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Impact of Biased Random Walk on the Average Delay of Opportunistic Single Copy Delivery in Manhattan Area
Jung Hyun Jun, Weihuang Fu and Dharma P. Agrawal

In Mobile Opportunistic Networks the cost and effectiveness of any opportunistic forwarding is measured by the expected message delay. Hence, its critical goal is to have low delay for a message to reach the destination. This paper studies the average delay of a message in a Mobile Opportunistic Network on Manhattan area.We first model the mobility of a message as a biased random walk in tilted grid and analyze the delay of a message based on the hitting time of a bias random walk.We derive a mathematical expression of expected delay for a walk starting from any point in titled grid for both biased and unbiased random walks and obtain a closed form approximation of average delay of a message for the case of unbiased random walk. The key result is that the average delay of a message in Mobile Opportunistic Networks is very sensitive to the bias level of a random walk at each stage of the walk (depends on the distance of its current position from the destination). Then, this key result implicitly infers why most of the smart message forwarding algorithm in Mobile Opportunistic Network deliver a message with reasonably short expected delay.

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