Closed Queueing Networks with Multiple Servers: Transient and Steady-State Approximations

摘要

Closed Markovian queueing networks are accepted as valuable tools for analyzing the performance of a variety of complex systems: flexible manufacturing systems and computer communication networks are just two examples. Despite such a rich class of problems being modeled as closed queueing networks,it is only recently that 'large' queueing networks have become computationally tractable. Most noticeable in the regard are the software packages PANACEA and QNA. PANACEA exploits integral representations and asymptotic expansions to compute product form solutions, whereas QNA approximates the closed model by a more tractable open queueing network. Our work is in the spirit of QNA: we show that the steady-state queue length distribution of a single-class closed Jackson network with multiple servers can, under certain conditions, be approximated by a multivariate normal distribution when the number of jobs, n, circulating in the system is sufficiently large. The approximation method was originally developed for single-class closed Jackson networks with multiple servers, but it has been extended to networks with Cox phase service time distributions, and multiple class networks with a pre-emptive resume priority queueing discipline at each service center.