AN APPLICATION OF GEGENBAUER POLYNOMIALS IN QUEUING THEORY

[摘要] The symmetric coupled processor model is a queueing system in which a server divides his service capacity between two independent streams of customers, unless one queue is empty, in which case the full capacity is granted to the other queue. Customers demand an exponentially distributed service time with mean mu-1 and their arrivals are determined according to their stream by two independent Poisson processes each with rate A. The symmetric coupled processor model can be represented by a continuous time Markov process X(t):= (X1(t), X2(t)), where X(i)(t) is the number of customers in the ith queue. Let p(m,n)(t) := Pr{X(t) = (m, n)). If rho = 2lambda/mu < 1, the equilibrium probabilities exist and are given by p(m, n) = lim(t--infinity)p(m,n)(t). We prove that the equilibrium probability p(n, n) can be written as p(n, n) = (1 - rho)rho2nSIMGA(k=0)(infinity)a(k)(n)rho(k), where the coefficients a(k)(n) are computed explicitly.

[发布日期] 1993-12-31

[效力级别]  Proceedings Paper

[关键词] QUEUING THEORY;GEGENBAUER POLYNOMIALS;SYMMETRICAL COUPLED PROCESSOR