Analysis of Finite Population Stochastic modeling with State-Dependent Arrival and Service Facilities

Abstract

This paper investigates a stock-dependent arrival process(SDAP) and queue-dependent service process(QDSP) in the stochastic queueing-inventory system(SQIS). The arriving units in the system are generated from the finite source population. The arrival process holds the properties of a quasi-random process and its intensity rate is defined based on the two-component demand rate(TCDR). The customer's departure time is exponentially distributed. The concepts of non-SDAP and SDAP, non-QDSP, and QDSP are to be generalized. The inventory system may have the perishable quality of the products. It adopts the $(s, Q)$ reordering policy whenever replenishment is required. Further, the joint probability distribution of a Markov process is derived and necessary system performance measures are computed. The comparative discussion is presented to improve the quality of this model.

Keywords

• stock-dependent arrival process
• non-stock dependent arrival process
• two component demand rate
• finite population
• queue-dependent service process