Analysis and Relative Evaluation of Connectivity of a Mobile Multi-Hop Network

In mobile multi-hop networks, a source node S and a destination node D sometimes encounter a situation where there is no multihop path between them when a message M, destined for D, arrives at S. In this situation, we cannot send M from S to D immediately; however, we can deliver M to D after waiting some time with the help of two capabilities of mobility. One of the capabilities is to construct a connected multi-hop path by changing the topology of the network during the waiting time (Capability 1), and the other is to move M closer to D during the waiting time (Capability 2). In this paper, we consider three methods to deliver M from S to D by using these capabilities in different ways. Method 1 uses Capability 1 and sends M from S to D after waiting until a connected multi-hop path appears between S and D. Method 2 uses Capability 2 and delivers M to D by allowing a mobile node to carry M from S to D. Method 3 is a combination of Methods 1 and 2 and minimizes the waiting time. We evaluate and compare these three methods in terms of the mean waiting time, from the time when M arrives at S to the time when D starts receiving M, as a new approach to connectivity evaluation. We consider a one-dimensional mobile multi-hop network consisting of mobile nodes flowing in opposite directions along a street. First, we derive some approximate equations and propose an estimation method to compute the mean waiting time of Method 1. Second, we theoretically analyze the mean waiting time of Method 2, and compute a lower bound of that of Method 3. By comparing the three methods under the same assumptions using results of the analyses and some simulation results, we show relations between the mean waiting times of these methods and show how Capabilities 1 and 2 differently affect the mean waiting time. key words: mobile multi-hop network, connectivity analysis, mobility, epidemic routing