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Waiting time and workload in queues with periodic Poisson input

Published online by Cambridge University Press:  14 July 2016

Austin J. Lemoine
Austin J. Lemoine*
Affiliation:
Ford Aerospace Corporation, San Jose, California
*
∗ Postal address: 1020 Guinda Street, Palo Alto, CA 94301, USA.
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Abstract

This paper develops moment formulas for asymptotic workload and waiting time in a single-server queue with periodic Poisson input and general service distribution. These formulas involve the corresponding moments of waiting-time (workload) for the M/G/1 system with the same average arrival rate and service distribution. In certain cases, all the terms in the formulas can be computed exactly, including moments of workload at each ‘time of day.' The approach makes use of an asymptotic version of the Takács [12] integro-differential equation, together with representation results of Harrison and Lemoine [3] and Lemoine [6].

Keywords

SINGLE-SERVER QUEUE WORKLOAD AT EACH TIME OF DAYMOMENTS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 26 , Issue 2 , June 1989 , pp. 390 - 397
Copyright
Copyright © Applied Probability Trust 1989 

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Footnotes

This research was supported in part by Air Force Office of Scientific Research Contract F49620-86-C-0022.

References

[1] Asmussen, S. (1987) Applied Probability and Queues. Wiley, Chichester.Google Scholar
[2] Asmussen, S. and Thorisson, H. (1987) A Markov chain approach to periodic queues. J. Appl. Prob. 24, 215–225.Google Scholar
[3] Harrison, J. M. and Lemoine, A. J. (1977) Limit theorems for periodic queues. J. Appl. Prob. 14, 566–576.Google Scholar
[4] Heyman, D. P. (1982) On Ross's conjecture about queues with non-stationary Poisson arrivals. J. Appl. Prob. 19, 245–249.Google Scholar
[5] Heyman, D. P. and Whitt, W. (1984) The asymptotic behavior of queues with time varying arrival rate. J. Appl. Prob. 21, 143–156.Google Scholar
[6] Lemoine, A. J. (1981) On queues with periodic Poisson input. J. Appl. Prob. 18, 889–900.Google Scholar
[7] Rolski, T. (1981a) Queues with non-stationary input stream: Ross's conjecture. Adv. Appl. Prob. 13, 603–618.Google Scholar
[8] Rolski, T. (1981b) Stationary Random Processes Associated with Point Processes. Lecture Notes in Statistics 5. Springer-Verlag, Berlin.Google Scholar
[9] Rolski, T. (1984) Comparison theorems for queues with dependent inter-arrival times. In Modeling and Performance Evaluation Methodology, ed. Baccelli, F. and Fayolle, G., Lecture Notes in Control and Information Sciences 60. Springer-Verlag, Berlin, pp. 42–67.Google Scholar
[10] Rolski, T. (1986) Upper bounds for single server queues with doubly stochastic Poisson arrivals. Math. Operat. Res. 11, 442–450.Google Scholar
[11] Rolski, T. (1987) Approximation of periodic queues. Adv. Appl. Prob. 19, 691–707.Google Scholar
[12] Takács, L. (1955) Investigation of waiting time problems by reduction to Markov processes. Acta Math. Acad. Sci. Hung 6, 101–129.Google Scholar