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On normalization constants for closed queueing networks with finite local buffers

Part of:Special processes

Published online by Cambridge University Press:  14 July 2016

Ulrich A. W. Tetzlaff
Ulrich A. W. Tetzlaff*
Affiliation:
George Mason University
*
∗ Postal address: George Mason University, School of Management, Fairfax, VA 22030–4444, USA. Email address: tetzlaff@som.gmu.edu
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Abstract

We present new closed form solutions for partition functions used to normalize the steady-state flow balance equations of certain Markovian type queueing networks. The results focus on single class closed product form networks with state space constraints at the queueing stations. They are achieved by combining the partition function of the open network, having finite local buffers with a delta function in order to fix the number of customers in the system.

Keywords

Partition functionsnormalization constantsqueueing networksfinite queues

MSC classification

Primary:60K25: Queueing theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 3 , September 1998, pp. 600 - 607
Copyright
Copyright © Applied Probability Trust 1998 

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References

Balsamo, S., and de Nitto Personè, V. (1994). A survey of product form queueing networks with blocking and their equivalences. Ann. Operat. Res. 48, 31–61.Google Scholar
Bertozzi, A., and McKenna, J. (1993). Multidimensional residues, generating functions, and their application to queueing networks. SIAM Rev. 35, 239–268.Google Scholar
Gerasimov, A. I. (1983). Analysis of queueing networks by polynomial approximation. Problems of Control and Information Theory 12, 219–228.Google Scholar
Gerasimov, A. I. (1993). The evaluation of normalization constants in multiclass multiserver queueing networks. Autom. and Remote Control 5, 119–130 (in Russian).Google Scholar
Gerasimov, A. I. (1995). On normalization constants in multiclass queueing networks. Operat. Res. 43, 704–711.Google Scholar
Gordon, J. J. (1990). The evaluation of normalization constants in closed queueing networks. Operat. Res. 38, 863–869.Google Scholar
Gordon, W. J., and Newell, G. F. (1967). Closed queueing systems with exponential servers. Operat. Res. 15, 254–265.Google Scholar
Harrison, P. G. (1985). On normalization constants in queueing networks. Operat. Res. 33, 464–468.Google Scholar
Koenigsberg, E. (1958). Cyclic queues. Operat. Res. Quart. 9, 22–35.Google Scholar
Kogan, Y. (1992). Another approach to asymptotic expansions for large closed queueing networks. Operat. Res. Lett. 11, 317–321.CrossRefGoogle Scholar
Lam, S. S. (1976). Store-and-forward buffer requirements in a packet switching network. IEEE Trans. Comm. 24, 394–403.Google Scholar
McKenna, J., Mitra, D., and Ramakrishnan, K. G. (1981). A class of closed Markovian queuing networks: integral representations, asymptotic expansions, and generalizations. The Bell System Technical Journal 60, 599–641.Google Scholar
Mitra, D., and McKenna, J. (1986). Asymptotic expansions for closed Markovian networks with state-dependent service rates. J. Assoc. Computing Machinery 33, 568–592.Google Scholar
Van Dijk, N. M., and Korezlioglu, H. (1992). On product form approximations for communication networks with losses: error bounds. Ann. Operat. Res. 35, 69–94.Google Scholar
Van Dijk, N. M. (1993). Queueing Networks and Product Forms. Wiley, Chichester.Google Scholar
Yao, D. D., and Buzacott, J.A. (1986). Models for flexible manufacturing systems with limited local buffers. Internat. J. Production Res. 24, 107–118.Google Scholar