Multiserver call center retrial queue under Bernoulli vacation schedule with two-way communication and orbital search

B. Krishna Kumar (), R. Sankar, R. Navaneetha Krishnan and R. Rukmani
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B. Krishna Kumar: Vellore Institute of Technology
R. Sankar: Anna University
R. Navaneetha Krishnan: Anna University
R. Rukmani: Pachaiyappa’s College

Telecommunication Systems: Modelling, Analysis, Design and Management, 2023, vol. 84, issue 1, No 2, 23-51

Abstract: Abstract This article deals with the steady-state behaviour of a finite orbit capacity multiserver call center retrial queue with Bernoulli vacation schedule in which the servers not only accept incoming calls but also make outgoing calls after some exponentially distributed idle time. In addition, upon each service completion of the outgoing call, the servers search for orbital calls, if any, with some probability or take a single vacation with the complementary probability. Search time is assumed to be negligible. Under the Markovian assumptions, the steady-state joint probability distribution of the number of incoming calls in the orbit and the status of the servers is determined by adopting matrix analytic methods. The three types of retrials, namely ideal retrial, vain retrial, and successful retrial for incoming calls are also discussed. The expressions for the Laplace–Stieltjes transforms (LSTs) of the busy period length of the system and the waiting time distribution of a tagged incoming call in the orbit are obtained. Moreover, the probability generating function for the number of retrials made by an incoming call is investigated. Some vital performance characteristics of the system and various moments of quantities of interest are studied. Finally, extensive numerical illustrations are presented to show the impact of the system parameters on the selected performance measures.

Keywords: Retrials; Two-way communication; Orbital search; First-step analysis; Busy period; Waiting time; Number of retrials (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11235-023-01025-1

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