Alternative methods of investigating the time dependent M/G/k queue

Abstract

The time dependent M/G/k queue is studied with the aim of obtaining good numerical approximations and descriptors of system behavior rather than exact closed form solutions. Five models that have been used to investigate this problem are presented: Simulation; first order models: "fluid approxi-mation " and equilibrium analysis; second order models: "diffusion approxi-mation " and Koopman's model. The assumptions used in postulating these models and their consequences are evaluated. The impracticality of direct numerical solution is reviewed. The second order models are investigated in detail. From the diffusion approximation information about the transient behavior of stationary M/G/l queues is obtained. Exact closed form expressions for the transient state probabilities of the stationary M/M/l queue (Morse) are given and the time constants for this system derived. The exact value of the time constant of the M/M/1 system is compared to the corresponding result from the approximat-

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