328
IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 8, AUGUST 2002
An Entropy-Based Model for Supporting and Evaluating Route Stability in Mobile Ad hoc Wireless Networks Beongku An and Symeon Papavassiliou, Member, IEEE
Abstract—In this letter, we propose an entropy-based modeling framework for supporting route stability in mobile ad hoc wireless networks. The basic motivations of the proposed modeling approach stem from the commonality observed in the location uncertainty in mobile ad hoc wireless networks and the concept of entropy. The corresponding results demonstrate that the proposed approach and parameters provide an accurate and efficient method of estimating and evaluating the route stability in dynamic mobile networks.
support route stability in self-organizing mobile ad hoc wireless networks. The corresponding methodology, results and observations can be used by the routing protocols to select the most stable route between a source and a destination, in an environment where multiple paths are available, as well as to create a convenient performance measure to be used for the evaluation of the stability and connectivity in mobile ad hoc networks.
Index Terms—Entropy, mobile ad hoc networks, routing, wireless networks.
II. MODELING
I. INTRODUCTION
M
OBILE ad hoc networks [1] are an ideal technology to establish instant communication infrastructure for military and civilian applications in which both hosts and routers are mobile. Their distributed nature eliminates single points of failure and makes mobile ad hoc networks more robust and survivable than other wireless networks. Such networks have dynamic, sometimes rapidly changing, random, multihop topologies. The goal of mobile ad hoc networking is to extend mobility into the realm of a set of wireless mobile nodes, where themselves form the network infrastructure in a self-organizing ad hoc fashion. Due to the random movement of nodes, the bandwidth and power limitations, and the lack of fixed infrastructure, the development of efficient protocols to support the various networking operations in mobile ad hoc networks (e.g., routing, resource allocation, quality of service (QoS) support, etc.) presents many issues and challenges [2]. Entropy [3], [4] presents the uncertanity and a measure of the disorder in a system. There are some common characteristics among self-organization, entropy, and the location uncertainty in mobile ad hoc wireless networks. These common characteristics have motivated our work in developing an analytical modeling framework using entropy concepts and utilizing mobility information as the corresponding variable features, in order to Manuscript received February 12, 2002. The associate editor coordinating the review of this letter and approving it for publication was Dr. I. S. Venieris. This work is supported in part by the New Jersey Commission on Science and Technology via the New Jersey Center for Wireless Networking and Internet Security, and in part by the New Jersey Commission on Higher Education via the NJI-Tower project. The authors are with the New Jersey Institute of Technology, Department of Electrical and Computer Engineering, University Heights, Newark, NJ 07102-1982 USA (e-mail:
[email protected];
[email protected]). Publisher Item Identifier 10.1109/LCOMM.2002.802046.
Every self-organizing system capable of change has certain variable features that can take on different values. For example, a particle can have different positions, move with different speeds, and have different directions. All these variable features can determine the characteristics of the system. In the following we consider a mobile ad hoc wireless netthe number of neighboring nodes work and lets denote by the corresponding set. We also of a mobile node , and by a set of variable features denoted associate with each node where node is a neighbor of node . In this letter by two nodes are considered neighbors if they can reach each other in one hop (e.g., direct communication). These variable features represent a measure of the relative speed among two nodes and are defined rigorously later in this section. Any change of the system can be described as a change of variable values in the course of time such as . In the following we assume that nodes exchange periodically mobility information [5] as well as other local information (e.g., node ID) with their neighbors [6]. , the velocity vector of node Let us also denote by and by , the velocity vector of node at time . and have two Please note that velocity vectors parameters, namely, speed and direction. The relative velocity between nodes and at time is defined as (1) of nodes Then the relative mobility between any pair is defined as their absolute relative during some time interval speed averaged over time . As mentioned before the variable features considered here is the relative mobility between two nodes. Therefore, we have
1089-7798/02$17.00 © 2002 IEEE
(2)
AN AND PAPAVASSILIOU: SUPPORTING AND EVALUATING ROUTE STABILITY IN MOBILE AD HOC WIRELESS NETWORKS
where is the number of discrete times that velocity information can be calculated and disseminated to other neighboring nodes within time interval . Based on this, we can define the at mobile during time interval . The enentropy tropy can be defined either within the whole neighboring range ), or for any subset of neighboring of node (e.g., within set at mobile nodes of interest. In general the entropy is calculated as follows: (3) . where we denote the set (or any subset) of the In this relation by the cardinality neighboring nodes of node , and by . If we want to calculate the local network (degree) of set refers to the set stability (with reference to node ), then thatincludes all the neighboring nodes of mobile node (e.g., ), while if we are interested in the stability of a part of represents the two neighboring nodes a specific route then of mobile node over that route. As can be observed from the is normalized so that previous relation the entropy . It should be noted that the entropy, as defined here, is small when the change of the variable values in the given region is severe and large when the change of the values is small [4]. In the following we describe how to apply this modeling framework in order to measure the route stability. The local route (or the part of the route that represents the links of the path is associated with an intermediate node), is stable if is small. large while the local route is unstable if However in general in a mobile ad hoc network the route between a source and destination may traverese multiple intermediate nodes (hops). Let us present the route stability (RS) as between two nodes and during some interval . We also define and evaluate two different measures to estimate and quantify end to end route stability, denoted and and defined as by follows, respectively (4) (5) denotes the number of intermediate mobile nodes where . Parameter over a route between the two end nodes can be used to measure the route availability and stability. That is large, there is available route and the route is is, if , while if is small, stable during some time interval even though there may be an available route, the route may be unstable. III. EVALUATION AND DISCUSSION In order to evaluate the proposed modeling framework and corresponding parameters a mobile ad hoc network consisting of 50 nodes that are placed randomly within a rectangular region of 1 km 1 km is modeled. Each node is assumed to have
