Queuing network model of uniformly distributed arrivals in a distributed supply chain using subcontracting

In this paper, a supply chain (four-input three-stage queuing network) receives uniformly distributed orders from clients. An input order is represented by two stochastic variables, occurrence time and the quantity of items to be delivered. The objective of this work is to compute the minimum response time, and thus the average number of items (optimum capacity) that can be delivered with this response time. Performance measures such as average queue lengths, average response times, and average waiting times of the jobs in the supply chain, and in the equivalent single-server network are derived, plotted and discussed.