Queueing models and stability of message flows in distributed simulators of open queueing networks

In this paper we study message flow processes in distributed simulators of open queueing networks. We develop and study queueing models for distributed simulators with maximum lookahead sequencing. We characterize the external arrival process, and the message feedback process in the simulator of a simple queueing network with feedback. We show that a certain natural modelling construct for the arrival process is exactly correct, whereas an obvious model for the feedback process is wrong; we then show how to develop the correct model. Our analysis throws light on the stability of distributed simulators of queueing networks with feedback. We show how the stability of such simulators depends on the parameters of the queueing network.