Comparison of Stable Path Selection Strategies for ... - IEEE Xplore

Comparison of Stable Path Selection Strategies for Mobile Ad Hoc Networks Natarajan Meghanathan Jackson State University [email protected]

Abstract The strategies for selecting paths in stabilityoriented mobile ad hoc network routing protocols make use of the knowledge of either past or future topology changes. Here, we study the performance of different stable path selection strategies in terms of number of route transitions and average hop count per path vis-à-vis the optimums for these metrics computed under the same conditions of network topology changes. The strategies that make use of knowledge of past topology changes include that of selecting the most recently formed path, the longest existing path, and the path having least sum of the age of its constituent links. The strategies making use of the knowledge of future topology changes include the mobility prediction mechanism [8] and the locationupdate broadcast based look-ahead mechanism [7]. Simulation results indicate strategies based on knowledge of future topology changes perform far better compared to those based on knowledge of past topology changes.

1. Introduction Path stability is a critical design issue to be considered while developing routing protocols for mobile ad hoc networks (MANETs). Frequent route discoveries can easily congest the network and also knock out the battery power of critical nodes. Mobile nodes in energy-constrained environments like that of the sensor networks and embedded networks cannot afford to lose their battery power quickly. For multimedia real-time applications, frequent route changes can result in out-of-order packet delivery resulting in high jitter. The application layer might get overloaded in handling lost and out-of-order packets. Thus, path stability is important from Quality of Service (QoS) point of view too. We quantify path stability as the number of route transitions (i.e., route discoveries) a

routing protocol incurs for the duration of a sourcedestination (s-d) session. A few stability-oriented routing protocols have been proposed for MANETs. These include Associativity Based Routing (ABR) [9], Signal Stability Adaptive Routing (SSA) [3], Route Lifetime Assessment Based Routing (RABR) [1] and Flow Oriented Routing Protocol (FORP) [8]. The strategy used by these protocols to select stable paths is either based on knowledge of past topology changes (e.g., ABR, SSA) or that of future topology changes (e.g., FORP, RABR). A statistical approach for predicting link and path lifetimes has been discussed in [5], and the authors recommend selecting a path having the highest estimated probability to persist for a required amount of time. However, in reality, protocols are often restricted to use quantifiable absolute metrics like link age (indicates how long two nodes have remained as neighbors), residual link lifetime (a measure of how long two nodes will stay as neighbors from the current instant), signal strength (a measure of the proximity of two nodes), etc to assess link and path stability. ABR uses the degree of association stability, which basically quantifies how long two nodes have stayed together as neighbors, to select paths. SSA categorizes links into two types: strongly-connected and weakly connected links. A link is said to be strongly connected if it has been active for a pre-defined period of time and the signal strength on that link is beyond a threshold. A link is considered to be weakly connected if the signal strength on that link is fluctuating, a possibility with recently formed links. FORP selects the route that will have the largest expiration time since the time of its discovery. The expiration time of a route is measured as the minimum of the predicted expiration time of its constituent links. RABR uses the average change in the received signal strength to predict the time when the received signal strength would fall below a critical threshold. In [7], we proposed an efficient algorithm to compute the optimal number of route transitions (OptTrans) to be incurred for the duration of an s-d

Proceedings of the International Conference on Networking, International Conference on Systems and International Conference on Mobile Communications and Learning Technologies (ICNICONSMCL’06) 0-7695-2552-0/06 $20.00 © 2006

