Parametric evaluation of uncertainty in Markovian queues

The Shannon entropy was an attempt to quantify the randomness in a model characterized by probability distributions. During the past few years, various generalizations of Shannon entropy have been introduced by various mathematicians and researchers in related fields. Most of these measures contain one, two and sometimes more than two parameters. These parameters help us in analyzing the variation in certain factors that affect a particular system. Since the steady state distribution (long run behavior) of any queue involves a probability function, it would be appropriate to express the uncertainty in any queuing system in terms of Shannon entropy (if possible) or in terms of any generalization it. In this paper we have tried to establish the significance of Renyi’s measure of entropy in the determination of uncertainty in queuing systems. M/M/1/∞ and M/M/1/N models (single sever Markovian queue with infinite capacity and finite capacity) is used as an example.