Multiserver Queue with Guard Channel for Priority and Retrial Customers

Abstract

This paper considers a retrial queueing model where a group of guard channels is reserved for priority and retrial customers. Priority and normal customers arrive at the system according to two distinct Poisson processes. Priority customers are accepted if there is an idle channel upon arrival while normal customers are accepted if and only if the number of idle channels is larger than the number of guard channels. Blocked customers (priority or normal) join a virtual orbit and repeat their attempts in a later time. Customers from the orbit (retrial customers) are accepted if there is an idle channel available upon arrival. We formulate the queueing system using a level dependent quasi-birth-and-death (QBD) process. We obtain a Taylor series expansion for the nonzero elements of the rate matrices of the level dependent QBD process. Using the expansion results, we obtain an asymptotic upper bound for the joint stationary distribution of the number of busy channels and that of customers in the orbit. Furthermore, we develop an efficient numerical algorithm to calculate the joint stationary distribution.

Retrial Queueing Models: A Survey on Theory and Applications

“…It should be noted only the last row of R n is non-zero in these models. Kajiwara and Phung-Duc [72] further extend the analysis of Phung-Duc [106] to an M/M/c/c retrial model with one guard channel for priority and retrial customers where the last two rows of the rate matrix R n are non-zero. Kim et al [76,77] refine the results of [86] by a generating function approach.…”