Transient analysis of non-Markovian retrial queueing system with priority services, second optional service, balking, server’s interruptions and a stand by server

This paper deals with the transient analysis of batch arrival retrial queueing system with general retrial times, priority service, balking, second optional service, Bernoulli vacation, extended vacation, breakdown, delayed repair and stand by server. Here we assume that customers arrive in batches according to compound Poisson processes, where the blocked customers either with probability p join priority queue or with complementary probability q leave the service area and enter the retrial group (called orbit) are consider as low priority customers. The service rule for both priority customers follows FCFS discipline and only the customer at the head of the queue or head in orbit is allowed to retry for service. The low priority customers may balk the queue(orbit) with probability qb or may join the orbit with probability q(1 − b). First service is the essential for each customer and second service is the optional, after completion of the essential service the customer have a option for second service with probability r1 or leave the system with probability (1 − r1). The main server has four interruptions, there are after completion of each service the server has a option to go vacation with probaility θ or continue for next service with probability (1 − θ), after completion of a vacation the server has option for extended vacation with probability r or continue to serve the next customer with probability (1 − r). While the server is working with the customer, it may breakdown at any instant and the server will be down for short interval of time. During these interruptions of the main server the stand-by-server serve the customers Further concept of delay time to repair is also introduced. 1Corresponding author. The retrial time, service time for both priority and non-priority customers, vacation time, extended vacation time, delay time and repair time are all follows general(arbitrary) distribution, breakdown time and service time of stand by server follow exponential distribution. Finally, we derive the probability generating function of service time, vacation time, extended vacation time, delay time and repair time and some important performance measures of the model. AMS subject classification: 60K25, 60K30, 90B22.