Queueing analysis of manufacturing systems with setups

Abstract

A manufacturing system with one server (machine), two classes of jobs, finite buffer sizes and nonnegligible setup times is analyzed. Classes are served in a fixed order. A new cycling service discipline called "triggered" cycling is introduced as a type of exhaustive cycling where a job must be present to process before the setup for that class takes place. The state of the machine, whether in setup or in processing, is explicitly considered in the model. Utilization, mean queue length and cycle time are derived by using Markovian analysis, first under a fixed lot size environment and then with random lot sizes. With lot sizes fixed (deterministic), increasing arrival rates, setup times and service times generally increase utilization, cycle time and queue length. Sensitivity analyses indicate a minimum exists for queue length with respect to lot size. When lot sizes are random, negligible variations in cycle time result, with somewhat smaller queue length as compared to the fixed lot size case. Despite lack of a product form solution to the problem, an approximate mean value analysis yielding cycle time is developed and the results are compared to Markovian analysis. Numerical studies show robustness of the mean value analysis for utilizations under 0.7.