Norman W. Garrick Traffic Stream Flow Equations

Norman W. Garrick Basic Stream Flow Parameters Three types of parameters 1.Spacing and Concentration 2.Headway and Flow 3.Speed

Norman W. Garrick Spacing is the distance between vehicles, s Concentration (or density) is the number of vehicles per unit length, k Spacing and Concentration s2s2 s3s3 s4s4 D s (ave) = 1 / k s1s1

Norman W. Garrick Headway is the time between vehicles passing a specific location, h Flow is the amount of vehicles passing a specific location in a specific time, q Headway and Flow h (ave) = 1 / q measurement point

Norman W. Garrick TMS and SMS Time Mean Speed - is based on the spot speed of the vehicles passing a specific point Space Mean Speed - is based on the average time it takes vehicles to cover a certain specified distance Time Mean Speed, u t = 1/n ∑ v i Space mean speed, u s = 1 / {1/n ∑ 1/v i }

Norman W. Garrick Relationship between Space and Time Parameters What is the concentration? k = 100 vehicles/mile What is the space? s = 1/k = 1/100 miles = 52.8 feet If the average speed = 10 miles What is the flow (q)? Flow is total number of vehicles passing any point Flow = 10*100 = 1000 vehicles/hr In other words, q = uk 100 vehicles D = 1 mile

Norman W. Garrick Representing Traffic Flow The fundamental equation of traffic stream flow is q = uk This equation is used in conjunction with the Traffic Flow Curves (next slide) in an attempt to characterize traffic flow on a macroscopic level. However, it should be understood that these analytical representation of traffic flow does not come close to accurately depicting the real life traffic which is a complex and non-linear phenomena. The complexity derive from the fact that we have a large number of vehicles interacting in a way that does not follow the laws of mechanics due to the reaction of the HUMAN driver

Norman W. Garrick Traffic Flow Curves u k

Norman W. Garrick Traffic Flow Curves u k

Norman W. Garrick Traffic Flow Curves u k u q

Norman W. Garrick Traffic Flow Curves u k u q One important point to note, FLOW increase with SPEED but only up to a point Why?

Norman W. Garrick Traffic Flow Curves u k u q k q

Norman W. Garrick What is the Maximum Theoretical Flow on a Highway? If we have observed Density and Speed we could estimate maximum flow The relationship between SPACE and SPEED depends on the ‘safety regime’ This safety regime is hard to characterize and depends on factors such as weather, age of drivers and other cultural factors The figure in the next slide is considered to give a SPACE/SPEED relationship that comes close to reality for American driving conditions

Norman W. Garrick Calculating Maximum Flow Spacing versus Speed Curve A from Figure in Text Spacing, ft

Norman W. Garrick Calculating Maximum Flow Speed versus Concentration (u-k) k = 1 / s (ave) u k

Norman W. Garrick Calculating Maximum Flow Flow versus Speed (u-q) In theory q max occurs at speed of about 40 mph u q

Norman W. Garrick Calculating Maximum Flow Flow versus Concentration (q-k) q = uk q max = 2000 veh/hr k q

Norman W. Garrick Traffic Flow Curves Maximum Flow, Jam Concentration, Freeflow Speed u k u q k q q max kjkj ufuf k j - jam concentration u = 0, k = k j q max - maximum flow u f - free flow speed k = 0, u = u f