Balagopal N, Deepthy C P, Jayaprasad P N, And Varghese Jacob. Discrete Time Queueing Inventory Models with Inventory Dependent Customer Arrival Under (s; S) Policy. Neural Parallel and Scientific Computations 28 (2020), No. 1, 37-52

https://doi.org/10.46719/npsc20202813

ABSTRACT.
In this paper, we presents two discrete queueing inventory models with positive service time and lead time where customers arrive according to a Bernoulli process and service time follows a geometric distribution. In model 1, we assume that an arriving customer joins the system only if the number in the queue is less than the number of items in the inventory at that epoch. In model 2, it is assumed that if the inventory level is greater than reorder level, $s$ at the time of arrival of a customer, then he necessarily joins. However, if it is less than or equal to $s$ (but larger than zero) then he joins only if the number of customers present is less than the on hand inventory. We analyse this queueing system using the matrix geometric method and we derive an explicit expression for the stability condition of the model-2. We obtain the steady-state behaviour of these systems and several system performance measures. An average system cost function is constructed for the models and are investigated numerically. The influence of various parameters on the system performances are also discussed through numerical example.

Subject Classification:
Keywords: AMS (MOS) Subject Classification. 60K25, 90B05, 91B70.
Key Words and Phrases: Queueing-inventory system; Inventory policy; Matrix-geometric method; Stationary distributions; Cost analysis.