On Approximating and Bounding GI/M/c Queues,
GEORGE WASHINGTON UNIV WASHINGTON D C PROGRAM IN LOGISTICS
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Approximate steady-state measures of effectiveness and state probabilities for GIMc and approximate bounds on these quantities for GIM1 are developed, requiring only the knowledge of the first two moments of GI. These are based on the ability to approximate and bound the single root, in 0,1, of the generating function equation associated with the GIMc queue. A method for obtaining this root for any GI, and the special cases GI gamma and hyperexponential H are discussed. Approximations to the root using GI gamma or H, where the first two moments of GI are matched to those of gamma and H, are shown empirically to be good when the traffic intensity is at least moderate greater than 0.5.
- Operations Research