Deadlock properties of queueing networks with finite capacities and multiple routing chains

Blocking in queueing network models with nite capacities can lead to deadlock situations. In this paper, deadlock properties are investigated in queueing networks with multiple routing chains. The necessary and suucient conditions for deadlock-free queueing networks with blocking are provided. An optimization algorithm is presented for nding deadlock-free capacity assignments with the least total capacity. The optimization algorithm maps the queueing network into a directed graph and obtains the deadlock freedom conditions from a speciied subset of cycles in the directed graph. In certain network topologies, the number of deadlock freedom conditions can be large, thus, making any optimization computationally expensive. For a special class of topologies, so-called tandem networks, it is shown that a minimal capacity assignment can be directly obtained without running an optimization algorithm. Here, the solution to the minimal capacity assignment takes advantage of the regular topology of tandem networks.