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Processor-sharing of two parallel lines

Published online by Cambridge University Press:  14 July 2016

Alan G. Konheim ,
Isaac Meilijson  and
Abraham Melkman
Alan G. Konheim*
Affiliation:
IBM T. J. Watson Research Center
Isaac Meilijson*
Affiliation:
Tel-Aviv University
Abraham Melkman*
Affiliation:
Ben Gurion University of the Negev
*
∗Postal address: Mathematical Sciences Department, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
∗∗Postal address: Department of Statistics, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel.
∗∗∗Postal address: Department of Mathematics, Ben Gurion University of the Negev, Beersheba, Israel.
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Abstract

An exponential server splits its service capacity between two independent Poisson streams of customers, unless one queue is empty, in which case the full service capacity is granted to the other queue. We present the stationary joint generating function of the two queue sizes explicitly in the form of an elliptic integral.

Keywords

PROCESSOR SHARINGSTATE-DEPENDENT BIRTH AND DEATH PROCESSESSTATIONARY QUEUE-SIZE JOINT DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 952 - 956
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

Research carried out while the second and third authors were visiting scientists at the IBM T. J. Watson Research Center, Yorktown Heights.

References

[1] Fayolle, G., King, P. J. B. and Mitrani, I. (1982) The solution of certain two-dimensional Markov models. J. Appl. Prob. 19,.CrossRefGoogle Scholar
[2] Rivlin, T. J. (1969) An Introduction to the Approximation of Functions. Blaisdell, Waltham, Ma. Google Scholar