Performance Analysis of a Semi-Open Queuing Network with Correlated Arrivals, Catastrophes, and Customer Impatience

This paper investigates the performance of a semi-open queuing network subject to external disruptions and customer impatience. The system features a multi-node structure where arrivals are governed by a correlated arrival process and the total capacity is limited. External catastrophes are accounted for, which result in the immediate clearance of all customers from the network followed by a recovery period. By modeling the network as a multi-dimensional Markov chain, we derive the explicit block structure of the infinitesimal generator. This mathematical framework allows for the evaluation of key stationary performance measures, such as the mean number of customers and various loss probabilities, considering the simultaneous impact of service interruptions and customer reneging.