Resource Allocation in General Queueing Networks

We consider the problem of how best to assign the service effort in a queueing network in order to minimize the expected delay under a cost constraint. We shall 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 approximation techniques, in particular, the residual-life approximation (Pollett (1984)) for the distribution of queueing times. This work generalizes results of Kleinrock (1964), who studied networks with exponentially distributed service times.