Linear Retrial Queue With Additional Service And Server Breakdown

This paper studies three kinds of queuing systems with linear retrial policy and server breakdown. They are as follows:(1) M/G/1 linear retrial queuing model with second optional service and server breakdown; (2) M/G/1 linear retrial queuing model with second optional service and delay time, in which server breakdown can only occur in the first phase of service; (3)Mξ/G/1 linear retrial queuing model with second optional service and Bernoulli vacations, in which server breakdown can only occur in the second phase of service. We carry out an extensive analysis of these models, including analysis of system steady state condition, generating functions of the number of customers in the orbit and the number of customers in the system, LST of the sojourn time of a customer in the service counter.In these models, we first obtain the existence condition of the steady state system, get the LST of the sojourn time of a customer in the service counter, calculate the average sojourn time of a customer in the service counter. Then, we use the theory of Markov process and the method of supplementary variable to establish the balance equations of steady-state system, get the generating function of the orbit size in each server’s state. In model (1), we introduce the concept of linear retrial policy, get the generating functions of the number of customers in the orbit and the number of customers in the system; model (2) gets the generating functions of the number of customers in the orbit and the number of customers in the system; in case of a batch of arrival, we get the generating function of the number of customers in the orbit in model (3).