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Sengupta's invariant relationship and its application to waiting time inference

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Hiroshi Toyoizumi
Hiroshi Toyoizumi*
Affiliation:
NTT Telecommunication Networks Laboratories
*
∗Postal address: NTT Multimedia Networks Laboratories, 3–9–11, Midori-cho, Musashino-shi, Tokyo 180, Japan. E-mail: toyo@hashi.tn1.ntt.jp
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Abstract

This paper presents a new proof of Sengupta's invariant relationship between virtual waiting time and attained sojourn time and its application to estimating the virtual waiting time distribution by counting the number of arrivals and departures of a G/G/1 FIFO queue. Since this relationship does not require any parametric assumptions, our method is non-parametric. This method is expected to have applications, such as call processing in communication switching systems, particularly when the arrival or service process is unknown.

Keywords

G/G/1 QUEUESENGUPTA'S INVARIANT RELATIONSHIPVIRTUAL WAITING TIMEATTAINED SOJOURN TIMECOMMUNICATION SWITCHING SYSTEMQUEUE INFERENCE

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G55: Point processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 795 - 799
Copyright
Copyright © Applied Probability Trust 1997 

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References

[1] Bertsimas, D. J. and Servi, L. D. (1992) Deducing queueing from transactional data: the queue inference engine revisited. Operat. Res. 40, 217–228.Google Scholar
[2] Brandit, A., Franken, P. and Lisek, B. (1990) Stationary Stochastic Models. Wiley, New York.Google Scholar
[3] Bremaud, P. (1991) An elementary proof of Sengupta's invariant relation and a remark on Miyazawa's conservation principle. J. Appl. Prob. 28, 950–954.Google Scholar
[4] Cohen, J. W. (1991) On the attained waiting time. Adv. Appl. Prob. 23, 660–661.Google Scholar
[5] Daley, D. J. and Servi, L. D. (1992) Exploiting Markov chains to infer queue length from transactional data. J. Appl. Prob. 29, 713–832.Google Scholar
[6] Daley, D. J. and Servi, L. D. (1997) Estimating waiting times from transactional data. ORSA J. Comput. To appear.Google Scholar
[7] Larson, R. C. (1990) The queue inference engine: deducing queue statistics from transactional data. Management Sci. 36, 586–601.Google Scholar
[8] Machihara, F. and Takahashi, Y. (1997) Invariance relationship for a G/G/1 queue with state dependent service time. Preprint.Google Scholar
[9] Miyazawa, M. (1979) A formed approach to queueing processes in the steady state and their applications. J. Appl. Prob. 16, 332–346.Google Scholar
[10] Sakasegawa, H. and Wolff, R. (1990) The equality of the virtual delay and attained waiting time distribution. Adv. Appl. Prob. 22, 257–259.Google Scholar
[11] Sengupta, B. (1989) An invariance relationship for the G/G/1 queue. Adv. Appl. Prob. 21, 956–957.Google Scholar
[12] Takahashi, Y. and Machihara, F. (1997) A note on the attained waiting time in a batch arrival single-server queue with balking. Preprint.Google Scholar
[13] Toyoizumi, H. (1992) Evaluating mean sojourn time estimates for the M/M/1 queue. Comput. Math. Appl. 24, 7–15.Google Scholar
[14] Toyoizumi, H. (1993) A simple method of estimating mean delay by counting arrivals and departures. In Proc. IEEE INFOCOM '93. pp. 829–834.CrossRefGoogle Scholar
[15] Yamazaki, G. and Miyazawa, M. (1991) The equality of the work load and total attained waiting time on average. J. Appl. Prob. 28, 238–244.Google Scholar