Analysis of MAP/PH₁, PH₂/2 queueing system with two types of heterogeneous servers, standby server, instantaneous feedback, working vacation, multiple vacations, breakdown, phase type repairs and impatient behaviour of customers
by G. Ayyappan; K. Thilagavathy
International Journal of Services and Operations Management (IJSOM), Vol. 48, No. 3, 2024

Abstract: In this article, we discuss two distinct types of heterogeneous servers, one of which is available at all times to provide service to arriving customers while the other is offering service in normal as well as vacation mode. Customers arrive based on the Markovian arrival process (MAP), and the service is distributed according to the phase-type (PH) distribution. While the main server-1 is providing service to the customers, if the main server-1 experiences a breakdown during service moments, the standby server will interrupt the main server-1 and begin providing service at a slower rate than the main server-1's service rate. The matrix-analytic method has been utilised to determine the average number of customers present in the system that was examined under steady-state probability vector. We examined the analysis of the system's busy period and the distribution of waiting time. Numerical and graphical results are presented to our model.

Online publication date: Fri, 28-Jun-2024

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