Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T07:11:57.116Z Has data issue: false hasContentIssue false
  • English
  • Français

Sojourn times in queuing networks with multiserver modes

Published online by Cambridge University Press:  14 July 2016

R. Schassberger  and
H. Daduna
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.
Get access Rights & Permissions [Opens in a new window]

Abstract

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

Keywords

PARTIAL BALANCEPRODUCT FORM
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 511 - 521
Copyright
Copyright © Applied Probability Trust 1987 

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] 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, 248–260.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, 735–754.Google Scholar
[3] Boxma, O. J. and Donk, P. (1982) On response-time and cycle-time distribution in cyclic queues. Performance Eval. 2, 181–194.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, 128–133.CrossRefGoogle Scholar
[5] Burke, P. J. (1968) The output process of a stationary M/M/s queuing system. Ann. Math. Statist. 39, 1144–1152.CrossRefGoogle Scholar
[6] Burke, P. J. (1972) Output processes and tandem queues. Proc. Symp. Computer-Communications Networks and Teletraffic, Brooklyn, 1972, ed. Fox, J., 419–428.Google Scholar
[7] Chow, W. M. (1981) The cycle time distribution of exponential cyclic queues. J. Assoc. Comput. Mach. 27, 281–286.CrossRefGoogle Scholar
[8] Daduna, H. (1982) Passage times for overtake-free paths in Gordon–Newell networks. Adv. Appl. Prob. 14, 672–686.CrossRefGoogle Scholar
[9] Daduna, H. (1983) On passage times in Jackson networks: Two-stations walk and overtake-free paths. Z. Operat. Res. 27, 239–256.Google Scholar
[10] Daduna, H. (1984) Burke's theorem on passage times in Gordon–Newell networks. Adv. Appl. Prob. 16, 867–886.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, 638–658.CrossRefGoogle Scholar
[15] Lemoine, A. J. (1979) On total sojourn time in networks of queues. Management Sci. 25, 1034–1045.CrossRefGoogle Scholar
[16] Melamed, B. (1982) Sojourn times in queueing networks. Math. Operat. Res. 7, 223–244.CrossRefGoogle Scholar
[17] Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768–773.CrossRefGoogle Scholar
[18] Reich, E. (1963) Note on queues in tandem. Ann. Math. Statist. 34, 338–341.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, 146–150.CrossRefGoogle Scholar
[20] Sekino, A. (1972) Response time distribution of multiprogrammed time-shared computer systems. Proc. 6th Annual Princeton Conf. Information Science and Systems, 613–619.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, 358–371.CrossRefGoogle Scholar
[22] Simon, B. and Foley, R. D. (1979) Some results on sojourn times in acyclic Jackson networks. Management Sci. 25, 1027–1034.CrossRefGoogle Scholar
[23] Towsley, D. (1980) Queuing network models with state-dependent routing. J. Assoc. Comput. Mach. 27, 323–337.CrossRefGoogle Scholar
[24] Walrand, J. and Varaiya, P. (1980) Sojourn times and the overtaking condition in Jacksonian networks. Adv. Appl. Prob. 12, 1000–1018:CrossRefGoogle Scholar
[25] Wong, J. (1979) Response time distribution of the M/M/m/N queuing model. Operat. Res. 27, 1196–1202.CrossRefGoogle Scholar