Analysis of MAP/PH/c Retrial Queue with Phase Type Retrials – Simulation Approach
In this paper we study a multi-server retrial queueing model in which customers arrive according to a Markovian arrival process (MAP) and the service times are assumed to be of phase type (PH-type). An arriving customer finding all servers busy will enter into a (retrial) orbit of infinite size. The customers in orbit will try to capture a free server after a random amount of time which is assumed to be of PH-type. Thus, every customer in the orbit has his/her own phase type distribution before attempting to get into service. Due to the complexity of the model and lack of attention to such models in the literature, we study this via simulation. After validating our simulated results against known results (both exact and approximation) for some special cases, we illustrate how one can underestimate or overestimate some key system performance measures by incorrectly assuming the retrial times to be exponential.
KeywordsService Time Phase Type Retrial Queue Retrial Model System Performance Measure
Unable to display preview. Download preview PDF.
- 4.Chakravarthy, S.R.: The batch Markovian arrival process: A review and future work. In: Krishnamoorthy, A., et al. (eds.) Advances in Probability Theory and Stochastic Processes, pp. 21–39. Notable Publications Inc., NJ (2001)Google Scholar
- 5.Chakravarthy, S.R.: Markovian Arrival Processes. Wiley Encyclopedia of Operations Research and Management Science (June 15, 2010)Google Scholar
- 9.Kelton, W.D., Sadowski, R.P., Swets, N.B.: Simulation with ARENA, 5th edn. McGraw-Hill, New York (2010)Google Scholar
- 13.Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore (1994 version is Dover Edition)Google Scholar
- 14.Neuts, M.F.: Structured Stochastic Matrices of M/G/1 type and their Applications. Marcel Dekker, NY (1989)Google Scholar
- 15.Neuts, M.F.: Models based on the Markovian arrival process. IEICE Transactions on Communications E75B, 1255–1265 (1992)Google Scholar
- 17.Senthilkumar, M., Sohraby, K., Kim, K.: On a multiserver retrial queue with phase type retrial time. In: Nadarajan, R., et al. (eds.) Mathematical and Computational Models, pp. 65–78. Narosa Publishing House, New Delhi (2012)Google Scholar