Webster’s delay formula revision by M+/G+/1 queuing model usage

Leszek Mindur, Grzegorz Sierpiński

Abstract


Webster’s delay model has been first time published almost 60 years ago (exactly in 1958). Next year will be a round anniversary. It became an occasion to verify the model. The method described in the paper discusses thesis of general shifted distribution of service times. Proposes delay model allows to use variance of service time as one of the parameters of a traffic flow at signalized intersection.


Keywords


Delay Model, Signalized Intersection, Variance of Service Time

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References


Akçelik R., Glossary of road traffic analysis terms, Akçelik & Associates Pty Ltd., August 2002.

Allsop R. E., Delay at a fixed time traffic signal – I: Theoretical analysis, "Transportation Science", 6 (1972)/3, pp. 260-285.

Canadian Capacity Guide for Signalized Intersections, Institute of Transportation Engineers, District 7 – Canada, Third Edition, December 2006.

Celiński I., Sierpiński G.. A dynamic management of a public transportation fleet, "LogForum", 9 (2013)/3, pp. 135-143.

Celiński I., Sierpiński G., Real time model for public transportation management, "LogForum", 10 (2014)/1, pp. 31-41.

Celiński I., Sierpiński G., Traffic Signal Control System with Extended Logic in the Context of the Modal Split, "IERI Procedia", 4 (2013), pp. 148 – 154 - http://dx.doi.org/10.1016/j.ieri.2013.11.022

Dion F., Rakha H., Kang Y. S., Comparison of delay estimates at under-saturated and over-saturated pre-timed signalized intersections, "Transportation Research. Part B", 38 (2004), pp. 99-122.

Gartner N., Messer C. J., Rathi A. K., Traffic Flow Theory. A State-of-the-Art Report, Transportation Research Board, Washington 2001 (Revised version of Special Report: Traffic Flow Theory, Washington 1975).

Handbuch für die Bemessung von Straßenverkehrsanlagen (HBS 2001). Forschungsgesellschaft für Straßen und Verkehrswesen, Köln, Januar 2002.

HCM2000, Highway Capacity Manual, Transportation Research Board, National Research Council, Washington DC 2000.

HCM2010, Highway Capacity Manual, Transportation Research Board of the National Academies 2010.

Hutchinson T. P., Delay at a fixed time traffic signal – II: Numerical comparisons of some theoretical expressions, "Transportation Science", 6 (1972)/3, pp. 286-305.

Kang Y. S., Delay stop and queue estimation for uniform and random traffic arrivals at fixed-time signalized intersections, Blacksburg, Virginia 2000.

Kleinrock L., Queueing systems, vol. I: Theory, A Wiley-Interscience Publication, Canada 1975.

Kuwahara M., Horiguchi R., Yoshii T., Standard verification process for traffic flow simulation model, Version 2, Traffic Simulation Committee, Japan Society of Traffic Engineers, 2002.

Liberadzki B., Mindur L., Uwarunkowania rozwoju systemu transportowego Polski, ITE-PIB, Warszawa–Radom 2007.

Luttinen R. T., Nevala R., Capacity and level of service of Finnish signalized intersections, Finnish Road Administration, Finnra Reports 25/2002.

Mindur L. (ed.), Technologie transportowe, ITE-PIB, Warszawa-Radom 2014.

Mindur M., Wzajemne związki i zależności między rozwojem gospodarki a transportem, ITE-PIB, Warszawa-Radom 2004.

Pypno Cz., Sierpiński G., Automated large capacity multi-story garage—Concept and modeling of client service processes, "Automation in Construction", 81C (2017), pp. 422-433.

Rajski J., Tyszer J., Modelowanie i symulacja cyfrowa, Wydawnictwo Politechniki Poznańskiej, Poznań 1986.

Sierpiński G., Model of Incentives for Changes of the Modal Split of Traffic Towards Electric Personal Cars, [in:] Mikulski J. (ed.), Transport Systems Telematics 2014, Telematics - Support for Transport, CCIS, vol. 471, Springer, Heidelberg 2014, pp. 450-460.

Sierpiński G., Verification of Webster’s delay model on signalized intersections with queueing theory analytical models usage, Dissertation, Institute of Civil Engineering, Wroclaw University of Technology, Report PRE no. 16/2006, Wrocław 2007.

Signalized intersections: International guide, U. S. Departament of Transportation, Federal Highway Administration, Publication No. FHWA-HRT-04-091, August 2004.

The method of capacity estimation for signalized intersection, GDDKiA, Warszawa 2004 (in Polish).

VISSIM - http://vision-traffic.ptvgroup.com/en-us/products/ptv-vissim/

Webster F. V., Cobbe B. M., Traffic signals, Road Research Paper No. 56, Her Majesty’s Stationary Office, London 1966.

Webster F. V., Traffic signal settings, Road Research Paper No. 39, Her Majesty’s Stationary Office, London 1958.

Woch J., Compresses queueing processes for single traffic flows, "The Archives of Transport", 10 (1998).

Zukerman M., An introduction to queueing theory and stochastic teletraffic models, The University of Melbourne, Melbourne 2006.


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