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Some moment results for certain tandem and multiple-server queues

Published online by Cambridge University Press:  14 July 2016

Barry Wolfson
Barry Wolfson*
Affiliation:
Wellesley College
*
∗Postal address: Department of Computer Science, Wellesley College, Wellesley, MA 02181, USA.
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Abstract

It is known that for a GI/G/1 queue, if the interarrival time has finite first moment, then the (k + 1)th moment of the service time is finite if the kth moment of the stationary workload is finite. This result is extended to certain tandem and multiple-server queues.

Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 901 - 910
Copyright
Copyright © Applied Probability Trust 1984 

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References

[1] Brumelle, S. (1971) Some inequalities for parallel server queues. Operat. Res. 19, 402–413.Google Scholar
[2] Kiefer, J. and Wolfowitz, J. (1955) On the theory of queues with many servers. Trans. Amer. Math. Soc. 78, 1–18.Google Scholar
[3] Kiefer, J. and Wolfowitz, J. (1956) On the characteristics of the general queueing process with applications to random walk. Ann. Math. Statist. 27, 147–161.CrossRefGoogle Scholar
[4] Lemoine, A. (1976) On random walks and stable GI/G/1 queues. Math. Operat. Res. 1, 159–164.CrossRefGoogle Scholar
[5] Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.Google Scholar
[6] Loynes, R. M. (1962) The stability of a queue with non-independent interarrival and service times. Proc. Camb. Phil. Soc. 58, 494–520.Google Scholar
[7] Miyazawa, ?. (1979) A formal approach to queueing processes in the steady state and their applications. J. Appl. Prob. 16, 332–346.Google Scholar
[8] Niu, S. (1980) Bounds for expected delays in some tandem queues. J. Appl. Prob. 17, 831–838.Google Scholar
[9] Sacks, J. (1960) Ergodicity of queues in series. Ann. Math. Statist. 31, 579–588.Google Scholar
[10] Veinott, A. F. (1965) Optimal policy in a dynamic single product nonstationary inventory model with several demand classes. Operat. Res. 13, 761–778.CrossRefGoogle Scholar
[11] Whitt, W. (1982) Existence of limiting distributions in the GI/G/s queue. Math. Operat. Res. 7, 88–94.CrossRefGoogle Scholar
[12] Wolff, R. (1977) An upper bound for multi-channel queues. J. Appl. Prob. 14, 884–888.Google Scholar
[13] Wolff, R. (1984) Conditions for finite ladder height and delay moments. Operat. Res. Google Scholar