Study of influences of negative arrival for single server retrial queueing system with Coxian phase type service

• Authors: Ayyappan Govindan;Muthu Ganapathi Subramanian;Gopal Sekar
• Venue: Proceedings of the 6th International Conference on Queueing Theory and Network Applications
• Year: 2011

Consider a single server retrial queueing system with negative arrival under Coxian phase type service in which customers arrive in a Poisson process with arrival rate λ. The negative arrival rate follows a Poisson distribution with parameter v. Let k be the number of phases in the service station. The service time follows an exponential distribution with parameter μj for jth phase where j = 1, 2, 3,. . ., k. The services in all phases are independent and only one customer at a time is in the service mechanism. Let qj be the probability that the customer moves from jth phase to (j + 1)th phase and (1 − qj) be probability to leave the system for j = 1, 2, 3,. . ., k −1. If the server is free at the time of a primary call arrival, the arriving call begins to be served in phase 1 immediately by the server. The sequence of phases could be arranged one after the other in a series formation, with the provision of termination after the completion of any phase that is the customer may itself terminate at any stage and leaves the system. If the server is busy, then the arriving customer goes to orbit and becomes a source of repeated calls. The negative arrival plays an important role in this paper and it controls the congestion in the orbit by removing one customer from the orbit and further we assume that it removes the customer from the orbit only if server is busy. Otherwise, the system state does not change. We assume that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Direct Truncation Method. Numerical studies have been done for analysis of mean number of customers in the orbit (MNCO), Truncation level (OCUT), Probabilities of server free, busy for various values of λ, q1, q2, q3,. . ., qk-1, μ1, μ2,. . ., μk, v, k and σ in elaborate manner and also various particular cases of this model have been discussed.