Document 
Eur. Phys. J. B 63, 341-347 (2008)
DOI: 10.1140/epjb/e2007-00346-5
Anticipative control of switched queueing systems
S. Lämmer1, R. Donner1 and D. Helbing2, 31 Dresden University of Technology, A.-Schubert-Str. 23, 01062 Dresden, Germany
2 Swiss Federal Institute of Technology, Scheuchzerstr. 70, CH-8092 Zurich, Switzerland
3 Collegium Budapest - Institute for Advanced Study, Szentháromság utca 2, 1014 Budapest, Hungary
traffic@stefanlaemmer.de
Received 20 August 2007 / Received in final form 8 October 2007 / Published online 19 December 2007
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.
02.30.Yy - Control theory.
02.30.Ks - Delay and functional equations.
89.75.-k - Complex systems.
89.40.-a - Transportation.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2008