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Lecture 16

# Lecture 16 - The Pennsylvania State University Department...

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The Pennsylvania State University Department of Civil and Environmental Engineering Lecture 16 -- Queuing Theory CE 321: Highway Engineering Fall 2007

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Introduction To model the arrival of vehicles in the traffic stream, we can use: a counting distribution (where we count the number of events of interest) or an interval distribution (where we measure the intervals between events of interest)
Traffic Stream Models Traditionally, in traffic engineering we have used the Poisson distribution to model the arrival of individual vehicles. This distribution is valid only if the traffic stream is free flowing so that a true random arrival pattern is observed. The assumption of a Poisson distribution of vehicle arrivals also implies a specific distribution of vehicle intervals or headways. This distribution is known as the exponential distribution. In cases where conditions become more congested, other distributions are used to describe vehicle arrivals and headways.

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Example: Poisson distributed probabilities of a certain number of vehicles arrive in time, t, for various values of lambda
Example: Exponentially distributed probabilities of headways greater than or equal to time, t

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Queuing Traffic queues, or waiting lines, result in time delays and loss of highway performance. In extreme cases, can account for 90 percent of travel time Queuing models used to understand formation and dissipation
Queuing Theory Queuing theory involves the mathematical study of queues Queues occur when the demand for a service exceeds the capacity to provide that service Decisions about how much capacity must be made frequently in the transportation field In places such as: Traffic signals Toll plazas

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