Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T04:37:24.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Product forms based on backward traffic equations

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Richard J. Boucherie
Richard J. Boucherie*
Affiliation:
CWI, Amsterdam
*
∗Present address: Universiteit van Amsterdam, Department of Econometrics, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper introduces a new form of local balance and the corresponding product-form results. It is shown that these new product-form results allow capacity constraints at the stations of a queueing network without reversibility assumptions and without special blocking protocols. In particular, exact product-form results for heavily loaded queueing networks are obtained.

Keywords

LOCAL BALANCEBLOCKINGQUEUEING NETWORK

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 508 - 518
Copyright
Copyright © Applied Probability Trust 1995 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research carried out partly while the author was with the Department of Econometrics, Vrije Universiteit, Amsterdam, and partly while the author was ERCIM fellow at CWI, Amsterdam. Supported by the European Grant BRA-QMIPS of CEC DG XIII.

References

[1] Baskett, F., Chandy, K. M., Muntz, R. R. and Palacios, F. G. (1975) Open, closed and mixed networks of queues with different classes of customers. Journal of the ACM 22, 248–260.Google Scholar
[2] Boucherie, R. J. (1992) Product-form in queueing networks. , Vrije Universiteit, Amsterdam (available from the author).Google Scholar
[3] Boucherie, R. J. and Van Dijk, N. M. (1991) Product forms for queueing networks with state dependent multiple job transitions. Adv. Appl. Prob. 23, 152–187.Google Scholar
[4] Van Dijk, N. M. (1993) Queueing Networks and Product Forms: A Systems Approach. Wiley, New York.Google Scholar
[5] Gordon, W. J. and Newell, G. F. (1967) Closed queueing systems with exponential servers. Operat. Res. 15, 254–265.Google Scholar
[6] Gordon, W. J. and Newell, G. F. (1967) Cyclic queueing systems with restricted length queues. Operat. Res. 15, 266–277.Google Scholar
[7] Hordijk, A. and Van Dijk, N. M. (1981) Networks of queues with blocking. In Performance '81, ed. Kylstra, F. J., pp. 51–65. North-Holland, Amsterdam.Google Scholar
[8] Jackson, J. R. (1957) Networks of waiting lines. Operat. Res. 5, 518–521.Google Scholar
[9] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[10] Serfozo, R. F. (1989) Markovian network processes: congestion dependent routing and processing. Queueing Systems 5, 5–36.Google Scholar
[11] Whittle, P. (1986) Systems in Stochastic Equilibrium. Wiley, New York.Google Scholar