Applications of Entropy Measures in Field of Queuing Theory

Authors: R.K.Tuli

Abstract:

In the present communication, we have studied different variations in the entropy measures in the different states of queueing processes. In case of steady state queuing process, it has been shown that as the arrival rate increases, the uncertainty increases whereas in the case of non-steady birth-death process, it is shown that the uncertainty varies differently. In this pattern, it first increases and attains its maximum value and then with the passage of time, it decreases and attains its minimum value.

Keywords: Entropy, Birth-death process, M/G/1 system, G/M/1system, Steady state, Non-steady state

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328058

References:

[1] Affendi, M.A.El. and Kouvatsos, D.D. (1983): "A maximum entropy analysis of the M/G/1 and G/M/1 queueing systems at equilibrium", Acta Informatica, 19, 339-355.
[2] Guiasu, S. (1986): "Maximum entropy condition in queueing theory", Journal of the Operational Research Society, 37, 293-301.
[3] Kapur, J. N. (1986): "Four families of measures of entropy", Indian Journal of Pure and Applied Mathematics, 17, 429-449.
[4] Kapur, J. N. (1995): "Measures of Information and Their Applications", Wiley Eastern, New York.
[5] Medhi, J. M. (1982): "Stochastic Processes", Wiley Eastern, New Delhi.
[6] Nanda, A. K. and Paul, P. (2006): "Some results on generalized residual entropy", Information Sciences, 176, 27-47.
[7] Prabhakar, B. and Gallager, R. (2003): "Entropy and the timing capacity of discrete queues", IEEE Transactions on Information Theory, 49, 357- 370.
[8] Rathie, P. N. (1971): "A generalization of the non-additive measures of uncertainty and information", Kybernetika, 76, 125-132.
[9] Rathie, P. N. and Taneja, I. J. (1991): "Unified (r-s) entropy and its bivariate measure", Information Sciences, 54, 23-39.
[10] Rao, M.C., Yunmei, V.B.C. and Wang, F. (2004): "Commulative residual entropy: a new measure of Information", IEEE Transactions on Information Theory, 50, 1220-1228.
[11] Renyi, A. (1961): "On measures of entropy and information", Proceedings 4th Berkeley Symposium on Mathematical Statistics and Probability, 1, 547-561.
[12] Shannon, C. E. (1948): "A mathematical theory of communication", Bell System Technical Journal, 27, 379-423, 623-659.
[13] Sharma, B. D. and Mittal, D. P. (1975): "New non-additive measures of entropy for a discrete probability distributions", Journal of Mathematical Sciences, 10, 28- 40.