Robust box bounds: throughput guarantees for closed multiclass queueing networks with minimal stochastic assumptions

To use queuing theory to analyze real systems such as computer communications networks, one makes assumptions that are, strictly speaking, untrue. The authors provide an exact analysis for cases with greatly relaxed assumptions. Service times can have general increasing failure rate distributions, different by class even at FIFO nodes. Routing can be arbitrary, including dependencies along the route, provided the number of visits to each node is a random variable. Only the mean service time and mean visit rates at nodes need be specified. A lower throughput bound is found which gives a minimum guaranteed throughput for each class; together with the familiar multiclass asymptotic upper bounds they give a convex feasible region in a multidimensional throughput space. A detailed analysis is given for systems with FIFO and infinite-server nodes, and the extension to processor-sharing nodes is described. The results can be reinterpreted as a set of bounds on the separate throughputs. This is equivalent to a circumscribed rectangular region called the robust box bounds