A revisit to queueing-inventory system with reservation, cancellation and common life time

Abstract

In this paper we consider a single server queueing-inventory system having capacity to store S items which have a common-life time (CLT), exponentially distributed with parameter $\gamma$. On realization of ${\textit{CLT}}$ a replenishment order is placed so as to bring the inventory level back to S, the lead time of which follows exponential distribution with parameter $\beta$. Items remaining are discarded on realization of ${\textit{CLT}}$. Customers waiting in the system stay back on realization of common life time. Reservation of items and cancellation of sold items before its expiry time is permitted. Cancellation takes place according to an exponentially distributed inter-occurrence time with parameter $i\theta$ when there are $(S-i)$ items in the inventory. In this paper we assume that the time required to cancel the reservation is negligible. Customers arrive according to a Poisson process of rate $\lambda$ and service time follows exponential distribution with parameter $\mu$. The main assumption that no customer joins the system when inventory level is zero leads to a product form solution of the system state distribution. Several system performance measures are obtained.