Performance bounds for queueing networks and scheduling policies

We introduce a new technique for obtaining upper and lower bounds on the performance of Markovian queueing networks and scheduling policies. Assuming stability, and examining the consequence of a steady-state for general quadratic forms, we obtain a set of linear equality constraints. Further, the conservation of time and material gives an augmenting set of linear equality and inequality constraints. Together, these allow us to bound the performance, either above or below, by solving a linear program. We illustrate this technique on several typical problems of interest in manufacturing systems. We illustrate the application of our method to GI/GI/1 queues. We obtain an analytic bound which improves upon Kingman´s bound for E₂/M/1 queues