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Busy periods in vehicle queues

Published online by Cambridge University Press:  14 July 2016

Leonard Shaw
Leonard Shaw*
Affiliation:
Technical University of Eindhoven, Holland
*
1 On leave from the Polytechnic Institute of Brooklyn.
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Extract

Queueing models have been used to describe the slowing or stopping of a stream of vehicles due to a traffic light, a merging disturbance, or an accident. The buildup of stopped vehicles, and their eventual dispersal after the delaying factor has been removed, has been likened to the busy period of a queue, e.g., Jewell (1964). Some studies have dealt with the total delay to all drivers involved in such a queue, Daley and Jacobs (1969), Gaver (1969); or the combination of this total delay and the distance of the last vehicle from the originating incident, McNeil (1969), Shaw (1970).

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 261 - 268
Copyright
Copyright © Applied Probability Trust 1971 

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Footnotes

Research was supported in part by the Urban Mass Transportation Division of the U.S. Department of Transportation under contract No. URT-29.

References

Cohen, J. W. (1969) The Single Server Queue. North-Holland Publishing Co., Amsterdam.Google Scholar
Daley, O. J. and Jacobs, D. R. (1969) The total waiting time in a busy period of a stable single server queue, I, II. J. Appl. Prob. 6, 550–572.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol II. John Wiley, New York.Google Scholar
Gaver, D. P. (1969) Highway delays resulting from flow-stopping incidents. J. Appl. Prob. 6, 137–153.Google Scholar
Jewell, W. S. (1964) Forced merging in traffic. Operat. Res. 12, 858–869.Google Scholar
Mcneil, D. R. (1969) Growth and dissipation of a traffic jam. Transportation Res. 3, 115–121.CrossRefGoogle Scholar
Shaw, L. (1970) On traffic jam queues. Transportation Res. 4, 281–292.Google Scholar