An efficient algorithm for the optimal number of route transitions in mobile ad hoc networks

We address the issue of finding a sequence of stable paths using the knowledge of future topology changes. We present an efficient polynomial time algorithm called OptTrans to determine the minimum required number of route transitions for a source-destination (s-d) session. Algorithm OptTrans operates on a simple greedy heuristic: Whenever an s-d path is required at time instant t, choose the longest-living s-d path since t. The above strategy is repeated over the duration of the s-d session. The sequence of such longest living stable paths is called the stable mobile path. Algorithm OptTrans is of O(n²T) 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 knowing the complete knowledge of future topology changes at the time of route selection, we introduce the notion of look-ahead window size Δ as the time for which the information about future topology changes are known. We study the performance of algorithm OptTrans by varying Δ from O to Δ_max, where Δ_max is the look-ahead window size beyond which there is no impact on the number of route transitions or the hop count. We also identify the tradeoff between hop count and the number of route transitions and show that both the minimum hop path and the stable path are not likely to be obtainable at the same time. We conclude the paper by presenting a preliminary design of a proactive stable path routing protocol that makes use of the look-ahead window concept proposed here. We explore the stochastic properties of the commonly used random-way point mobility model and propose an efficient technique to dissipate location update broadcasts by each node. We show that there exist a critical number of s-d sessions above which the location-update overhead in our proactive stable path routing approach would be less than the broadcast-based on-demand route discovery overhead.