• MULTI SERVER RETRIAL QUEUEING SYSTEM WITH CHANNEL TRANSFER UNDER UNRELIABLE SERVERS

Abstract

Consider a Multi server Retrial queueing system with channel transfer under unreliable servers in which arrival rate follows a Poisson distribution with parameter λ and service time follows an exponential distribution with parameter µ. Let c be the number of servers in the system. The breakdown of service follows an exponential distribution with parameter α and repair of service follows an exponential distribution with parameter β. If any one of the server 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 break down 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 σ. 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. If there is breakdown in service for a customer then the server goes to the state of breakdown and this customer will be transfer to a next server who is idle in the system and suppose if all servers are busy during that time then this customer will be moved into a waiting space in front of the system with the assumption that the maximum number of waiting spaces is equal to the number of servers. 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, Mean number of busy servers, Mean number of servers in breakdown, Truncation level and various system measures.