STRUCTURE-REVERSIBILITY AND DEPARTURE FUNCTIONS OF QUEUING-NETWORKS WITH BATCH MOVEMENTS AND STATE-DEPENDENT ROUTING

We consider characterizations of departure functions in Markovian queu eing networks with batch movements and state-dependent routing in disc rete-time and in continuous-time. For this purpose, the notion of stru cture-reversibility is introduced, which means that the time-reversed dynamics of a queueing network corresponds with the same type of queue ing network. The notion is useful to derive a traffic equation. We als o introduce a multi-source model, which means that there are different types of outside sources, to capture a wider range of applications. C haracterizations of the departure functions are obtained for any routi ng mechanism of customers satisfying a recurrent condition. These resu lts give a unified view to queueing network models with linear traffic equations. Furthermore, they enable us to consider new examples as we ll as show limited usages of this kind of queueing networks.