Title: A Markovian two server queue with state dependent hybrid service discipline

Authors: R. Kalyanaraman; B. Anurathi

Addresses: Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India ' Department of Mathematics, Annamalai University, Annamalai Nagar, Tamil Nadu, India

Abstract: A Markovian two server model is constructed by assuming a new concept. The concept is that upto the service of N customers, the two servers act as homogeneous servers after which the servers act like heterogeneous servers. In practice, in particular, if the servers are human beings, they cannot serve in the same spirit till the end of the busy period. These practical situations lead to study of queues with heterogeneous servers. This model is analysed in steady state by deriving the difference equations and applying the recursive concept for solution. For this model the waiting time distribution and some system performance measures are obtained, particular cases are derived. The practical applicability of the model is tested by presenting some numerical illustrations. A cost model is developed by defining the total expected cost function and also sensitivity analysis is carried out to investigate the effect of system parameters on the expected cost function.

Keywords: two server queue; homogeneous server; heterogeneous server; performance measures.

DOI: 10.1504/IJMOR.2025.147860

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.3, pp.413 - 434

Received: 26 Jul 2023
Accepted: 01 Aug 2023
Published online: 05 Aug 2025 *

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