TY - JOUR
T1 - Bounding Queuing System Performance with Variational Theory
AU - Li, Jia
AU - Zhang, H. Michael
N1 - Funding Information:
Part of this work was funded by a University of Otago, Division of Science Postgraduate Publishing Award. Thanks also to Dr D. H.V. Smith for comments on an earlier draft and the technical staff at the Zoology Department, University of Otago for provision of equipment and Anemia used in these experiments.
Publisher Copyright:
© 2015 The Authors. Published by Elsevier B.V.
PY - 2015
Y1 - 2015
N2 - Queuing models are often used for traffic analysis, but analytical results concerning a system of queues are rare, thanks to the interdependence between queues. In this paper, we present an analysis of queuing systems to obtain bounds of their performance without studying the details of individual queues. Queuing dynamics is formulated in continuous-time, subject to variations of demands and bottleneck capacities. Our analysis develops new techniques built on the closed-form solution to a generalized queuing model for a single bottleneck. Taking advantage of its variational structure, we derive the upper and lower bounds for the total queue length in a tandem bottleneck system and discuss its implication for the kinematic wave counterpart. Numerical experiments are conducted to demonstrate the appropriateness of the derived upper and lower bounds as approximations in a stochastic setting.
AB - Queuing models are often used for traffic analysis, but analytical results concerning a system of queues are rare, thanks to the interdependence between queues. In this paper, we present an analysis of queuing systems to obtain bounds of their performance without studying the details of individual queues. Queuing dynamics is formulated in continuous-time, subject to variations of demands and bottleneck capacities. Our analysis develops new techniques built on the closed-form solution to a generalized queuing model for a single bottleneck. Taking advantage of its variational structure, we derive the upper and lower bounds for the total queue length in a tandem bottleneck system and discuss its implication for the kinematic wave counterpart. Numerical experiments are conducted to demonstrate the appropriateness of the derived upper and lower bounds as approximations in a stochastic setting.
KW - queuing systems
KW - traffic flow
KW - variational solution
UR - http://www.scopus.com/inward/record.url?scp=84959365683&partnerID=8YFLogxK
U2 - 10.1016/j.trpro.2015.06.027
DO - 10.1016/j.trpro.2015.06.027
M3 - Article
AN - SCOPUS:84959365683
SN - 2352-1457
VL - 7
SP - 519
EP - 535
JO - Transportation Research Procedia
JF - Transportation Research Procedia
ER -