Performance analysis of an unreliable M / G /1 retrial queue with two-way communication
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Performance analysis of an unreliable M/G/1 retrial queue with two‑way communication Muthukrishnan Senthil Kumar1 · Aresh Dadlani2 · Kiseon Kim3 Received: 26 December 2017 / Revised: 15 June 2018 / Accepted: 4 August 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an M/G/1 retrial queue is investigated where the single server, subject to active failures, primarily attends incoming calls and directs outgoing calls only when idle. The incoming calls arriving at the server follow a Poisson arrival process, while outgoing calls are made in an exponentially distributed time. On finding the server unavailable (either busy or temporarily broken down), incoming calls intrinsically join the virtual orbit from which they re-attempt for service at exponentially distributed time intervals. The system stability condition along with probability generating functions for the joint queue length distribution of the number of calls in the orbit and the state of the server are derived and evaluated numerically in the context of mean system size, server availability, failure frequency and orbit waiting time. Keywords Retrial queueing system · Server breakdown · Coupled switching · Performance evaluation · Steady-state distribution Mathematics Subject Classification 60K25 · 62N05
* Aresh Dadlani [email protected] Muthukrishnan Senthil Kumar [email protected] Kiseon Kim [email protected] 1
Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore 641‑004, India
2
Department of Electrical and Computer Engineering, School of Engineering, Nazarbayev University, Astana, Kazakhstan 010000
3
School of Electrical Engineering and Computer Science, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea
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1 Introduction Blended call centers have recently evolved as an effective and profitable communication asset in bridging companies and their customers. Unlike conventional call centers, such modern communication systems are capable of managing a mixture of both, inbound and outbound call operations that require instant service (Bhulai and Koole 2003; Aksin et al. 2007). An outgoing call is initiated by the server only when no incoming call is in the system. This feature, commonly referred to as coupled switching or two-way communication, yields higher productivity by reducing the idle time experienced by the serving operator (Artalejo and Phung-Duc 2012; Legros et al. 2017). Moreover, incoming calls that find the server busy enter a virtual orbit and tend to retry for service after some random time (Artalejo and GomezCorral 2008). As a result, in-depth analysis of the influence of retrying customer calls on the dynamics of coupled switching in call centers is of great significance not only to the research co
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