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session. Given the complete knowledge of future topology changes, algorithm OptTrans is based on the following greedy strategy: Whenever an s-d path is required at time instant t, choose the longest living s-d path since t. The above strategy is applied over the duration of the s-d session and sequence of long-living stable paths called the stable mobile path is computed in O(n2T2) complexity, where n is the number of nodes in the network and T is the duration of the s-d session. To account for the possibility of not having complete knowledge of topology changes in practice, we introduced the notion of “look-ahead” window that represents the time for which future topology changes are known. We proposed that prior to changing its direction; each node broadcasts a location-update message that contains information about its current location, targeted location and velocity with which the node decides to move to that targeted location. Assuming clock across all nodes is synchronized, it is then possible to predict the location of the node until it reaches its target. The prediction is more likely to hold true assuming the direction of motion and velocity of node does not change during this travel. Using such location-update messages from all its peers, each node can locally maintain an approximate view of the global network topology for the near future. Algorithm OptTrans can be then applied over this locally maintained global network topology and the stable route can be selected at the source node itself. Such a proactive stable path routing approach has been shown to be better than the on-demand shortest path routing approach with increase in number of source-destination sessions and/or node velocity. Our objective in this paper is to compare the underlying route selection strategies of the stabilityoriented routing protocols using extensive simulations. Evaluating path selection strategies rather than the protocols using those strategies avoids getting bogged down with protocol-specific results and also helps a network designer in choosing the right strategy when a new protocol is developed. No prior comparison has been made of the stable path selection strategies with respect to the optimum number of route transitions for the same conditions of network topology changes. The strategies we compare include those of selecting the most recently formed s-d path (i.e., whose oldest link has the minimum age among the oldest links of all paths), the longest existing s-d path (i.e., whose youngest link has the maximum age among the youngest links of all paths), the s-d path that has the least sum of the age of its constituent links, the s-d path that has the maximum predicted route expiration time and the s-d path that would exist for the longest time

computed using the location-update broadcast based “look-ahead” approach of algorithm OptTrans. The rest of the paper is organized as follows: In Section 2, we give a brief overview of algorithm OptTrans. Section 3 describes the stable path selection strategies studied in this paper. Section 4 explains the simulation environment and presents the simulation results. We conclude the paper in Section 5.

2. Algorithm OptTrans 2.1. Mobile graph and mobile path We use the notion of mobile graph and mobile path to represent the sequence of network topology and path changes [4]. A mobile graph, GM = G1G2 … GT, is the sequence of static graphs that represents the network topology changes over some time scale T. A mobile path, defined for a source-destination (s-d) pair, in a mobile graph is the sequence of s-d paths PM = P1P2 … PT, where Pi is a static path between the s-d pair in Gi = (Vi, Ei). Each static path Pi is represented as the sequence of vertices v0v1 … vl, such that v0 = s and vl = d and (vj-1,vj) ∈ Ei for j = 1,2, …, l. The timescale T normally corresponds to the duration of an s-d session. Let wi(Pi) denote the weight of a static path Pi in Gi. For additive path metrics, like hop count, end-to-end delay and energy consumption, wi(Pi) is simply the sum of the link weights along the path. Thus, for a given s-d pair, if Pi = v0v1 … vl such that v0 = s and vl = d, l

wi ( Pi ) =

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(1)

j =1

For a given mobile graph GM = G1G2 … GT and s-d pair, the weight of a mobile path PM = P1P2 … PT is T −1

T

w( PM ) =

∑ wi ( Pi ) + ∑ Ctrans ( Pi , Pi +1 ) i =1

(2)

i =1

where C trans ( Pi , Pi +1 ) is the transition cost incurred to change from path Pi in Gi to path Pi+1 in Gi+1. Note Ctrans ( Pi , Pi +1 ) has to be represented in the same unit as that of the path metric used to compute wi(Pi).

2.2. Stable mobile path and shortest mobile path The stable mobile path for a given mobile graph and s-d pair is the sequence of static paths such that the number of route transitions is the minimum. In other words, we optimize


∑ wi (v j −1 , v j )

T −1

∑ Ctrans ( Pi , Pi +1 ) in equation (2) at i =1

whatever be the cost of the other term

T

∑ wi ( P i ) . For i =1

the shortest (minimum hop) mobile path, we assume the link weights are unity and optimize the term T

