A diffusion model for packet travel time in a random multihop medium

We consider a wireless network in which packets are forwarded opportunistically from the source towards the destination, without accurate knowledge of the direction that they should take. A Brownian motion model that includes the effect of packet losses, and subsequent retransmission after a time-out, is used to compute the average travel time of the packet. The results indicate that the average travel time is always finite provided that a time-out is used, and that there is an element of randomness in the manner in which successive nodes are being chosen. We show that the average packet travel time can be minimized by a judicious choice of the time-out, and its optimum value in turn depends on other system parameters such as packet-loss probabilities. We present simulations that illustrate the analytical results.