M/M/c Retrial Queueing System with Breakdown and Repair of Services

The aim of this research was to study the unreliable nature of the servers under Retrial queueing system. These kinds of models are readily available in real life namely booking in Railway system, Call centres etc., so the analysis of such real models is most important. Consider a multi server retrial queueing system with breakdown and repair of services in which arrival rate follows a Poisson distribution with parameter ? and service time follows an exponential distribution with parameter . Let c be the number of servers in the system. The breakdown of service follows an exponential distribution with parameter a and repair of service follows an exponential distribution with parameter . If any one of the servers is free at the time of a primary call arrival, the arriving call begins to be served immediately by one of the free servers and customer leaves the system after service completion. Otherwise, if c servers are busy or c servers are in breakdown then the arriving customer goes to orbit and becomes a source of repeated calls. The pool of sources of repeated calls may be viewed as a sort of queue. Every such source produces a poisson process of repeated calls with intensity s. If an incoming repeated call finds any one of the servers is free, it is served and leaves the system after service, while the source which produced this repeated call disappears. The access from the orbit to the service facility follows the classical retrial policy. This model is solved by using direct truncation method. Numerical study have been done for analysis of Mean Number of Customers in the Orbit (MNCO), Mean Number of Busy Servers (MNBS), Mean Number of Servers in Breakdown (MNSB) and various system measures.