Abstract
We analyze a queueing-inventory system which can model airline and railway reservation systems. An arriving customer to an idle server joins for service immediately with exactly one item from inventory at the moment of service completion if there are some on-hand inventory, or else he accesses to a buffer of varying size (the buffer capacity varies and equals to the number of the items in the inventory with maximum size S). When the buffer overflows, the customer joins an orbit of infinite capacity with probability p or is lost forever with probability 1−p. Arrivals form a Poisson process, and service time has phase type distribution. The time between any two successive retrials of the orbiting customer is exponentially distributed with parameter depending on the number of customers in the orbit. In addition, the items have a common life time with exponentially distributed. Cancellation of orders is possible before their expiry and intercancellation times are assumed to be exponentially distributed. The stability condition and steady-state probability vector have been studied by Neuts–Rao truncation method using the theory of Level Dependent Quasi-Birth-Death (LDQBD) processes. Several stationary performance measures are also computed. Furthermore, we provide numerical illustration of the system performance with variation in values of underlying parameters and analyze an optimization problem.
Highlights
In real life, people often purchase products for future use or cancel the purchased products due to some reasons
A significant contribution for the development of queueinginventory system is [1], where stationary distribution of joint queue length and inventory process was derived in explicit product form for various M/M/1-system with inventory under different inventory management policies
Krishnamoorthy et al [13] made a detailed review of inventory models with positive service time and suggested possible directions for future research
Summary
People often purchase products for future use or cancel the purchased products due to some reasons. Krishnamoorthy et al [13] made a detailed review of inventory models with positive service time and suggested possible directions for future research One may refer this for the development taken place in queueing-inventory with retrial customers which contains some of the finest contributions such as [14,15,16,17,18]. Cancellation, and common life time was first introduced in the queueing-inventory system by Krishnamoorthy et al [19] with a constant retrial rate In their model, customers arrive according to a Poisson process and service time follows an exponentially distributed. E aim of our research is to present stationary distribution and optimal inventory policies for service system with an attached inventory under reservation, cancellation of orders, common life time, and retrial. By comprehensively analyzing the influence of various factors on the profit, it is illustrated that the change trend of the profit on the system parameters is in line with the actual situation, which provides an effective and scientific basis for the inventory manager
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