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Relations between queue-size and waiting-time distributions

Published online by Cambridge University Press:  14 July 2016

Masao Mori
Masao Mori*
Affiliation:
Ibaraki University
*
∗Postal address: Department of Information Engineering, Faculty of Engineering, Ibaraki University, Nakanarusawa 4–12–1, Hitachi, Japan.
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Abstract

Two types of representations for relation between queue-size and waiting-time distributions are studied. By using these, an incomplete but conceptually nice generalization of Pollaczek–Khinchine formula for mean waiting time for M/G/c is obtained.

Keywords

MULTISERVERPOLLACZEK–KHINCHINE FORMULA
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 822 - 830
Copyright
Copyright © Applied Probability Trust 1980 

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References

Brumelle, S. L. (1972) A generalization of L = ?W to moments of queue length and waiting times. Operat. Res. 20, 1127–1136.Google Scholar
Haji, R. and Newell, G. F. (1971) A relation between stationary queue and waiting time distribution. J. Appl. Prob. 8, 617–620.Google Scholar
Hokstad, P. (1978) Approximation for the M/G/m queue. Operat. Res. 26, 510–523.Google Scholar
Kiefer, J. and Wolfowitz, J. (1955) On the theory of queues with many servers. Trans. Amer. Math. Soc. 80, 470–501.Google Scholar
König, D., Schmidt, V. and Stoyan, D. (1976) On some relations between stationary distributions of queue lengths and imbedded queue lengths in G/G/s queueing systems. Math. Operationsforsch. Statist. 7, s. 577–586.Google Scholar
Lee, A. M. and Longton, P. A. (1957) Queueing process associated with airline passenger check-in. Operat. Res. Quart. 10, 56–71.CrossRefGoogle Scholar
Lemoine, A. J. (1974) On two stationary distributions for the stable GI/G/ì queue. J. Appl. Prob. 11, 849–852.CrossRefGoogle Scholar
Marshall, K. T. (1968) Some inequalities in queueing. Operat. Res. 16, 651–665.Google Scholar
Miyazawa, M. (1977) Time and customer processes in queues with stationary inputs. J. Appl. Prob. 14, 349–357.Google Scholar
Miyazawa, M. (1979) A formal approach to queueing processes in the steady state and their applications. J. Appl. Prob. 16, 319–331.Google Scholar
Mori, M. (1974) A note on a (J, X)-process with continuous state space and its applications to the queueing theory. Research Report on Information Sciences B-2, Tokyo Institute of Technology.Google Scholar
Mori, M. (1975) Some bounds for queues. J. Operat. Res. Soc. Japan , 18, 152–181.Google Scholar
Nozaki, S. A. and Ross, S. M. (1978) Approximations in finite capacity multi-server queues with Poisson arrivals. Operat. Res. 15, 826–834.Google Scholar
Stoyan, D. (1976) Approximations for M/G/s queues. Math. Operationsforsch. Statist. 7, 587–594.CrossRefGoogle Scholar
Stoyan, D. (1977) Further stochastic order relations among GI/GI/1 queues with a common traffic intensity. Math. Operationsforsch. Statist., ser. Optimization 8, 541–548.CrossRefGoogle Scholar
Takahashi, Y. (1977) An approximation formula for the mean waiting time of an M/G/c queue. J. Operat. Res. Soc. Japan 20, 150–163.Google Scholar