OREGON TECH CIV475 Lindgren1 CIV 475 Traffic Engineering Mannering / Kilareski Chapter 5 Models of Traffic Flow

OREGON TECH CIV475 Lindgren2 Basic Traffic Stream Models - CIV 371 zspeed (u) km/h or miles/hr zconcentration or density (k) vehicles/km zflow (q) vehicles/hr zbasic identity q=uk

OREGON TECH CIV475 Lindgren3 Plot speed vs. concentration k Concentration (veh/km) u Speed (km/h)

OREGON TECH CIV475 Lindgren4 Plot flow vs. concentration k Concentration (veh/km) q Flow (veh/hr)

OREGON TECH CIV475 Lindgren5 Plot speed vs. flow q Flow (veh/hr) u Speed (km/h)

OREGON TECH CIV475 Lindgren6 Key points zSpeed at very light flow - u f free flow speed zSpeed at maximum flow - u m zDensity at very low speed - k j jam density zRemember !! Fundamental relationship q=ku

OREGON TECH CIV475 Lindgren7 Example (5.1 page 147) zCapacity=3,300veh/hr zfree flow speed=90km/h zAt what speed(s) would a flow of 2,100 veh/hr occur? zAssume linear speed-density relation

OREGON TECH CIV475 Lindgren8 Beyond the basics zThe model just presented ( and the non- linear models of CIV 371 ) are macroscopic or “big picture” types of models zWith these models we are predicting the number of vehicles passing a point on the roadway in a large time period ( usually one hour )

OREGON TECH CIV475 Lindgren9 Beyond the basics zOften times in traffic engineering, we need a more “microscopic” level of traffic model ysuch as a model to predict when vehicles will arrive at a traffic signal zA useful family of models are known as “vehicle arrival models”

OREGON TECH CIV475 Lindgren10 Vehicle Arrival Models Deterministic, uniform arrival model ydefinition: deterministic-model will produce the same result each time if given the same input yopposite: stochastic-model will produce different results each time if given the same input a.k.a. mechanistic zAccording to this model, if flow is 360veh/hr what will be the time between each arrival

OREGON TECH CIV475 Lindgren11 Vehicle Arrival Models Poisson Model zcommon non-uniform arrival model zassumes that the vehicles arrive at some random rate zappears to model traffic well if the traffic stream is light - moderate congestion and non-cyclic (I.e. isolated, not close to traffic light etc.)

OREGON TECH CIV475 Lindgren12 Poisson Model P(n) -probability that n vehicles arrive in time t -average vehicle arrival rate n!-factorial of n Poisson Model is a good choice if the variance of the observed data is close to the mean

OREGON TECH CIV475 Lindgren13 Example (5.2 page 149) z360veh/hr are counted zassuming Poisson distribution of arrivals, estimate probabilities of having 0,1,2,3,4, and 5 or more vehicles arriving in 20s interval zIs Poisson model a good choice for this situation?

OREGON TECH CIV475 Lindgren14

OREGON TECH CIV475 Lindgren15 z5.2 was an example of a “counting distribution” analysis zThe Possion Model can easily be adapted to model vehicle headways ydefinition: headway-time interval between vehicles (I.e. front-bumper to front-bumper )

OREGON TECH CIV475 Lindgren16

OREGON TECH CIV475 Lindgren17 zPoisson Headways zFor a flow of 500veh/hr, what is the probability of having a headway that is 2 seconds or more