Double‐sided queues and their applications to vaccine inventory management

We consider a double‐sided queueing model with batch Markovian arrival processes (BMAPs) and finite discrete abandonment times, which arises in various stochastic systems such as perishable inventory systems and financial markets. Customers arrive at the system with a batch of orders to be matched by counterparts. While waiting to be matched, customers become impatient and may abandon the system without service. The abandonment time of a customer depends on its batch size and its position in the queue. First, we propose an approach to obtain the stationary joint distribution of age processes via the stationary analysis of a multi‐layer Markov modulated fluid flow process. Second, using the stationary joint distribution of the age processes, we derive a number of queueing quantities related to matching rates, fill rates, sojourn times and queue length for both sides of the system. Last, we apply our model to analyze a vaccine inventory system and gain insight into the effect of uncertainty in supply and demand processes on the performance of the inventory system. It is observed that BMAPs are better choices for modeling the supply/demand process in systems with high uncertainty for more accurate performance quantities.