Generalized Jackson Networks
In this chapter we consider a queueing network that generalizes the Jackson network studied in Chapter 2, by allowing renewal arrival processes that need not be Poisson and i.i.d. service times that need not follow exponential distributions. (However, we do not allow the service times of the network to be state-dependent; in this regard, the network is more restrictive than the Jackson network. Nevertheless, this network has been conventionally referred to as the generalized Jackson network.) Unlike the Jackson network, the stationary distribution of a generalized Jackson network usually does not have an explicit analytical form. Therefore, approximations and limit theorems that support such approximations are usually sought for the generalized Jackson networks.
KeywordsReflection Mapping Closed Network Jackson Network Nonnegative Orthant Workload Process
Unable to display preview. Download preview PDF.
- Berman, A. and R.J. Plemmons. (1979). Nonnegative Matrices in the Mathematical Sciences,Academic Press.Google Scholar
- Chen, H. and A. Mandelbaum. (1991a). Leontief systems, RBV’s and RBM’s, in The Proceedings of the Imperial College Workshop on Applied Stochastic Processes, ed. by M.H.A. Davis and R.J. Elliotte, Gordon and Breach Science Publishers.Google Scholar
- Chen, H. and A. Mandelbaum. (1994). Hierarchical modelling of stochastic networks, Part II: strong approximations, in D.D. Yao (ed.), Stochastic Modeling and Analysis of Manufacturing Systems, 107–131, Springer-Verlag.Google Scholar
- Chen, H. and X. Shen. (2000). Computing the stationary distribution of SRBM in an orthant. In preparation.Google Scholar
- Cottle, R.W., J.S. Pang and R.E. Stone. (1992). The Linear Complementarity Problem,Academic Press.Google Scholar
- Johnson, D. P. (1983). Diffusion Approximations for Optimal Filtering of Jump Processes and for Queueing Networks, Ph. D Dissertation, University of Wisconsin.Google Scholar
- Mandelbaum, A. (1989). The dynamic complementarity problem (preprint).Google Scholar