Queueing System with Potential for Recruiting Secondary Servers

Srinivas R. Chakravarthy, Alexander N. Dudin (), Sergey A. Dudin and Olga S. Dudina
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Srinivas R. Chakravarthy: Department of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI 48504, USA
Alexander N. Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Sergey A. Dudin: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
Olga S. Dudina: Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus

Mathematics, 2023, vol. 11, issue 3, 1-24

Abstract: In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process ( MAP ). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD -type queue. However, one can also study this model as a GI / M /1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented.

Keywords: MAP; QBD process; GI / M /1-queue; computational probability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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