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Download file# M/G/k with Exponential Setup

journal contribution

posted on 01.04.2000, 00:00 by Anshul Gandhi, Mor Harchol-BalterIn this paper, we consider the M/G/k queueing system with setup times. This particular queueing
model is common in manufacturing systems, where idle machines are turned off to save on
operating costs, as well as in server farms, where idle servers are turned off to conserve power.
While recent literature has analyzed the M/M/k system with exponential setup times, no closedform
solutions were obtained. We provide the first analytical closed form expressions for the mean
response time, limiting distribution of the system states, as well as the z-transform for the number
of jobs in system for the M/M/k system with exponential setup times. In particular, we prove the
following decomposition property: the mean response time of the M/M/k system with exponential
setup times differs from the mean response time of an M/M/k system without setup times, by a
constant factor, which is the mean of the exponential setup time. Using matrix analytic methods
and simulations, we show that the above decomposition property may also hold for the M/G/k
system with exponential setup times.