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Weak convergence in an appointment system

Published online by Cambridge University Press:  14 July 2016

C. W. Anderson
C. W. Anderson*
Affiliation:
Birkbeck College, London
*
∗Now at the University of Sheffield.
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Abstract

It is assumed that customers at a service facility have appointments at times 0,1,2, … for which they may be unpunctual by random amounts or may never arrive at all. A weak convergence theorem is proved for the process which counts the number of arrivals. This makes it possible to carry over the results of Iglehart and Whitt (1970a) to obtain heavy traffic functional limit theorems for queues with arrivals by appointment.

Keywords

WEAK CONVERGENCEAPPOINTMENT SYSTEMQUEUE WITH APPOINTMENTSSCHEDULED ARRIVALSHEAVY TRAFFIC LIMIT THEOREMCOUNTING PROCESSQUEUE LENGTH
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 188 - 194
Copyright
Copyright © Applied Probability Trust 1975 

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References

Billingsley, P. (1968) Convergence of Probability Measures. John Wiley and Sons, New York.Google Scholar
Iglehart, D. L. (1973) Weak convergence in queueing theory. Adv. Appl. Prob. 5, 570–594.CrossRefGoogle Scholar
Iglehart, D. L. and Whitt, W. (1970a) Multiple channel queues in heavy traffic, I. Adv. Appl. Prob. 2, 150–177.CrossRefGoogle Scholar
Iglehart, D. L. and Whitt, W. (1970b) Multiple channel queues in heavy traffic, II: sequences, networks and batches. Adv. Appl. Prob. 2, 355–369.CrossRefGoogle Scholar