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A comparison of the stationary distributions of GI/M/c/n and GI/M/c

Published online by Cambridge University Press:  14 July 2016

F. Simonot
F. Simonot*
Affiliation:
ESSTIN
*
∗Postal address: ESSTIN-Parc. R. Bentz, 54500, Vandoeuvre, France. E-mail address: simonofr@esstin.u-nancy.fr
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Abstract

In this note, we compare the arrival and time stationary distributions of the number of customers in the GI/M/c/n and GI/M/c queueing systems as n tends to infinity. We show that earlier results established for GI/M/1/n and GI/M/1 remain true. Namely, it is proved that if the interarrival time c.d.f. H is non lattice with mean value λ−1 and if the traffic intensity is strictly less than one, then the convergence rates in l1norm of the arrival and time stationary distributions of GI/M/c/n to the corresponding stationary distributions of GI/M/c are geometric and are characterized by ω, the unique solution in (0,1) of the equation z = ∫∞0 exp{-μc(1-z)t}dH(t).

Keywords

GI/M/c/nMarkov chainconvergence ratel1 norm
Type
Short Communications
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 510 - 515
Copyright
Copyright © Applied Probability Trust 1998 

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References

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