AN EFFICIENT METHOD FOR PERFORMANCE ANALYSIS OF BLENDED CALL CENTERS WITH REDIAL

This paper considers a multiserver retrial queue with two-way communication for blended call centers. Primary incoming calls arrive at the servers according to a Poisson process and request an exponentially distributed service time. Incoming calls that find all the servers fully occupied join the orbit and retry to occupy a server again after some random time. A retrial incoming call behaves the same as a primary incoming call. A server not only serves as an incoming call but also makes an outgoing call after some random idle time. We assume that the distribution of the duration of outgoing calls is different from that of incoming calls. Artalejo and Phung-Duc (2012) have extensively studied the single server case and have obtained some preliminary results for the multiserver model. In this paper, we present an extensive analysis for the multiserver model in which, we propose a new formulation by a level-dependent quasi birth-and-death (QBD) process, whose block matrices have some special block structure. Based on a matrix continued fraction approach and a censoring technique, we develop an efficient algorithm utilizing the special structure for computing the stationary distribution. Furthermore, we derive explicit formulae for the mean number of incoming calls and that of outgoing calls in the servers. Through various numerical results, we study the characteristics of the queueing system and find some insights into the optimal outgoing call rate.