CE 310 - Module 4 (1).pdf

Discuss traffic Identify the Analyze variable analysis; variables of traffic relationships of the analysis; and fundamentals in traffic flow Flow is often measured over the course of an hour; in whi...

Discuss traffic Identify the Analyze variable analysis; variables of traffic relationships of the analysis; and fundamentals in traffic flow Flow is often measured over the course of an hour; in which case the resulting value is typically referred to as volume. Thus, when the term “volume” is used, it is generally understood that the corresponding value is in units of vehicles per hour (veh/h). 𝒏 𝒒= 𝒕 where: q = traffic flow n = number of vehicles passing through t = duration of time interval  𝒏 The time between the passage of the 𝒉𝒊 𝒕 = ෍ 𝒉𝒊 ℏ= ෍ front bumpers of successive vehicles, at 𝒏 𝒊=𝟏 some designated highway point. where: hi – time headway of the ith vehicle ℏ – average time headway Average speed of all vehicles passing a point on a roadway over a specified time (instantaneous point speed). σ 𝒖𝒊 𝝁𝒕 = 𝒏 where: 𝜇𝑡 = time mean speed 𝑢𝑖 = observed speed of ith vehicle. Average speed of all vehicles occupying a given section of roadway over a specified time (essentially, the inverse of travel time for all vehicles over the specified section length). 𝒏 𝒏𝒅 𝚺𝒅𝒊 𝝁𝒔 = 𝝁𝒔 = = 𝟏 σ 𝒕𝒊 𝒏𝒕 σ 𝝁𝒊 where: 𝜇𝑠 - space-mean speed d – length of roadway section 𝑡𝑖 - observed time for the ith vehicle to travel 𝜇𝑖 - observed speed of the ith vehicle The density can be related to the individual spacing between successive vehicles (measured from front bumper to front bumper) 𝒏 𝟏 𝒌= = 𝒒 = 𝒌μ𝒔 𝒅 𝑠ҧ where: k - density The increase in traffic density will affect the average operating speed of vehicles and will decline from the free-flow value (known as free-flow speed). Eventually the highway section will become so congested that the traffic will come to a stop. This high-density condition is known as jam density 𝒌 𝒌𝒋 𝝁𝒇 𝝁𝒔 = 𝝁𝒇 (𝟏 − ) 𝒒= ( ) 𝒌𝒋 𝟐 𝟐 where: 𝜇𝑓 - free-flow speed 𝑘𝑗 – jam density Using the assumption of a linear speed- density relationship, and using the relationship, q = kμs, a parabolic flow-density model can be obtained: 𝒌𝟐 𝒒 = 𝝁𝒇 (𝒌 − ) 𝒌𝒋 where: 𝑞𝑐𝑎𝑝 - traffic flow at capacity – highest rate of traffic flow the highway can handle 𝑘𝑐𝑎𝑝 – corresponding traffic density 𝑢𝑐𝑎𝑝 – corresponding speed Referring to the linear speed-density model and rearranging the equation gives us: 𝝁𝒔 𝒌 = 𝒌𝒋 (𝟏 − ) 𝝁𝒇 𝝁𝟐𝒔 𝒒 = 𝒌𝒋 (𝝁𝒔 − ) 𝝁𝒇 The speeds of five vehicles were measured at the midpoint of a 0.5 km section of NLEX. The speeds for vehicles 1, 2, 3, 4, and 5 were 44, 42, 51, 49, and 46 km/h, respectively. Assuming all vehicles were traveling at constant speed over this roadway section, calculate the time-mean and space-mean speeds. Vehicle time headways and spacings were measured at a point along a highway, from a single lane, over the course of an hour. The average values were calculated as 2.5 s/veh for headway and 200 ft./veh. (61 m/veh.) for spacing. Calculate the average speed of the traffic. From a following data of a freeway surveillance, there are 5 vehicles under observation and the following distances are the distance each vehicle had traveled when observed every 2 seconds. Compute the space mean speed in kph. VEHICLES DISTANCE (m) 1 24.4 2 25.8 3 24.7 4 26.9 5 22.9 The following data were taken on five vehicles traveling a 1.5 km. portion of the NLEX. Compute the space-mean speed in kph. VEHICLES TIME (min) 1 1.2 2 1.0 3 1.4 4 1.3 5 1.2 Given from an observation along EDSA during rush hour, Mean free speed = 64 kph Jam density = 120 veh/km a. Determine the maximum flow of traffic b. Determine the velocity at which the flow of traffic is maximum c. Determine the density at which the flow of traffic is maximum. A section of highway is known to have a free-flow speed of 55 km/h and a capacity of 3300 veh/h. In each hour, 2100 vehicles were counted at a specified point along this highway section. If the linear speed-density relationship applies, what would you estimate the space- mean speed of these 2100 vehicles to be?