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Maximum Entropy Condition in Queueing Theory
The Journal of the Operational Research Society
Vol. 37, No. 3 (Mar., 1986), pp. 293-301
Stable URL: http://www.jstor.org/stable/2582209
Page Count: 9
You can always find the topics here!Topics: Probability distributions, Entropy, Customers, Queueing theory, Steady state theory, Operations research, Information theory, Mathematical moments, Probabilistic modeling, Information economics
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The main results in queueing theory are obtained when the queueing system is in a steady-state condition and if the requirements of a birth-and-death stochastic process are satisfied. The aim of this paper is to obtain a probabilistic model when the queueing system is in a maximum entropy condition. For applying the entropic approach, the only information required is represented by mean values (mean arrival rates, mean service rates, the mean number of customers in the system). For some one-server queueing systems, when the expected number of customers is given, the maximum entropy condition gives the same probability distribution of the possible states of the system as the birth-and-death process applied to an M/M/1 system in a steady-state condition. For other queueing systems, as M/G/1 for instance, the entropic approach gives a simple probability distribution of possible states, while no close expression for such a probability distribution is known in the general framework of a birth-and-death process.
The Journal of the Operational Research Society © 1986 Operational Research Society