Analysis of assembly/disassembly queueing networks with blocking after service and general service times

Abstract

In this paper, multi-stage assembly/disassembly (A/D) queueing networks are analyzed. We consider finite buffer capacities between the stations, generally distributed service times, and synchronization constraints at assembly and disassembly stations. We then describe a decomposition approach for the performance evaluation of such an (A/D) system, especially for the throughput and the variance of the inter-departure times. The two-station subsystems are analyzed as G/G/1/N stopped-arrival queueing systems. The virtual arrival and service rates, and the coefficients of variation are determined using a heuristic approach. A system of decomposition equations which is 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. We consider A/D queueing networks with blocking. Our paper extends the work of Manitz (Comput Oper Res 35:2520–2536, 2008) by considering disassembly operations. In addition to that, we give the variability measures of the output process at every station. By considering general service times, it generalizes the work of Gershwin and Burman (Ann Oper Res 93:91–115, 2000). Station failures can be incorporated with the completion-time concept proposed by Gaver (J R Stat Soc 24:73–90, 1962). A comparison to various simulation results shows that the queueing-model based approach presented in this paper yields very good approximations of performance measures.