Transient Solution of a Two-Heterogeneous Servers’ Queuing System with Retention of Reneging Customers
- 54 Downloads
In this paper, the transient solution of a Markovian queuing system with two heterogeneous servers and retention of reneging customers is obtained. The explicit transient probabilities of system size are obtained using probability generating function technique. The corresponding steady-state probabilities are also derived. Further, the time-dependent mean and variance are obtained. Finally, a numerical example is provided to study the behavior of the system. The numerical results show that the heterogeneous system performs better than its homogeneous counterpart.
KeywordsRetention of reneging customers Heterogeneous servers Probability generating function Transient solution Steady-state probabilities
Mathematics Subject Classification90B22
The authors would like to thank the anonymous referees for their constructive comments which helped to bring this paper in the current form. One of the authors (Dr. Rakesh Kumar) would like to thank the UGC, New Delhi, India, for financial support given to him for this research work under the Major Research Project vide Letter No. F.-43-434/2014(SR).
- 7.El-Paoumy, M.S., Nabwey, H.A.: The Poissonian queue with balking function, reneging and two heterogeneous servers. Int. J. Basic Appl. Sci. 11(6), 149–152 (2011)Google Scholar
- 8.El-Sherbiny, A.A.: The truncated heterogeneous two-server queue: M/M/2/N with reneging and general balk function. Int. J. Math. Arch. 3, 2745–2754 (2012)Google Scholar
- 17.Madheswari, S.P., Suganthi, P., Josephine, S.A.: Retrial queueing system with retention of reneging customers. Int. J. Pure Appl. Math. 106, 11–20 (2016)Google Scholar
- 23.Yue, D., Yue, W., Yu, J., Tian, R.: A Heterogeneous two-server queueing system with balking and server breakdowns. In: The Eighth International Symposium on Operations Research and Its Applications (ISORA’09) Zhangjiajie, China, 20–22 September 2009, pp. 230–244 (2009)Google Scholar
- 24.Wang, Z., Lei, X.: Study on customer retention under dynamic markets. In: Second International Conference on Networks Security, Wireless Communications and Trusted Computing (NSWCTC), 24–25 April 2010, Wuhan, Hubei, pp. 514–517 (2010)Google Scholar