Exact-order asymptotic analysis for closed queueing networks

In this paper we study the asymptotic behavior of a general class of product-form closed queueing networks as the population size grows large. We first characterize the asymptotic behavior of the normalization constant for the stationary distribution of the network in exact order. This result then enables us to establish the asymptotic behavior of the system performance metrics, which extends a number of well-known asymptotic results to exact order. We further derive new, computationally simple approximations for performance metrics that significantly improve upon existing approximations for large-scale networks. In addition to their direct use for the analysis of large networks, these new approximations are particularly useful for reformulating large-scale queueing network optimization problems into more easily solvable forms, which we demonstrate with an optimal capacity planning example. © Applied Probability Trust 2012.