In this paper, we study a single server Markovian queue with state dependent accessible services, reneging and feedback of customers. The server can accommodate at the most $d$ customers in the service station, after which the new arrivals have to wait in the primary queue of infinite waiting space. All arrivals demand First Essential Service (FES), after completing FES, customers decide to joi...

An M/M/1 queueing system with second optional service and unreliable server is studied. We consider that the server works at different rate rather than being idle during the vacation period. The customers arrive to the system according to Poisson process with state dependent rates depending upon the server’s status. All customers demand the first essential service whereas only some of them dema...

This investigation deals with MX/G/1 queueing model with setup, bulk- arrival, loss-delay and balking. The provision of second optional service apart from essential service by an unreliable server is taken into consideration. We assume that the delay customers join the queue when server is busy whereas loss customers depart from the system. After receiving the essential service, the customers m...

We study an M/G/1 queue with second optional service. Poisson arrivals with mean arrival rate λ (> 0), all demand the first ‘essential’ service, whereas only some of them demand the second ‘optional’ service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B1(v) and that of the second optional service with gene...

This paper examines the Bernoulli admission control policy for the two phase bulk arrival retrial queueing system wherein the customers has the option either to take second phase of service or to leave the system after completing first essential phase of service. In addition, the arrival rate of the customers depends upon the server status. After the service completion of each individual custom...