Skip to main content Accessibility help
×
Home

Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes

  • Richard J. Boucherie (a1) and Nico M. Van Dijk (a1)

Abstract

Reversible spatial birth-death processes are studied with simultaneous jumps of multi-components. A relationship is established between (i) a product-form solution, (ii) a partial symmetry condition on the jump rates and (iii) a solution of a deterministic concentration equation. Applications studied are reversible networks of queues with batch services and blocking and clustering processes such as those found in polymerization chemistry. As illustrated by examples, known results are hereby unified and extended. An expectation interpretation of the transition rates is included.

Copyright

Corresponding author

Postal address for both authors: Faculteit der Economische Wetenschappen en Econometrie, Vrije Universiteit, Postbus 7161, 1007 MC Amsterdam, The Netherlands.

References

Hide All
[1] Bertsekas, D. P. and Gallager, R. G. (1987) Data Networks. Prentice-Hall, Englewood Cliffs, NJ.
[2] Chandy, K. M. and Martin, A. J. (1983) A characterization of product-form queueing networks. JACM 30, 286299.
[3] Daduna, H. and Schassberger, R. (1983) Networks of queues in discrete time. Z. Operat. Res. 27, 159175.
[4] Van Dongen, P. G. J. and Ernst, M. H. (1987) Fluctuations in coagulating systems. J. Statist. Phys. 49, 879926.
[5] Van Dongen, P. G. J. and Ernst, M. H. (1984) Kinetics of reversible polymerization. J. Statist. Phys. 37, 301324.
[6] Ernst, M. H. (1984) Kinetic theory of clustering. In International Summer School on Fundamental Problems in Statistical Mechanics, VI Trondheim, Norway, June 1984, ed. Cohen, E. G. D.. North-Holland, Amsterdam.
[7] Foschini, G. J. and Gopinath, B. (1983) Sharing memory optimally. IEEE Trans. Comm. 31, 352360.
[8] Gihman, I. I. and Skorohod, A. V. (1975) The Theory of Stochastic Processes II. Springer-Verlag, Berlin.
[9] Hordijk, A. and Van Dijk, N. M. (1983) Networks of queues. Part I: Job-local-balance and the adjoint process. Part II: General routing and service characteristics. In Lecture Notes in Control and Informational Sciences 60, Springer-Verlag, Berlin, 158205.
[10] Van Kampen, N. G. (1981) Stochastic Processes in Physics and Chemistry. North-Holland, Amsterdam.
[11] Kaufman, J. S. (1981) Blocking in a shared resource environment. IEEE Trans. Commun. 29, 14741481.
[12] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.
[13] Krzesinski, A. E. (1987) Multiclass queueing networks with state-dependent routing. Performance Evaluation 7, 125143.
[14] Lam, S. S. (1977) Queueing networks with population size constraints. IBM J. Res. Develop. 21, 370378.
[15] Lushnikov, A. A. (1978) Coagulation in finite systems. J. Coll. Interf. Sci. 65, 276285.
[16] Pittel, B. (1979) Closed exponential networks of queues with saturation: the Jackson-type stationary distribution and its asymptotic analysis. Math. Operat. Res. 4, 357378.
[17] Pujolle, G. (1988) Discrete-time queueing systems with a product form solution. MASI Research Report.
[18] Schassberger, R. and Daduna, H. (1983) A discrete-time technique for solving closed queueing models of computer systems. Technical Report, Technische Universität Berlin.
[19] Serfozo, R. F. (1988) Markovian network processes with system-dependent transition rates. Research Report, Georgia Institute of Technology.
[20] Stockmayer, W. H. (1943) Theory of molecular size distributions and gel formation in branched chain polymers. J. Chem. Phys. 11, 4555.
[21] Taylor, P. G., Henderson, W., Pearce, C. E. M. and Van Dijk, N. M. (1988) Closed queueing networks with batch services. Technical Report, University of Adelaide.
[22] Towsley, D. F. (1980) Queueing networks with state-dependent routing. JACM 27, 323337.
[23] Van Dijk, N. M. (1988) Product forms for random access schemes. Computer Networks and ISDN Systems.
[24] Walrand, J. (1983) A discrete-time queueing network. J. Appl. Prob. 20, 903909.
[25] Whittle, P. (1986) Systems in Stochastic Equilibrium. Wiley, New York.
[26] Yao, D. D. and Buzacott, J. A. (1987) Modeling a class of flexible manufacturing systems with reversible routing. Operat. Res. 35, 8793.

Keywords

Spatial birth-death processes with multiple changes and applications to batch service networks and clustering processes

  • Richard J. Boucherie (a1) and Nico M. Van Dijk (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed