A queueing-inventory system with two classes of customers
نویسندگان
چکیده
We consider a queueing-inventory system with two classes of customers. Customers arrive at a service facility according to Poisson processes. Service times follow exponential distributions. Each service uses one item in the attached inventory supplied by an outside supplier with exponentially distributed lead time. We find a priority service rule to minimize the long-run expected waiting cost by dynamic programming method and obtain the necessary and sufficient condition for the priority queueinginventory system being stable. Formulating themodel as a level-dependent quasi-birth-and-death (QBD) process, we can compute the steady state probability distribution by Bright–Taylor algorithm. Useful analytical properties for the cost function are identified and extensive computations are conducted to examine the impact of different parameters to the system performance measures. & 2010 Elsevier B.V. All rights reserved.
منابع مشابه
Queueing Inventory System in a Two-level Supply Chain with One-for-One Ordering Policy
Consider a two-level inventory system consisting of one supplier and one retailer. The retailer faces a Poisson demand with a known rate and applies base stock (one-for-one ordering) policy. That is, his inventory position is set to a pre-determined level, so the demand pattern is transferred exactly to the supplier. The supplier has an inventory system and a service unit with exponentially dis...
متن کاملDiscrete Time Analysis of Multi-Server Queueing System with Multiple Working Vacations and Reneging of Customers
This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customer...
متن کاملA Queueing-Inventory System with Repair Center for Defective Items and One-for-One Ordering Policy
In this paper we consider a system consisting of a supplier with a single processing unit, a repair center, and a retailer with Poisson demand. We assume that the retailer applies one-for-one ordering policy with backorders for his inventory control. The retailer’s orders form a queue in the supplier processing unit. We also assume that a certain fraction of the products produced by the supplie...
متن کاملPartial-Fraction Decomposition Approach to the M/H2/2 Queue
Here, a two server queueing system with Poisson arrivals and two different types of customers (M/H2/2 queue) is analyzed. A novel straightforward method is presented to acquire the exact and explicit forms of the performance measures. First, the steady state equations along with their Z-transforms are derived for the aforementioned queueing system. Using some limiting behaviors of the steady-st...
متن کاملThe M/M/1 queue with inventory, lost sale, and general lead times
We consider an M/M/1 queueing system with inventory under the (r,Q) policy and with lost sales, in which demands occur according to a Poisson process and service times are exponentially distributed. All arriving customers during stockout are lost. We derive the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory when lead times are random...
متن کامل