Discrete-time analysis of closed queueing networks in material flow systems

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For the analysis of closed material flow systems such as automated guided vehicle system, queueing networks can be used. But so far, there are only methods available that calculate the mean value and variance of performance indicators. The ability to determine the quantiles of performance indicators, which knowledge of is often required in logistics and particularly in material flow planning is not given. An alternative to the continuous-time analysis is the discrete-time approach. Since the assumption of independent arrival rates in closed queueing systems is invalid, they could not yet be modeled by the discrete-time approach with general distributed service times. The goal of this research project is the development of discrete-time methods for calculating performance indicators that are important to know during the rough planning phase of a closed queueing network. Given a generally distributed service time, the methods should yield in the calculation of the discrete-time probability distributions of performance indicators such as waiting times or the number of customers in a single queueing system. The results of the research project are an exact method, based on Markov chain processes, as well as for the analysis of large networks, two approximate methods. A comparison of the methods regarding the quality of the results and the computational effort is also to be investigated.