Calculating equilibrium probabilities for λ(n)/C k /1/N queues
- 28 May 1980
- journal article
- Published by Association for Computing Machinery (ACM) in ACM SIGMETRICS Performance Evaluation Review
- Vol. 9 (2) , 117-125
- https://doi.org/10.1145/1009375.806155
Abstract
Equilibrium state distributions are determined for queues with load-dependent Poisson arrivals and service time distributions representable by Cox's generalized method of stages. The solution is obtained by identifying a birth-death process that has the same equilibrium state distribution as the original queue. Special cases of two-stage (C 2 ) and Erlang-k (E k ) service processes permit particularly efficient algorithms for calculating the load - dependent service rates of the birth-death process corresponding to the original queue. Knowing the parameters of the birth-death process, the equilibrium state probabilities can be calculated straight-forwardly. This technique is particularly useful when subsystems are reduced to flow-equivalent servers representing the complementary network.Keywords
This publication has 2 references indexed in Scilit:
- Solution of Queuing Problems by a Recursive TechniqueIBM Journal of Research and Development, 1975
- A use of complex probabilities in the theory of stochastic processesMathematical Proceedings of the Cambridge Philosophical Society, 1955