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Correlation functions in queueing theory

Published online by Cambridge University Press:  14 July 2016

S. K. Srinivasan ,
R. Subramanian  and
R. Vasudevan
S. K. Srinivasan
Affiliation:
Indian Institute of Technology, Madras
R. Subramanian
Affiliation:
Indian Institute of Technology, Madras
R. Vasudevan
Affiliation:
Institute of Mathematical Sciences, Madras
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Abstract

The object of this paper is to study the actual waiting time of a customer in a GI/G/1 queue. This is an important criterion from the viewpoint of both the customers and the efficient functioning of the counter. Suitable point processes in the product space of load and time parameters for any general inter-arrival and service time distributions are defined and integral equations governing the correlation functions are set up. Solutions of these equations are obtained and with the help of these, explicit expressions for the first two moments of the number of customers who have waited for a time longer than w in a given time interval (0, T) are calculated.

Keywords

CORRELATION FUNCTIONSQUEUESPOINT PROCESSESLOADBUSY PERIODIDLE PERIODWAITING TIMEPRODUCT DENSITYMARKOV CHAIN
Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 604 - 616
Copyright
Copyright © Applied Probability Trust 1972 

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