An Algorithmic Solution for the Stationary Distribution of M/M/c/K Retrial Queue

We present an algorithmic solution for the stationary distribution of M/M/c/K retrial queue which consists of an orbit with infinite capacity and a service facility that has c exponential servers and waiting space of size K− c. The behavior of queue length process in the retrial queue is described by level dependent quasi-birth-and-death (LDQBD) process due to repeated attempts. The algorithm is based on the generalized truncation method (GTM) proposed by Nuets and Rao [9] which is use of the level independent QBD process except the first N levels as an approximation of the original LDQBD process and the truncation level N is enlarged until the satisfactory solution is obtained. As the authors indicated, the method in Nuets and Rao [9] may not perform very well when the system is highly congested. Main features of our algorithm are to develop a very simple and effective method for deriving inverse of the matrices in the diagonal blocks and to provide the stable and efficient ways for computing the rate matrices and the boundary probability vectors. Our approach can overcome drawbacks of the algorithms in Nuets and Rao [9] and can be applied not only to the system with very large number s of servers and very large size K− s of waiting space but also to the highly congested system.