Optimal scheduling of servers in a queueing system with constraints [packet radio networks]

The problem addressed considers random arrivals (or generation) of packets at the nodes and poses the question of (a) existence of schedules that guarantee finite queueing delays and/or (b) finding schedules that produce minimum queueing delay. As such a problem involves interacting queueing systems, it is not feasible to attempt to solve it for a PRN (packet radio network) of general topology. Instead the focus is on a simple tandem topology with elementary routing requirements. A set of N deterministic servers, the ith of which receives from exogenous sources customers at a Bernoulli rate of λ_i, is considered. The servers are ordered from 1 to N and they are constrained so that no two consecutive servers can be busy at the same time. This model represents a PRN in which there are N links connecting N+1 nodes in tandem and in which each of the first N nodes receives packets at rates λ_i and wishes to deliver them to its neighbor on the right (the model can easily incorporate the case in which there are messages that need to be transmitted to the left neighboring node)