Transient Solution of an M/M/1 Retrial Queue with Reneging from Orbit

Authors

A. Azhagappan, St. Anne’s College of Engineering and Technology, Panruti
E. Veeramani, St. Anne’s College of Engineering and Technology, Panruti
W. Monica, St. Anne’s College of Engineering and Technology, Panruti
K. Sonabharathi, St. Anne’s College of Engineering and Technology, Panruti

Abstract

In this paper, the transient behavior of an M/M/1 retrial queueing model is analyzed where the customers in the orbit possess the reneging behavior. There is no waiting room in the system for the arrivals. If the server is not free when the occurrence of an arrival, the arriving customer moves to the waiting group, known as orbit and retries for his service. If the server is idle when an arrival occurs (either coming from outside the queueing system or from the waiting group), the arrival immediately gets the service and leaves the system. Each individual customer in the orbit, retrying for his service, becomes impatient and starts reneging from the orbit. Here the reneging of customers is due to the long wait in the orbit. Using continued fractions, the transient probabilities of orbit size for this model are derived explicitly. Average and variance of orbit size at time t are also obtained. Further, numerical illustrations of performance measures are done to analyze the effect of parameters.

Recommended Citation

Azhagappan, A.; Veeramani, E.; Monica, W.; and Sonabharathi, K. (2018). Transient Solution of an M/M/1 Retrial Queue with Reneging from Orbit, Applications and Applied Mathematics: An International Journal (AAM), Vol. 13, Iss. 2, Article 4.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/4