Different variants of unreliable server: An economic approach

Abstract

This chapter investigates a single-server finite-capacity service system in a Markovian environment for different variants of unreliable servers. Three diverse mathematical models are discussed using the queueing-theoretic approach and nomenclatures: customers’ impatience, working breakdown, service pressure condition, and threshold-based recovery policy. The Chapman–Kolmogorov differential-difference equations for each model are established, and the matrix method is employed to exhibit the steady-state queue-size distribution. In addition, explicit closed-form expressions of various system performance measures are provided, which are used to construct an expected total cost function. We also develop a cost optimization problem to determine the optimal operating policy at a minimum expected cost of the service system. As a classical optimizer, the quasi-Newton method is employed to ascertain the solution to the developed cost optimization problem. Furthermore, a comparative analysis is performed between each developed model for the detailed study using various combinations of system design parameters and default cost elements. Finally, several graphs and tables provide managerial insights to understand the research findings better.