Queueing-model based analysis of assembly lines with finite buffers and general service times

In this paper, we study the production process on multi-stage assembly lines. These production systems comprise simple processing as well as assembly stations. At the latter, workpieces from two or more input stations have to be merged to form a new one for further processing. As the flow of material is asynchronous with stochastic processing times at each station, queueing effects arise as long as buffers provide waiting room. We consider finite buffer capacities and generally distributed processing times. Processing is a service operation to customer items in the sense of a queueing system. The arrival stream of customer items is generated by processing parts at a predecessor station. This paper describes an approximation procedure for determining the throughput of such an assembly line. Exact solutions are not available in this case. For performance evaluation, a decomposition approach is used. The two-station subsystems are analyzed by G/G/1/NG/G/1/N stopped-arrival queueing models. In this heuristic approach, the virtual arrival and service rates, and the squared coefficients of variation of these subsystems are determined. A system of decomposition equations which are solved iteratively is presented. Any solution to this system of equations indicates estimated values for the subsystems’ unknown parameters. The quality of the presented approximation procedure is tested against the results of various simulation experiments.Scope and purpose: We consider assembly lines, i.e. flow production systems with a convergent flow of material and synchronization constraints. By considering assembly operations, our paper generalizes the work of Buzacott, Liu and Shanthikumar [Multistage flow line analysis with the stopped arrival queue model. IIE Transactions 1995;27:444–55], in which flow lines as series production systems are analyzed. It also extends the work of Helber [Performance analysis of flow lines with non-linear flow of material, Lecture notes in economics and mathematical systems, vol. 473, Berlin, Heidelberg, New York: Springer; 1999] and Jeong and Kim [Performance analysis of assembly/disassembly systems with unreliable machines and random processing times. IIE Transactions 1998; 30(1):41–53], who analyze assembly systems, by considering general service times. Station failures can be incorporated with the completion time concept proposed by Gaver [A waiting line with interrupted service, including priorities. Journal of the Royal Statistical Society 1962;24(2):73–90. [47]]. The comparison to various simulation results shows that the queueing-model based approach presented in this paper yields quite good approximations of the throughput.