Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T21:20:32.139Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simple Performability Estimate for Jackson Networks with an Unreliable Output Channel

Published online by Cambridge University Press:  27 July 2009

Nico M. van Dijk
Nico M. van Dijk
Affiliation:
University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Abstract

Open Jackson networks are studied in which departures can be blocked such as due to a breakdown of an output channel. A simple performance estimate is provided along with an explicit error bound.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 4 , October 1995 , pp. 603 - 614
Copyright
Copyright © Cambridge University Press 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.)

References

1.Adan, I.J.B.F. & van der Wal, J. (1989). Monotonicity of the throughput in single server production and assembly networks with respect to buffer sizes. In Altiok, T. and Perros, H.G. (eds.), Queueing networks with blocking. Amsterdam: North-Holland, pp. 345–356.Google Scholar
2.Adan, I.J.B.F. & van der Wai, J. (1989). Monotonicity of the throughput of a closed queueing network in the number of jobs. Operations Research 37: 935–957.CrossRefGoogle Scholar
3.Barbour, A. (1976). Network of queues and the method of stages. Advances in Applied Probability 8: 584–591.CrossRefGoogle Scholar
4.Courtois, P.J. (1977). Decomposability: Queueing and computer system application. New York: Academic Press.Google Scholar
5.Courtois, P.J. & Semal, P. (1986). Bounds on conditional steady-state distributions in large Markovian and queueing models. In Teletraffic analysis and computer performance evaluation. Amsterdam: North-Holland.Google Scholar
6.Goyal, A.Lavenberg, S.S. & Trivedi, K.S. (1986). Probabilistic modelling of computer system availability. Annals of Operations Research 8: 285–306.CrossRefGoogle Scholar
7.Goyal, A. & Tantawi, A.N. (1987). Evaluation of performability for degradable computer systems. IEEE Transactions on Computers 36(6): 738–744.CrossRefGoogle Scholar
8.Haverkort, B.R. & Niemegeers, I.G. (1988). A theory of describing performability models. Research Report, Twente University, Enschede, The Netherlands.Google Scholar
9.Hordijk, A. & Schassberger, R. (1982). Weak convergence of generalized semi-Markov processes. Stochastic Processes and Applications 12: 271–291.CrossRefGoogle Scholar
10.Jaiswal, N.K. (1968). Priority queues. New York: Academic Press.Google Scholar
11.Meyer, J.F. (1982). Closed form solutions of performability. IEEE Transactions on Computers 31: 648–657.CrossRefGoogle Scholar
12.Muntz, R.R., Souza e Silva, E. de & Goyal, A. (1989). Bounding availability of repairable computer systems. Performance Evaluation Review 17: 29–38.CrossRefGoogle Scholar
13.Ross, S.M. (1970). Applied probability models with optimization application. San Francisco: Holden Day.Google Scholar
14.Shanthikumar, J.G. & Yao, D.D. (1987). Stochastic monotonicity of the queue length in closed queueing networks. Operations Research 35: 583–588.CrossRefGoogle Scholar
15.Shanthikumar, J.G. & Yao, D.D. (1988). Monotonicity properties in cyclic queueing networks with finite buffers. In Queueing networks with blocking. Amsterdam: North-Holland, pp. 344–352.Google Scholar
16.Shanthikumar, J.G. & Yao, D.D. (1988). Throughput bounds for closed queueing networks with queue-dependent service rates. Performance Evaluations 9: 69–78.CrossRefGoogle Scholar
17.Smith, R.M., Trivedi, K.S. & Ramesh, A.V. (1988). Performability analysis: Measures, an algorithm and a case study. IEEE Transactions on Computers C-37(4): 406–417.CrossRefGoogle Scholar
18.Souza e Silva, E. de & Gail, H.R. (1989). Calculating availability and performability measures of repairable computer system using randomization. Journal of the Association for Computing Machines 36.Google Scholar
19.Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: Wiley.Google Scholar
20.Tijms, H.C. (1986). Stochastic modelling and analysis. A computational approach. New York: Wiley.Google Scholar
21.van Dijk, N.M. (1988). Simple bounds for queueing systems with breakdowns. Performance Evaluation 8: 117–128.CrossRefGoogle Scholar
22.van Dijk, N.M. (1992). Approximate uniformization for continuous-time Markov chains an application to performability analysis. Stochastic Processes and Applications 40: 339–357.CrossRefGoogle Scholar
23.van Dijk, N.M. & van der Wai, J. (1987). Simple bounds and monotonicity results for multiserver exponential tandem queues. Queueing Systems 4: 1–16.CrossRefGoogle Scholar
24.Whitt, W. (1981). Comparing counting processes and queues. Advances in Applied Probability 13: 207–220.CrossRefGoogle Scholar
25.Whitt, W. (1982). Continuity of generalized semi-Markov processes. Mathematics Operations Research 5: 495–501.Google Scholar