Multiserver retrial Queues with Two Types of nonpersistent Customers

We consider M/M/c/K (K ≥ c ≥ 1) retrial queues with two types of nonpersistent customers, which are motivated from modelling of service systems such as call centers. Arriving customers that see the system fully occupied either join the orbit or abandon receiving service forever. After an exponentially distributed time in the orbit, each customer either abandons the system forever or retries to occupy a server again. For the case of K = c = 1, we present an analytical solution for the generating functions in terms of confluent hypegeometric functions. In the general case, the number of customers in the system and that in the orbit form a level-dependent quasi-birth-anddeath (QBD) process whose structure is sparse. Based on this sparse structure, we develop a numerically stable algorithm to compute the joint stationary distribution. We show that the computational complexity of the algorithm is linear to the capacity of the queue. Furthermore, we present a simple fixed point approximation model for the case where the algorithm is time-consuming. Numerical results show various insights into the system behavior.