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The total waiting time in a busy period of a stable single-server queue, I.

Published online by Cambridge University Press:  14 July 2016

D. J. Daley
D. J. Daley*
Affiliation:
The Johns Hopkins University, Baltimore, Maryland
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Extract

A quantity of particular interest in the study of (road) traffic jams is the total waiting time X of all vehicles involved in a given hold-up (Gaver (1969): see note following (2.3) below and the first paragraph of Section 5). With certain assumptions on the process this random variable X is the same as the sum of waiting times of customers in a busy period of a GI/G/1 queueing system, and it is the object of this paper and its sequel to study the random variable in the queueing theory context.

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 550 - 564
Copyright
Copyright © Applied Probability Trust 

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References

Anscombe, F. J. (1952) Large-sample theory of sequential estimation. Proc. Camb. Phil. Soc. 48, 600–607.Google Scholar
Daley, D. J. and Jacobs, D. R. Jr. (1969) The total waiting time in a busy period of a stable single-server queue, II. J. Appl. Prob. 6, 565–572.Google Scholar
Darroch, J., Newell, G. and Morris, R. (1964) Queues for a vehicle actuated traffic light. Operat. Res. 12, 882–895.Google Scholar
Gaver, D. P. (1969) Highway delays resulting from flow-stopping incidents. J. Appl. Prob. 6, 137–153.Google Scholar
Gleser, L. J. (1965) On the asymptotic theory of fixed-size sequential confidence bounds for linear regression parameters. Ann. Math. Statist. 36, 463–467.Google Scholar
Heyde, C. C. (1966) Some renewal theorems with application to a first passage problem. Ann. Math. Statist. 37, 699–710.CrossRefGoogle Scholar
Heyde, C. C. (1967) Asymptotic renewal results for a natural generalization of classical renewal theorems. J. R. Statist. Soc. B 29, 141–150.Google Scholar
LoèVe, M. (1963) Probability Theory. Van Nostrand, Princeton.Google Scholar
Slater, L. J. (1966) Generalized Hypergeometric Functions. Cambridge University Press, Cambridge.Google Scholar
Widder, D. V. (1941) The Laplace Transform. Princeton University Press, Princeton.Google Scholar