∑ wi ( P i ) , irrespective of the cost of transition. i =1

2.3. Algorithm description Algorithm OptTrans (pseudo code in Figure 1) to find the stable mobile path uses the following greedy strategy: Whenever a path is required, select a path that will exist for the longest time. Let GM=G1G2 … GT be the mobile graph generated by sampling the network topology at instants t1, t2, …, tT of an s-d session. When an s-d path is required at sampling time instant ti, the strategy is to find a mobile sub graph G(i, j) = Gi ∩ Gi+1 ∩ … ∩ Gj such that there exists at least one s-d path in G(i, j) and no s-d path exists in G(i, j+1). A minimum hop s-d path in G(i, j) is selected. Such a path exists in each of the static graphs Gi, Gi+1, …, Gj. If sampling instant tj+1 ≤ tT, the above procedure is repeated by finding the s-d path that can survive for the maximum amount of time since tj+1. A sequence of such maximum lifetime static s-d paths over the timescale of a mobile graph GM forms the stabile mobile s-d path in GM. Input: GM = G1G2 … GT, source s, destination d // stable mobile path Output: PS Auxiliary Variables: i, j Initialization: i=1; j=1 Begin OptTrans 1 while (i ≤ T) do 2

Find a mobile graph G(i, j)=Gi ∩ Gi+1 ∩ … ∩ Gj such that there exists at least one s-d path in G(i, j) and {no s-d path exists in G(i, j+1) or j = T}

3

PS = PS U {minimum hop path in G(i, j) }

4

i=j+1

3. Stable path selection strategies This section introduces the stable path selection strategies studied in this paper. The age of a link at a given instant indicates how long the link has been existing until that instant where as the predicted residual lifetime of a link at a given instant indicates how long the link is likely to exist since that instant. The age of a path is defined differently for each of the selection strategies.

3.1. Most recently formed path This strategy gives preference to paths that are recently formed compared to paths that have been existing for a long time. The oldest link of a path is defined as the link that has existed for the maximum amount of time among the constituent links of the path. Let the age of an s-d path Pis-d,t at time t, age(Pis-d,t) represent the age of the oldest link of the path. Let Ps-d, t = {P1s-d,t , P2s-d,t, …,} be the set of available s-d paths at time t. The strategy is to choose the path that is the most recently formed (i.e., whose oldest link is the youngest among the oldest links of all s-d paths) at time t. The route chosen according to this strategy has age equal to Min(age(Pis-d,t )), ∀ Pis-d,t ∈ Ps-d, t

3.2. Longest existing path This strategy gives preference to paths that have been existing for a long time compared to paths formed relatively recently. The youngest link of a path is defined as the link that has existed for the least amount of time among the constituent links of the path. Let the age of an s-d path Pis-d,t at time t, age(Pis-d,t) represent the age of the youngest link of the path. Let Ps-d, t = {P1s-d,t , P2s-d,t,…,} be the set of available s-d paths at time t. The strategy is to choose the path that has the largest age (i.e., whose youngest link is the oldest among the youngest links of all s-d paths) at time t. The route chosen according to this strategy has age equal to Max(age(Pis-d,t )), ∀ Pis-d,t ∈ Ps-d, t

3.3. Mobility prediction

5 end while 6 return PS End OptTrans Figure 1. Pseudo code for algorithm OptTrans

Su. et. al., proposed a mechanism [8] to predict link expiration time based on the location and mobility information provided by GPS (Global Positioning System) [6]. The clock at all nodes is assumed synchronized. Given the motion parameters of two neighbors, one can then determine the duration of time the two neighbors will remain connected.


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Let two nodes i and j be within the transmission range of each other. Let (xi, yi) and (xj, yj) be the coordinates of the mobile hosts i and j respectively. Let vi, vj be the velocities and Θi, Θj, where (0 ≤ Θi, Θj < 2π) indicate the direction of motion of nodes i and j respectively. The amount of time the two nodes i and j will stay connected, Di-j, can be predicted as: Di − j =

− (ab + cd ) + (a 2 + c 2 )r 2 − (ad − bc) 2 a 2 + c2

(3)

where, a = vi cosΘi – vj cosΘj; b = xi – xj; c = vi sinΘi – vj sinΘj d = yi – y j We take a snapshot of the network topology at time instant t when an s-d route is required. We form a weighted graph of the network topology with the nodes as vertices and links as edges. The weight of a link (i, j) is the predicted link expiration time Di-j. The residual expiration time of an s-d path, RETs-d is the minimum of the predicted expiration time of its constituent links. The s-d path that has the maximum predicted residual expiration time is then selected.

