ISSN:
1572-9443
Keywords:
Asymptotics
;
head of the line processor sharing
;
loss probability
;
many queues
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
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 rateλA, 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 rateμn, and splits its capacity equally amongst the jobs at the head of each nonempty queue. The normal traffic casep=λ/μ〈 1 is considered, and it is assumed thatn≫1 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 nδ2≫ 1 and (r+ 1)2≪nδ, and in this caseL ∼r!/(nδ)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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01153535
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