A matrix continued fraction approach to multiserver retrial queues

Tuan Phung-Duc, Hiroyuki Masuyama, Shoji Kasahara, Yutaka Takahashi
2011 Annals of Operations Research  
We consider basic M/M/c/c (c ≥ 1) retrial queues where the number of busy servers and that of customers in the orbit form a level-dependent quasi-birth-and-death (QBD) process with a special structure. Based on this structure and a matrix continued fraction approach, we develop an efficient algorithm to compute the joint stationary distribution of the numbers of busy servers and retrial customers. Through numerical experiments, we demonstrate that our algorithm works well even for M/M/c/c
more » ... l queues with large value of c. Keywords Multiserver retrial queue · Level-dependent QBD · Matrix continued fraction · Call center · Resource dimensioning · System planning Mathematics Subject Classification (2000) 68M20 · 90B22 · 60K25 Introduction This paper considers M/M/c/c retrial queues, in which if an arriving customer finds an idle server, he starts to be served, otherwise he moves to a virtual orbit, stays there for an exponentially distributed time and retries to get service. Retrial queues arise in various systems such as telecommunications, computer networks and call centers [1, 6, 7, 21, 22, 27, 31] . Aguir et al. [1] investigate the impact of retrials on the performance of call centers, using a fluid approximation. Artalejo and Pla [6] further evaluate the effect of customer retrials on operations of telecommunication systems, by a retrial queue with
doi:10.1007/s10479-011-0840-4 fatcat:xawxu2bxrrgqjlmcgqnzqev3ca