A Markovian Batch Arrival Queueing System With Disasters, Working Breakdowns, and Impatience: Mathematical Modeling and Economic Analysis

Abstract

Machining systems are essential for many industrial applications, such as manufacturing, processing, and assembly. However, these systems are often exposed to various sources of uncertainty and disruption, such as disasters and customer impatience. These factors can adversely affect the performance, reliability, and profitability of the machining systems. Consequently, modeling and analyzing machining systems under these conditions becomes crucial. In this paper, we deal with a Markovian multi-server queueing system with batch arrival, Bernoulli feedback, and customers’ impatience (balking and reneging). The system undergoes disastrous interruptions that force all customers– whether waiting or currently in service–to exit, leading to server failures. Moreover, the system dynamically alternates between main servers and substitute servers based on the occurrence of disasters. These substitute servers operate at reduced rates compared to the main servers. Our contributions include deriving the stability condition for the system and obtaining the probability generating function of steady-state probabilities, enabling us to derive essential performance measures. Additionally, we develop a cost model and conduct an economic analysis for the system.