A Two-Server Queue with Interdependence between Arrival and Service Processes

Abstract

In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and service processes. The transitions in this Markov chain follow a semi-Markov rule and the exponential distribution governs the sojourn times in the states. The stability condition of the system is derived and the stationary distribution is calculated for the system in equilibrium. Several important performance measures are provided, and numerical illustrations of the model are presented.

On V-Geometric Ergodicity Markov Chains of the Two-Inertia Systems

“…In stochastic process [9][10][11][12], Markov chains can be used to model issues such as system performance degradation, stability, and system aging [13,14]. Krishnamoorthy & Kozyrev [15] conducted a novel analysis of the system by simulating the dwell time in states using semi-Markov rules and exponential distributions, through the transformation of the product space of three Markov chains. Wang et al [16] established a joint optimization model for emergency engineering equipment maintenance and spare parts inventory strategy considering demand priority.…”