Location Query, a host first looks into its location table for an answer. On a hit, this host responds to the issuer of this query with the copy found in its location table. On a miss, it forwards the query to a next-hop host for further service. The selection of a next-hop host makes a joint use of the peer-tree indexing structure and the underlying network connectivity. The selection of a next-hop host also follows the procedure illustrated in Algorithm 1.

5.1. Success Rates of Answering Location Queries

A location query is answered by either the up-to-date location upon a hit, or a "not found" message upon a query failure. The success rate of answering location queries is defined as the ratio of the number of location queries that are successfully answered to the total number of location queries that have been issued. The comparison of the success rates between the PTLS service and the GLS service [19] is shown in Figure 3(a). The success rate of the PTLS service is generally higher than GLS, especially when there are more than hosts in a network. The higher success rates in PTLS signifies that forwarding chains are unlikely broken in the PTLS service when each mobile host is surrounded by many neighbors (ref. Figure 3(b)).

5.2. Bandwidth Consumptions

The comparison of the average per-host bandwidth consumption between PTLS and GLS is shown in Figure 4(a). The per-host bandwidth consumption goes up with increasing densities of mobile hosts in a network. PTLS consumes less amount of bandwidth than GLS. The number of times a service packet is forwarded highly contributes to bandwidth consumptions in a location service. Service packets in PTLS are forwarded almost only once on average as shown in Figure 4(c), while service packets in GLS generally take more hops as shown in Figure 4(d). This fact indicates that one service-level forwarding between two location servers in GLS may correspond to multiple geographic hops in the underlying network topology [19].

5.3. Robustness

5.4. Storage Demand

The per-host storage demand for holding location replicas is evaluated by the ratio of the number of location replicas held in each host to the total number of hosts. The per-host storage demand in the PTLS service is shown in Figure 4-(b). Each host only needs to hold location replicas for less than of other hosts in most scenarios. The per-host storage demand is higher in some scenarios, but the storage demand is no more than .