Greedy Dynamic Routing on Arrays

We study the problem of dynamic routing on arrays. We prove that a large class of greedy algorithms perform very well on average. In the dynamic case, when the arrival rate of packets in anN×Narray is at most 99% of network capacity, we establish an exponential bound on the tail of the delay distribution. Moreover, we show that in any window ofTsteps, the maximum queue-size isO(1+logT/logN) with high probability. We extend these results to the case of bit-serial routing, and to the static case. We also calculate the exact value of the ergodic expected delay and queue-sizes under the farthest first protocol for the one-dimensional array, and for the ring when the arrivals are Poisson.