Head of the line processor sharing for many symmetric queues with finite capacity |
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Authors: | J. A. Morrison |
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Affiliation: | (1) AT&T Bell Laboratories, Room 2C-378,600 Mountain Avenue, 07974 Murray Hill, NJ, USA |
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Abstract: | In this paper the steady-state behavior of many symmetric queues, under the head of the line processor-sharing discipline, is investigated. The arrival process to each of n queues is Poisson, with rateA, and each queue hasr waiting spaces. A job arriving at a full queue is lost. The queues are served by a single exponential server, which has a mean raten, and splits its capacity equally amongst the jobs at the head of each nonempty queue. The normal traffic casep=/< 1 is considered, and it is assumed thatn1 andr= 0(1). A 2-term asymptotic approximation to the loss probabilityL is derived, and it is found thatL = 0(n–r), for fixedp. If6=(1–p)/p 1, then the approximation is valid if n2 1 and (r+ 1)2n, and in this caseL r!/(n)r. Numerical values ofL are obtained forr = 1,2,3,4 and 5,n = 1000,500 and 200, and various values ofp< 1. Very small loss probabilities may be obtained with appropriate values of these parameters. |
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Keywords: | Asymptotics head of the line processor sharing loss probability many queues |
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