Packet routing with arbitrary end-to-end delay requirements

We study the problem of scheduling packets to meet an arbitrary set of delay requirements. Consider a connectionoriented network in which a set of sessions is defined. Each session i follows a fixed route and requests an end-to-end delay requirement A;. The packet injections for each session are subject to a specified session rate and burst size; the packet movement is restricted to one packet per link per time step. If an arbitrary set of delay requirements is schedulable for every link in isolation and for every session in isolation, we present a simple distributed protocol in which every session i achieves a delay bound of O((a + log &)A;). Here, u is a term that depends logarithmically on the burst sizes; m is the number of links in the network and prnin is the smallest session rate. In addition, we show the existence of a schedule that achieves a hound of O(aAi). We also construct an example to show that the a factor cannot be removed in general. Hence, per-session schedulability and per-link schedulability is not sufficient to guarantee network schedulability for arbitrary delay requirements. This provides a contrast with previous work in that the bounds are not simply composed of a per-link delay bound and a per-session bound. Finally, we examine the problem of route selection in which the session routes are not given (I priori. Our aim is to choose the routes so that the delay requirements can be met.