The Time to Drive Through a No-Passing Zone

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Abstract
A no-passing zone is a one-line, one-way highway with one entrance and one exit. Interarrival time between successive cars have a known distribution; the distribution of cars’ preferred speeds is also known; interarrival times and preferred speeds are all mutually independent random variables. Each car drives at its preferred speed until obstructed by the car ahead. When obstructed by a slower car, a car closes the distance between the two to zero (cars have zero length) and assumes the speed of the slower car. Thus platoons are formed which behave like individual cars. We find the distribution of the time to drive through the zone and of related random variables. We also find the distribution of the gap in time between platoons leaving the zone and of the number of cars in a platoon. In general, the results are tractable only when arrivals are Poisson or deterministic.

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