Multi Server Batch Service Systems in Push and Pull Operating Mode - a Performance Comparison

In this paper, we present a comparative performance analysis of a multi server batch service system working in `pull' and in `push' mode. Applications can be found in dimensioning problems of novel manufacturing systems where the flow of parts is coordinated according to the Kanban principle. We model a manufacturing system having N batch service machines, each of capacity b, and a common storage with S places. Provided that there are already i ; 1 servers active, the service period of another server is initialized when the service starting threshold a i of waiting customers has been reached. The analysis is done using standard method applied in Markov systems. Numerical results are shown for several `push' and their corresponding `pull' systems in order to demonstrate the difference in qualitative behaviour introduced by the two coordination policies. Quantitative performance studies for special sets of system parameters are made as far as waiting times, blocking probabilities and amountofwork in progress are concerned. It turns out that, of course, system time behaviour is significantly better in `pull' mode than in `push' mode as far as the mean time spent in the system as well as robustness against variation of traffic intensity are concerned. Beyond that, system behaviour is rather linear for `pull' systems in that the mean number of activated servers is directly proportional to the traffic intensity