State-of-the-Art—Networks of Queues—A Survey of Equilibrium Analysis

Queueing network models abound in applications, but despite their importance many of the results for these models, both classical and recent, are not well known. The intent of this paper is to provide an overview of available equilibrium results for “general Jackson systems,” that is, queueing network models of the sort introduced in the classical papers of Jackson [Jackson, J. R. 1957. Networks of waiting lines. Oper. Res.5 518–521; Jackson, J. R. 1963. Jobshop-like queueing systems. Management Sci.10 131–142.]. In addition, we discuss methodology which has been employed to obtain the equilibrium results and we call attention to some important open problems. Detailed discussions are limited to a small group of papers which seem important to us, and there is considerable emphasis on recent work appearing in the applied probability literature. The list of references does include, however, work not reviewed here, along with other survey and background material.