Chapter 5 _2_

Chapter 5 _2_ - Queuing Theory and Flow Analysis The...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Queuing Theory and Flow Analysis The formation of traffic queues during congested periods is a source of considerable time delay and results in a loss of highway performance.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Outline s Traffic Flow Models s Arrival/departure Patterns s Poisson Model s Queuing Theory s D/D/1 Queuing s M/D/1 Queuing s M/M/1 Queuing
Background image of page 2
3 Queuing Theory
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 Queuing Theory Source: http://www.sierraclub.org/sprawl/report04/commuting.asp
Background image of page 4
5 s Flow arrival pattern in time: s Uniform (like e.g. 360 veh/h) Arrival/Departure Patterns Time Uniform Distribution f(t)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 s Flow arrival pattern in time: s Nonuniform (random process e.g. Poisson model) Arrival/Departure Patterns Time f(t)
Background image of page 6
7 Poisson Model ! ) ( ) ( n e t n P t n λ - = P(n) Volume (# of vehicles) P(n): probability of having n vehicles λ : average vehicle flow per unit time t= duration of the time interval
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 Example The average arrival rate is 240 vehicles/hr at a roadway section. Calculate the probability of having exactly 0, 4, 8, and 12 vehicles in a 60- second interval.
Background image of page 8
9 3600 q = λ Using Poisson model for distribution of the time intervals between the arrivals of vehicles: ! ) 3600 / ( ) ( 3600 / n e qt n P qt n - = Veh/hr Veh/s Poisson Model
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Probability of having no vehicles arrive in time interval “t”: P(0) 3600 / ) 0 ( qt e P - = This is equivalent to the probability of a vehicle headway (h) being greater than or equal to the time interval “t”. 3600
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 29

Chapter 5 _2_ - Queuing Theory and Flow Analysis The...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online