Anticipative control of switched queueing systems

Abstract

The relevant dynamics of a queueing process can be anticipated by taking future arrivals into account. If the transport from one queue to another is associated with transportation delays, as it is typical for traffic or productions networks, future arrivals to a queue are known over some time horizon and, thus, can be used for an anticipative control of the corresponding flows. A queue is controlled by switching its outflow between “on” and “off” similar to green and red traffic lights, where switching to “on” requires a non-zero setup time. Due to the presence of both continuous and discrete state variables, the queueing process is described as a hybrid dynamical system. From this formulation, we derive one observable of fundamental importance: the green time required to clear the queue. This quantity allows to detect switching time points for serving platoons without delay, i.e., in a “green wave” manner. Moreover, we quantify the cost of delaying the start of a service period or its termination in terms of additional waiting time. Our findings may serve as a basis for strategic control decisions.