329
constant radio range of m. That is, any pair of nodes within a distance of meters are considered to be neighbors. Throughout our eavaluation we assume that a link fails, or reappears, as a node goes out or in transmission range of another node, due to the mobility of the nodes. Mobile nodes are assumed to be moving around throughout the network. The speed and the direction of each move are uniformly distributed, with km/h and direction range , respecspeed range tively. If a mobile arrives at the boundary of the given network coverage area, the node reenters into network. We have performed two sets of experiments. In the first one (refer to as Experiment 1) our objective is to evaluate the potential use of the developed framework and parameters as the decision factor in selecting the most stable routes, between a source and a destination whenever multiple routes are available, as well as to gain some insight about estimating the potential stability of a selected route. Therefore, we select one communication pair of nodes and at various points during the system operation we select three different routes between the source and destination (in the following tables they are denoted by Route1, Route2, and Route3, respectively). At the same time of route selection, we and calculate the expected corresponding route stability based on relations (4) and (5), respectively, for each one of these routes. Moreover, for each one of the routes we measure the lifetime of the route, that is, the time from route establishment until the specific route breaks. In order to assess the capability of the proposed method to evaluate the route stability and study its effectiveness under different environments in Tables I and II, we present the corresponding results for two different mobility scekm/h and mobility2 narios (refer to as mobility1 with km/h). The results reported here correspond to with three different points (identified in the tables as point 1, point 2, and point 3, respectively) during the operation of the system where we selected new routes between the source and destination. As we observe from these tables, the lifetime of the route between a pair of end nodes is large when the route stability estimated by our proposed model is high. As expected, in Table I (mobility1) the route stability and route lifetime present better values than the corresponding ones in Table II (mobility2), since mobile nodes are moving with lower speed and therefore overall the system presents a more stable topology. In the second experiment (refer to as Experiment 2) we evaluate the overall average route availability and stability between different pair of nodes (source and destination), without considering any specific path or route for each pair. Specifically in this experiment we consider three different pair of nodes and we are interested in studying the available connectivity between these pairs of nodes. Therefore we consider a time ins as the time interval where mobiles exchange terval of information, and calculate the route stability within that time interval, while at the same time we calculate new routes between the different pair of nodes, if required. Tables III and IV present the corresponding numerical results (average values for the whole duration of the experiment). In these tables we represent by Route1, Route2, and Route3 the three corresponding communicating pairs of nodes. The route avaliability denotes the percentage of time that a route was available between the source mobile node and the corresponding destination mobile
330
IEEE COMMUNICATIONS LETTERS, VOL. 6, NO. 8, AUGUST 2002
TABLE I ROUTE STABILITY—EXPERIMENT 1—MOBILITY1 (v
= 20 km/h)
TABLE II ROUTE STABILITY—EXPERIMENT 1—MOBILITY2 (v
= 40 km/h)
TABLE III ROUTE STABILITY—EXPERIMENT 2—MOBILITY1 (v
= 20 km/h)
quantify, and evaluate the end to end route stability in dynamic mobile ad hoc networks. IV. CONCLUDING REMARKS
TABLE IV ROUTE STABILITY—EXPERIMENT 2—MOBILITY2 (v
= 40 km/h)
In this letter, we propose an entropy-based modeling framework for supporting and evaluating route stability in mobile ad hoc wireless networks. The basic motivations of the proposed modeling approach stem from the common comcepts of location uncertainty in mobile ad hoc wireless networks and entropy. The corresponding results have demonstrated that the proposed modeling can be used as the ideal vehicle by various routing protocols for evaluation, selection, and assignment of priorities to various routes according to route stability, in order to enhance the offered connectivity and QoS. Furthermore, the proposed concepts and approaches can be extended into a clustered self-organizing mobile ad hoc wireless network for supporting QoS and stability in multicast services. REFERENCES
node during the experiment. As we can see from Tables III and IV, the routes with higher estimated route stability values (as calculated by relations (4) and (5)) have also higher measured route avalability. As expected, in Table III (mobility1) the route stability and availability present better values than the corresponding ones in Table IV (mobility2), since mobile nodes are moving with lower speed and therefore overall the system presents a more stable topology. As can be concluded from all the results presented in this section the proposed model and corresponding parameters provide a very good measure to estimate,
[1] E. M. Royer and C.-K. Toh, “A review of current routing protocols for ad hoc mobile wireless networks,” IEEE Pers. Commun., vol. 6, no. 2, pp. 46–55, Apr. 1999. [2] S. Papavassiliou, S. Tekinay, K. Malick, and K. Walker, “Performance evaluation framework and quality of service issues for mobile ad hoc networks in the MOSAIC ATD,” in Proc. IEEE MILCOM 2000, Oct. 2000, pp. 297–303. [3] A. Bhattacharya and S. K. Das, “LeZi-update: An information-theoretic approach to track mobile users in PCS networks,” in Proc. Mobicom’99, Seattle, WA, 1999. [4] A. Shiozaki, “Edge extraction using entropy operator,” Comp. Vis., Graphics, Image Processing, vol. 36, pp. 1–9, 1986. [5] B. An and S. Papavassiliou, “A mobility-based clustering approach to support mobility management and multicast routing in mobile ad-hoc wireless networks,” Int. J. Network Manage. (JNM), vol. 1, no. 6, pp. 387–395, Dec. 2001. [6] C. R. Lin and M. Gerla, “Adaptive clustering for mobile wireless networks,” IEEE J. Select. Areas Commun., vol. 15, pp. 1265–1275, Sept. 1997.
