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Unformatted text preview: The Pennsylvania State University Department of Civil and Environmental Engineering Lecture 16  Queuing Theory CE 321: Highway Engineering Fall 2007 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. 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 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 – Parking garages – Railroad station platforms...
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This note was uploaded on 04/11/2008 for the course C E 321 taught by Professor Pietrucha,martinkeller,michaelwi during the Spring '07 term at Pennsylvania State University, University Park.
 Spring '07
 PIETRUCHA,MARTINKELLER,MICHAELWI

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