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On ‘stop=repeat' servicing for non-exponential queueing networks with blocking

Published online by Cambridge University Press:  14 July 2016

Nico M. Van Dijk*
Affiliation:
Free University, Amsterdam
*
Postal address: Faculteit der Economische Wetenschappen en Econometrie, Postbus 7161, 1007 MC Amsterdam, The Netherlands.

Abstract

Non-exponential queueing networks with blocking are studied under two types of blocking protocols: the ‘stop' and the ‘repeat' protocol under which services are to be either stopped or repeated respectively upon blocking. The two protocols are shown to be stationary equivalent when the system satisfies a partial balance condition. This condition is related to product-form results. The results are illustrated by closed and open network applications with reversible and nonreversible routing.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1991 

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References

[1] Akyildiz, I. F. (1989) Product form approximations for queueing networks with multi servers and blocking. IEEE Trans. Comput. 38, 99114.Google Scholar
[2] Akyildiz, I. F. and Von Brand, H. (1990) Exact solutions for open, closed and mixed queueing networks with rejection blocking. Theoret. Comput. Sci. To appear.Google Scholar
[3] Barbour, A. (1976) Networks of queues and the method of stages. Adv. Appl. Prob. 8, 584591.Google Scholar
[4] Baskett, F., Chandy, M., Muntz, R. and Palacios, J. (1975) Open, closed and mixed networks of queues with different classes of customers. J. Assoc. Comput. Mach. 22, 248260.Google Scholar
[5] Burman, D. Y., Lehoczky, J. P. and Lin, Y. (1982) Insensitivity of blocking probabilities in a circuit switching network. J. Appl. Prob. 21, 850859.Google Scholar
[6] Chandy, K. M., Howard, J. H. and Towsley, D. F. (1977) Product form and local balance in queueing network. J. Assoc. Comput. Mach. 24, 250263.Google Scholar
[7] Chandy, K. M. and Martin, A. J. (1983) A characterization of product-form queueing networks. J. Assoc. Comput. Mach. 30, 286299.Google Scholar
[8] Cohen, J. W. (1979) The multiple phase service network with generalized processor sharing. Acta Informat. 12, 245284.CrossRefGoogle Scholar
[9] Hordijk, A. and Schassberger, R. (1982) Weak convergence of generalized semi-Markov processes. Stoch. Proc. Appl. 12, 271291.Google Scholar
[10] Hordijk, A. and Van Dijk, N. M. (1981) Networks of queues with blocking. In Performance '81, ed. Kylstra, K. J., North-Holland, Amsterdam, pp. 5165.Google Scholar
[11] Hordijk, A. and Van Dijk, N. M. (1983) Network of queues. Part I: Job-local-balance and the adjoint process. Part II: General routing and service characteristics. Lecture Notes in Control and Informational Sciences 60, Springer-Verlag, Berlin, 158205.Google Scholar
[12] Hordijk, A. and Van Dijk, N. M. (1983) Adjoint processes, job-local-balance and insensitivity of stochastic networks. Bull. 44th Session Internat. Statist. Inst. 50, 776788.Google Scholar
[13] Kaufman, J. (1981) Blocking in a shared resource environment. IEEE Trans. Commun. 29, 14741481.Google Scholar
[14] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, Chichester.Google Scholar
[15] Jackson, J. R. (1963) Jobshop-like queueing systems. Management Sci. 10, 131142.Google Scholar
[16] Lam, S. S. (1977) Queueing networks with capacity constraints. IBM J. Res. Devel. 21, 376378.Google Scholar
[17] Noetzel, A. S. (1979) A generalized queueing discipline for product form network solutions. J. Assoc. Comput. Mach. 26, 779793.CrossRefGoogle Scholar
[18] Onvural, R. O. and Perros, H. C. (1986) On equivalencies of blocking mechanisms in queueing networks with blocking. Operat. Res. Letters 5, 293297.Google Scholar
[19] Pittel, B. (1979) Closed exponential networks of queues with saturation. The Jackson-type stationary distribution and its asymptotic analysis. Math. Operat. Res. 4, 357378.Google Scholar
[20] Schassberger, R. (1978) The insensitivity of stationary probabilities in networks of queues. Adv. Appl. Prob. 10, 906912.CrossRefGoogle Scholar
[21] Van Dijk, N. M. (1989) Stop=recirculate for exponential product form queueing networks with departure blocking. Operat. Res. Lett. To appear.Google Scholar
[22] Van Dijk, N. M. and Veltkamp, J. P. (1988) Product forms for stochastic interference systems. Prob. Eng. Inf. Sci. 3, 355376.Google Scholar
[23] Van Dijk, N. M. and Tijms, H. C. (1986) Insensitivity in two-node blocking models with applications. In Teletraffic Analysis and Computer Performance Evaluation. North-Holland, Amsterdam, 329340.Google Scholar
[24] Whittle, P. (1985) Partial balance and insensitivity. J. Appl. Prob. 22, 168175.Google Scholar
[25] Yao, P. D. and Buzacott, J. A. (1987) Modeling a class of flexible manufacturing systems with reversible routing. Operat. Res. 35, 8793.Google Scholar