3.4. Minimum sum of link ages The age of a path is defined as sum of the ages of its constituent links. The idea is to give preference to most recently formed links. Aiming to minimize sum of link ages, also helps to lessen the number of constituent links in the path – a feature not available with the strategy of selecting the most recently formed path.

3.5. Location-update mechanism The location–update message is broadcasted by a node before it changes its velocity or direction or targeted destination location or any combination of these. The location update message contains all the required information (e.g., the time of broadcast, coordinates of the starting location and the targeted location and velocity of movement) necessary to track the location of the node until it reaches its targeted location or before the next direction/ velocity change. The assumption is all clocks are synchronized. Let tpi and tqi be respectively the time instants at which node i has broadcasted its most recent locationupdate message and the time instant at which node i reaches its targeted location specified in its most recent location-update broadcast. Let tx be the time instant at which an s-d path needs to be found. A mobile graph G(x, x+z) = Gx Gx+1 Gx+2, …, Gx+z is constructed such that there exists at least one s-d path in G(x , x+z) and no s-d path exists in G(x, x+z+1). If there exists more than one s-d path in G(x, x+z), the minimum hop

mobile path is chosen. The most recent location-update message of each node i (i ≠ s), broadcasted at time instant tpi and valid until tqi, will be used to locate node i in G(x, x+z). Node i will be included in G(x, x+z) only if tpi ≤ tx ≤ tx+z ≤ tqi. If tx+z < T, the above procedure is continued by setting tx = tx+z+1.

4. Simulations The node mobility model used in all of our simulations is the Random waypoint model [2], a widely used mobility model in MANET studies. Each node starts moving from an arbitrary location to a randomly selected destination with a randomly chosen speed in the range [0 .. vmax]. Once the destination is reached, the node selects another location and continues to move with a different speed. The vmax values used are 10 and 40 m/s. Pause time is 0 seconds. We obtain a centralized view of the network topology by generating the mobility trace files for 1000 seconds. The transmission range of nodes is assumed to be 250 m. Each data point in Figures 2 through 5 is an average of 10 s-d sessions run on 4 mobility trace files, each starting at a time uniformly distributed between 0 to 50 seconds and ending at 1000 seconds. We conducted the simulations for two different network topologies: one rectangular, 1500m x 300m (25, 50 and 75 nodes) and another square, 1000m x 1000m (50, 100 and 150 nodes). In terms of the average coverage per m2, 25 nodes in 1500m x 300m rectangular topology is equivalent to 50 nodes in 1000m x 1000m square topology. Similarly, 50 nodes and 75 nodes in the 1500m x 300m is equivalent to 100 and 150 nodes in 1000m x 1000m respectively.

4.1. Simulation results The number of route transitions incurred by mobility-prediction and location-update mechanisms, not far different from each other, is the lowest among all the stable path selection strategies but it is still 50100% more than the optimal number of route transitions. On the other hand, the average hop count of the paths identified by the mobility prediction mechanism is 50-100% more than that identified by the location-update mechanism. The location-update broadcast based look-ahead mechanism is capable of selecting routes based on their predicted residual lifetime and breaks the tie among equal residual lifetime routes by choosing the route with the lowest hop count. The mobility prediction mechanism selects paths only based on the predicted lifetimes of the links. As a result, the mobility-prediction mechanism ends up with


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Figure 2. [vmin…vmax] = [0…10m/s], 1500m x 300m Network





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paths that have higher hop count even though their lifetimes may be only slightly higher than the ones chosen by the location-update mechanism. Compared to the strategy of choosing older links and paths, the strategy of relying on younger links seems to be far better. Younger links are more likely to stay for a longer time even though they may be formed between two nodes that may have just moved towards each other. It takes a considerable amount of time for the two nodes to drift away. But, older links are likely to break anytime in a dynamically changing topology. Even though two nodes may be moving parallel to each other for a long time with the relative velocity being zero, they are more likely to change directions anytime in the near future. The strategy of selecting the path that has minimum sum of its link ages yields a lower hop count (15 – 25% less) compared to the strategy of choosing the most recently formed path, because the former is sensitive to both link ages and the number of links, while the latter is sensitive only to link age. In the case of shortest path routing, we see a reduced number of route transitions in the square topology compared to that incurred in the rectangular topology. This can be explained due to the difference in the effective coverage per m2 according to the Border effect (loss of coverage due to boundaries of the network shape). For the same area, coverage in a square topology is more uniform compared to that in a rectangular topology. Since, the physical length of links in a multi-hop shortest path is likely to be close to the transmission range of nodes, loss of effective coverage results in a relatively larger hop count per path for rectangular topologies compared to that of square topologies. As the number of hops increases and the vulnerability of each hop to fail remaining the same, shortest path routing in a rectangular topology incurs more route transitions than that in a square topology. Border effect does not significantly influence the number of route transitions and average hop count per route incurred by most of the stable path selection strategies because these strategies aim for links having longer lifetime and hence select links whose physical length is only around 50-65% of the transmission range of nodes. Loss of effective coverage at the boundaries is offset by increase in the number of hops. Though, the hop count increases, reduction in the vulnerability of each link to fail results in paths having relatively longer lifetime compared to shortest hop paths.

5. Conclusions We compared the performance of different stable path selection strategies in terms of the number of route

transitions and average hop count per path compared to the theoretical optimums for these metrics obtained under the same conditions of network topology changes. Simulation results indicate strategies making use of future topology changes, though bound to incur overhead in propagating the topology change information, can perform far better when compared to strategies that make use of past topology changes. If we want to minimize the overhead of propagating the topology change information and would like to use only the knowledge of past topology changes, then the strategy of choosing the path that has the minimum sum of the ages of its constituent links is a better choice.

6. References [1] S. Agarwal, A. Ahuja, J. P. Singh and R. Shorey, “RouteLife Time Assessment Based Routing Protocol for Mobile Ad Hoc Networks,” Proceedings of IEEE ICC, June 2000. [2] C. Bettstetter, H. Hartenstein and X. Perez-Costa, “Stochastic Properties of the Random-Way Point Mobility Model,” Wireless Networks, pp. 555 – 567, Vol. 10, No. 5, September 2004. [3] R. Dube, C. D. Rais, K-Y. Wang and S. K. Tripathi, “Signal Stability based Adaptive Routing for Ad hoc Wireless Networks,” IEEE Personal Communications, Vol. 4, No. 1, pp. 36 – 45, February 1997. [4] A. Farago and V. R. Syrotiuk, “MERIT: A Scalable Approach for Protocol Assessment,” Mobile Networks and Applications, Vol. 8, No. 5, pp. 567 – 577, October 2003. [5] M. Gerharz, C de Waal, P. Martini and P. James, “Strategies for Finding Stable Paths in Mobile Wireless Ad Hoc Networks,” Proceedings of the 28th IEEE International Conference on Local Computer Networks, pp. 130-139, October 2003. [6] Kaplan ED (ed.), Understanding the GPS: Principles and Applications, Artech House: Boston, MA; 1996. [7] N. Meghanathan and A. Farago, “An Efficient Algorithm for the Optimal Number of Route Transitions in Mobile Ad Hoc Networks,” IEEE International Conference on Wireless and Mobile Computing, Networking and Communications, August 2005. [8] W. Su, S-J Lee and M. Gerla, “Mobility Prediction and Routing in Ad Hoc Wireless Networks,” International Journal of Network Management, vol. 11, no. 1, pp. 3-30, Jan-Feb. 2001. [9] C-K. Toh, “Associativity-Based Routing for Ad hoc Mobile Networks,” IEEE Personal Communications, Vol. 4, No. 2, pp. 103 – 139, March 1997.


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