Article Information  
Transient Analysis of Hysteresis Queueing Model Using Matrix Geometric Method

Keywords: Hysteresis, Runge-Kutta, Threshold, Transient, Markov Distribution.

Mehran University Research Journal of Engineering & Technology

Volume 30 ,  Issue 4

Wajiha  Shah , Syed Asif Ali  Shah , Faisal Karim Shaikh ,

References
1. Bini, D.A., and Meini, B.,"On the Solution of a Nonlinear Matrix Equation Arising in Queueing Problems", SIAM Journal Matrix Analysis. Applied, Volume 17, pp. 906-926, 1996.
2. Ritter, M., "Wetwork Buffer Requirements of the Rate Based Control Mechanism for ABR Services", IEEE INFOCOM, March 1996.
3. Baker and Philips, C., "Numerical Solution of Non-Linear Problems", Clarendon Press, Oxford, 1981.
4. Akar, N., Oguz, N., and Sohraby, K., "A Novel Computational Method for Solving Finite QBD Processes", Communication in Statistic, Statistic Model, March, 2000.
5. Bermann, A., and Plemmons, R., "Nonnegative Matrices in Mathematical Sciences", Academic Press, New York, 1979.
6. Bright, L., and Taylor, P.G., "Equilibrium Distributions for Level-Dependent Quasi-Birth-and-Death Processes", Matrix-Analytic Methods in Stochastic Models, Lecture Notes in Pure and Applied Mathematics, Volume 183, pp. 359-375, 1997.
7. Lenin, R.B., and Parthasarathy, P.R., "Transient Analysis in Discrete Time of Markovian Queues with Quadratic Rates", Southwest Journal of Pure and Applied Mathematics, Volume 3, pp. 1-15, 2000.
8. Bini, D.A., Latouche, G., and Meini, B., "Numerical Methods for Structured Markov Chains", Oxford University Press, 2005.
9. Gun, L., and Makowski, A., "Matrix Geoemtric Solution for Finite Capacity Queues with Phase-Type Distributions", Proceedings of Twelfth IFIP WG 7.3 International Symposium on Computer Performance Modelling, Brussels, Belgium, December 7-9, 1987.
10. Guo, C.H., "On the Numerical Solution of a Nonlinear Matrix Equation in Markov Chain", Linear Alg. Appl., pp. 175 -186, 1999.
11. Tadi, L., Benkhauf, L., Aggoun, L., "A Hysteresis Queueing System with Random Server Capacity", Computers and Mathematics with Applications, Volume 38, pp. 51-61, 1999.
12. Thiagarajan, L., and Chakraverthy, S.R., "A Stochastic Model for a Hysteresis Based Priority Queueing Strategy for ATM Networks with Batch Arrival Process-Theory", Computer and Communication, 1998.
13. Jain, M., and Piya, K., "Performance Analysis of Distributed Video-on-Demand (VOD) System", International Journal of Information and Communication Technology, Volume 2, No. 3, pp. 260-278, 2010.
14. Shah, W., "Performance Modelling of Queueing Systems Using Matrix Geometric Method", Ph.D. Thesis, Faculty of Electrical Engineering and Information Technology, Vienna University of Technology, Wien, Austria, April, 2010.