The deviation matrix of the M/M/1//spl infin/ and M/M/1/N queue, with applications to controlled queueing models

We give closed expressions for the deviation matrices of the M/M/1//spl infin/ and the M/M/1/N queue. It is applied to controlled queueing models by solving the dynamic programming optimality equation for Bernoulli policies; after which we can execute a single step of policy iteration by calculating the bias vector of the Bernoulli policies directly from the deviation matrix.