Optimal capacity assignment in general queueing networks

We consider the problem of how best to assign the service capacity in a queueing network in order to minimise the expected delay under a cost constraint. We study systems with several types of customers, general service time distributions, stochastic or deterministic routing, and a variety of service regimes. For such networks there are typically no analytical formulae for the waiting time distributions. Thus, we shall approach the optimal allocation problem using an approximation technique: specifically, the residual-life approximation for the distribution of queueing times. This work generalises results of Kleinrock, who studied networks with exponentially distributed service times. We illustrate our results with reference to data networks.