Analysis of the queueing-inventory system that provides inventory based on the server's acceptance

초록

This article scrutinizes a queueing-inventory system (QIS) that consists of a single server, S items, and a finite waiting zone with a visible queue. An ordinary client enters the waiting zone regardless of the queue length. A deliberate client, depending on the queue length, may choose either to join the waiting zone or enter an orbit of infinite capacity. The arrivals of both client types follow independent Poisson processes. During the service, the server decides whether to provide inventory or not, after verifying the client's demand status. Here, the (s, Q) policy is adopted for restocking items. A deliberate client in the orbit makes repeated attempts to join the waiting zone following a constant retrial policy. We assume that some clients may become impatient due to long waiting time in a waiting zone. The service duration, lead time, retrial duration, and impatience time follow exponential distributions with different parameters. The steady-state probabilities are computed, and the system's essential performance metrics are derived. Subsequently, the optimal total expected cost is determined through numerical analysis and visually represented in a graph.

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