Two commodity queueing inventory system with random common lifetime, two demand classes and pool of customers

This paper analyzes a two-commodity perishable queueing inventory system with random common lifetimes commodity-wise, positive service time, and individual ordering policy. We have considered two types of customers: priority customers and non-priority customers. There is a buffer of finite capacity for the priority customers and a pool with infinite capacity made available for the non-priority customers. The arrival of these customers is occurred by two independent Poisson processes. The lifetimes of each of the commodities and service times follow independent exponential distributions. The matrix geometric approach is used to analyze the model's steady-state behavior and we computed various system performance measures. This article examines the effects of the common lifetime parameters on the measures of performance, such as average cycle time, the average number of reorders due to the realization of the common lifetime of commodities, etc. Also, a sensitivity analysis of the system parameters on the performance measures is carried out. Further, a cost function is constructed based on the performance measures, and its convexity is examined numerically.