Some Properties of Presence Detectors

G. F. Newell
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G. F. Newell: University of California, Berkeley, California

Transportation Science, 1970, vol. 4, issue 3, 311-321

Abstract: Presence detectors on highways record whether or not there are any cars on some nonzero length section of highway. The absence of cars is used as a criterion for switching a vehicle-actuated signal. The problem considered here is the following. Cars pass the detector according to a Poisson process, at velocities that are independent, identically distributed random variables. Starting at some arbitrary time origin, how long will it be before the detector of length L is empty for the first time. It is shown that, in most cases, this time is nearly the same as if all cars had the same velocity q / k , q = flow, k = spacial density, and is rather insensitive to the distribution of the velocities.

Date: 1970
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:4:y:1970:i:3:p:311-321

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