Journal of Applied Science and Engineering

Published by Tamkang University Press

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S. N. Singh1 and S. B. Tiwari This email address is being protected from spambots. You need JavaScript enabled to view it.1

1Department of Mathematics & Statistics, Dr. R. M. L. Avadh University, Faizabad-224001 (U.P.), India


 

Received: July 14, 2011
Accepted: September 10, 2012
Publication Date: March 1, 2013

Download Citation: ||https://doi.org/10.6180/jase.2013.16.1.13  


ABSTRACT


Present work deals with the study of queueing system by maximizing the generalized entropy subject to some constraints. Generalized entropy is simply applied to obtain the widest probabilistic model subject only to constraints expressed by mean value as the mean arrival rate, the mean service rate, or the mean number of customers in the system. Some interesting theorems in queueing theory dealing with maximum entropy condition have been proved when the queueing system is in a steady state condition and if the requirements of a birth and death stochastic process are satisfied. Also, some results obtained by Guiasu and Jain can be derived as particular case of the present work.


Keywords: Generalized Entropy, Queueing System, Euler Equation, Exponential Distribution, Information Theory


REFERENCES


  1. [1] Shannon, C. E., “A Mathematical Theory of Communication,” Bell System Technical Journal, Vol. 27, pp. 379423 (1948).
  2. [2] Jaynes, E. T., “Prior Probabilities,” IEEE Trans Systems Sci Cybern, Vol. 4, pp. 227241 (1968).
  3. [3] Guiasu, S., “Maximum Entropy Condition in Queueing Theory,” J Opl Res Soc, Vol. 37, No. 3, pp. 293301 (1986).
  4. [4] Chaudhry, M. L. and Templeton, J. G. C., A First Course in Bulk Queues, New York, John Wiley & Sons (1988).
  5. [5] Wang, K. H., Chan, M. C. and Ke, J. C., “Maximum Entropy Analysis of the M[x]/M/1 Queueing System with Multiple Vacations and Server Breakdowns,” Computers & Industrial Engineering, Vol. 52, pp. 192202 (2007).
  6. [6] Singh, S. N., Jaiswal, J. and Tiwari, S. B., “Maximum Entropy Condition in Queueing System M/M/1: / FCFS,” Nat Acad Sci Lett, Vol. 30, No. 7 & 8, pp. 237242 (2007).
  7. [7] Borzadaran, G. R. M., “A Note on Maximum Entropy in Queueing Problems,” Economic Quality Control, Vol. 24, No. 2, pp. 263267 (2009).
  8. [8] Guan, L., Awan, I. U., Phillips, I., Grigg, A. and Dargie, W., “Performance Analysis of a ThresholdBased Discrete-Time Queue Using Maximum Entropy,” Simulation Modelling Practice and Theory, Vol. 17, pp. 558568 (2009).
  9. [9] Jain, M., “A Maximum Entropy Analysis for Mx /G/1 Queueing System at Equilibrium,” JKAU Eng Sci, Vol. 10, No. 1, pp. 5765 (1418 AH/1998 AD).
  10. [10] Mathai, A. M. and Haubold, H. J., “Pathway Model, Tsallis Statistics, Superstatistics and a Generalized Measure of Entropy,” Physica A, Vol. 375, pp. 110 122 (2006).