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Sojourn times in queuing networks with multiserver modes

Published online by Cambridge University Press:  14 July 2016

R. Schassberger*
Affiliation:
Technische Universität Berlin
H. Daduna*
Affiliation:
Universität Hamburg
*
Postal address: Technische Universität Berlin, Fachbereich Mathematik, Strasse des 17 Juni 135, D-1000 Berlin 12, W. Germany.
Postal address: Technische Universität Berlin, Fachbereich Mathematik, Strasse des 17 Juni 135, D-1000 Berlin 12, W. Germany.

Abstract

This paper generalizes previous results for sojourn-time distributions along so-called overtake-free routes in product-form networks of queues.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1987 

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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 J. Assoc. Comput. Mach. 22, 248260.CrossRefGoogle Scholar
[2] Boxma, O. J. (1983) Response time distributions in cyclic queues. 44th Session Int. Statist. Inst, Madrid, Bull. Int. Statist. Inst. Vol. II, 735754.Google Scholar
[3] Boxma, O. J. and Donk, P. (1982) On response-time and cycle-time distribution in cyclic queues. Performance Eval. 2, 181194.CrossRefGoogle Scholar
[4] Boxma, O. J., Kelly, F. P. and Konheim, A. G. (1984) The product form for sojourn time distributions in cyclic exponential queues. J. Assoc. Comput. Mach. 31, 128133.CrossRefGoogle Scholar
[5] Burke, P. J. (1968) The output process of a stationary M/M/s queuing system. Ann. Math. Statist. 39, 11441152.CrossRefGoogle Scholar
[6] Burke, P. J. (1972) Output processes and tandem queues. Proc. Symp. Computer-Communications Networks and Teletraffic, Brooklyn, 1972, ed. Fox, J., 419428.Google Scholar
[7] Chow, W. M. (1981) The cycle time distribution of exponential cyclic queues. J. Assoc. Comput. Mach. 27, 281286.CrossRefGoogle Scholar
[8] Daduna, H. (1982) Passage times for overtake-free paths in Gordon–Newell networks. Adv. Appl. Prob. 14, 672686.CrossRefGoogle Scholar
[9] Daduna, H. (1983) On passage times in Jackson networks: Two-stations walk and overtake-free paths. Z. Operat. Res. 27, 239256.Google Scholar
[10] Daduna, H. (1984) Burke's theorem on passage times in Gordon–Newell networks. Adv. Appl. Prob. 16, 867886.CrossRefGoogle Scholar
[11] Fayolle, G., Iasnogorodski, R. and Mitrani, I. (1983) Distribution of sojourn times in a queuing network with overtaking. Proc. 9th Int. Conf. Performance Evaluation, Maryland.Google Scholar
[12] Kawashima, T. and Torigoe, N. (1983) Cycle time distribution in a central server queuing system with multi-server stations. Preprint.Google Scholar
[13] Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
[14] Kelly, F. P. and Pollett, P. K. (1983) Sojourn times in closed queuing networks. Adv. Appl. Prob. 15, 638658.CrossRefGoogle Scholar
[15] Lemoine, A. J. (1979) On total sojourn time in networks of queues. Management Sci. 25, 10341045.CrossRefGoogle Scholar
[16] Melamed, B. (1982) Sojourn times in queueing networks. Math. Operat. Res. 7, 223244.CrossRefGoogle Scholar
[17] Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768773.CrossRefGoogle Scholar
[18] Reich, E. (1963) Note on queues in tandem. Ann. Math. Statist. 34, 338341.CrossRefGoogle Scholar
[19] Schassberger, R. and Daduna, H. (1983) The time for a round trip in a cycle of exponential queues. J. Assoc. Comput. Mach. 30, 146150.CrossRefGoogle Scholar
[20] Sekino, A. (1972) Response time distribution of multiprogrammed time-shared computer systems. Proc. 6th Annual Princeton Conf. Information Science and Systems, 613619.Google Scholar
[21] Sevcik, K. C. and Mitrani, I. (1981) The distribution of queueing network states at input and output instants. J. Assoc. Comput. Mach. 28, 358371.CrossRefGoogle Scholar
[22] Simon, B. and Foley, R. D. (1979) Some results on sojourn times in acyclic Jackson networks. Management Sci. 25, 10271034.CrossRefGoogle Scholar
[23] Towsley, D. (1980) Queuing network models with state-dependent routing. J. Assoc. Comput. Mach. 27, 323337.CrossRefGoogle Scholar
[24] Walrand, J. and Varaiya, P. (1980) Sojourn times and the overtaking condition in Jacksonian networks. Adv. Appl. Prob. 12, 10001018:CrossRefGoogle Scholar
[25] Wong, J. (1979) Response time distribution of the M/M/m/N queuing model. Operat. Res. 27, 11961202.CrossRefGoogle Scholar