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Computation of Queue Size Distribution for a General Network of Exponential Server Queues

IP.com Disclosure Number: IPCOM000081723D
Original Publication Date: 1974-Jul-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 2 page(s) / 43K

Publishing Venue

IBM

Related People

Kobayashi, H: AUTHOR [+2]

Abstract

In the publication of H. Kobayashi and M. Reiser, "Recursive Algorithms for a General Network of Exponential Server Queues", IBM Technical Disclosure Bulletin, Vol. 16, No. 3, August 1973, pp 705-714, there are described summation algorithms which enable an efficient computation of the average queue size in a general network of exponential server queues, whose solution is found in the publication of J. R. Jackson, Management Sci., 10, 1963. In this connection, the computational expression for obtaining average values of all N servers is (N+1)N O(K/2/). where K is an upper bound on the number of customers.

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Computation of Queue Size Distribution for a General Network of Exponential Server Queues

In the publication of H. Kobayashi and M. Reiser,

"Recursive Algorithms for a General Network of Exponential Server Queues", IBM Technical Disclosure Bulletin, Vol. 16, No. 3, August 1973, pp 705-714, there are described summation algorithms which enable an efficient computation of the average queue size in a general network of exponential server queues, whose solution is found in the publication of J. R. Jackson, Management Sci., 10, 1963. In this connection, the computational expression for obtaining average values of all N servers is (N+1)N O(K/2/). where K is an upper bound on the number of customers.

With the technique described herein, the entire marginal distribution at each of the N servers can be obtained with half of the computations required previously to obtain average values, i.e., only N(N+1) over 2 O(K/2/) operations. It is readily apparent that this is a significant improvement, which appreciably enhances the algorithms set forth in the above-referred to IBM Technical Disclosure Bulletin publication.

There is first discussed herein a short statement of the solution of a relatively general class of queueing networks, this solution being known as "product form solution" and the detailed explanation thereof is to be found in the above-referred to Management Science publication, and in RC 4254, "Recursive Algorithms for General Queuing Networks with Exponential S...