A Queuing Model Approach to Stochastic Supply/Demand Systems

Abstract

Abstract This paper is part of a series reporting initial results on developing queuing models for certain types of stochastic demand/supply systems. Interarrival time of a unit of demand or supply is exponentially distributed. Excess supply results in a positive queue, and excess demand, a negative queue. Instant pairing off’s imply that queue can be either positive, or negative, but not both at the same time. In each case, a cost per unit time is associated with a unit of excess. Objectives are to analyze queuing behavior and the possibilities of reducing and controlling shortages and/or oversupplies. Preliminary results include the following: Suppose that the rates of supply and demand are λ and μ respectively and ρ=λ/μ; that the costs per time of a unit of oversupply and shortage are c’ and c’ respectively and c=c’/c″; and that the maximum numbers of units of excesses are the same finite k. Then as k approaches ∞, the optimum ρ* which minimizes the expected total cost per unit time is an increasing fu...