International Journal of Computer Applications |
Foundation of Computer Science (FCS), NY, USA |
Volume 44 - Number 15 |
Year of Publication: 2012 |
Authors: M. Geetha Rani, C. Elango |
10.5120/6340-8619 |
M. Geetha Rani, C. Elango . Markov Process for Service Facility systems with perishable inventory and analysis of a single server queue with reneging – Stochastic Model. International Journal of Computer Applications. 44, 15 ( April 2012), 18-23. DOI=10.5120/6340-8619
In this paper, we develop a supply network model for a service facility system with perishable inventory (on hand) by considering a two dimensional stochastic process of the form (L, X) = , where L (t) is the level of the on hand inventory and X (t) is the number of customers at time t. The inter-arrival time to the service station is assumed to be exponentially distributed with mean 1/?. The service time for each customer is exponentially distributed with mean 1/ µ. The maximum inventory level is S and the maximum capacity of the waiting space is N. The replenishment process is assumed to be (S-1, S) with a replenishment of only one unit at any level of the inventory. Lead time is exponentially distributed with parameter ?. The items are replenished at a rate of ? whose mean replenishment time is 1/?. Item in inventory is perishable when it's utility drops to zero or the inventory item become worthless while in storage. Perishable of any item occurs at a rate of ?. Once entered a queue, the customer may choose to leave the queue at a rate of ? if they have not been served after a certain time (reneging). The steady state probability distributions for the system states are obtained. A numerical example is provided to illustrate the method described in the model.