The M/G/1 retrial queue: New descriptors of the customer’s behavior

Abstract

We consider queuing systems where customers are not allowed to queue; instead of that they make repeated attempts, or retrials, in order to enter service after some time. The performance of telephone systems and communication networks modelled as retrial queues differs from standard waiting lines because typically the retrial group is an invisible queue which cannot be observed. As a result, the original flow of primary arrivals and the flow of repeated attempts become undistinguished. Our aim in this paper is to consider some aspects of this problem. Thus, we focus on the main retrial model of M/G/1 type and investigate the distribution of the successful and blocked events made by the primary customers and the retrial customers.

Connect Time Limits and Performance Measures in a Dial-Up Modem Pool System

“…The research on retrial queues is fairly extensive and extremely rigorous in mathematical analysis. A complete literature review of the field is beyond the scope of this study, and would, to a great extent, duplicate the work in previous surveys (see Amador & Artalejo, 2009;Artalejo & Gómez-Corral, 2008;Falin, 1990;Kernane, 2008;and Yang & Templeton, 1987).…”

Two-Facility Location Problem with Infinite Retrial Queue

“…A retrial queue under Bernoulli vacation schedules is discussed in Ke and (2009) where they consider a batch arrival retrial queue with general retrial times. New descriptors of the customer's behavior in a M G / / 1 retrial queue is analyzed by Amador and Artalejo (2009) where they investigate the distribution of the successful retrials, the successful arrivals and the blocked retrials. Moreover, Kumar et al (2009) analyze a multi-server feedback retrial queueing system with finite waiting position as a quasi-birth-and-death (QBD) process and investigate the necessary and sufficient condition for stability of the system.…”