Performance analysis of an unreliable M/G/1 retrial queue with two-way communication

Muthukrishnan Senthil Kumar (), Aresh Dadlani () and Kiseon Kim ()
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Muthukrishnan Senthil Kumar: PSG College of Technology
Aresh Dadlani: Nazarbayev University
Kiseon Kim: Gwangju Institute of Science and Technology

Operational Research, 2020, vol. 20, issue 4, No 14, 2267-2280

Abstract: 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; 60K25; 62N05 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s12351-018-0417-y

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