Vehicles moving along a multi-lane road section maintain fixed speeds. Each vehicle, however. moves at its own speed that may differ from the speeds of other vehicles. Vehicle trajectories and speeds in a rectangular area are defined by t = 0 - 1 minute and x = 0 -1 mile (see figure below).

a) Estimate the hourly volume, time-mean speed and approximated space-mean speed from the spot observation at point x = 0.1 mi during the period t = 0 - 1 min

b) Estimate the traffic density and space mean speed from the instantaneous observation at time t= 0.1 min between point x=0 mi and x=1 mi

Community Answer

So first put all your data points into a table as below. We have 13 data points and calculate the average speed Time mean speed = the average of all the speeds and is calculated as follows Time-Mean Speed, bar(v)_(TMS)= avg. speed =(sumv_(i))/(n)=(sum(d)/(t_(i)))/(n) So our time mean speed = 40.946 mph -------------------------------------------------------------------------------------------------------------------- 13 vehicles are observed in 1 minute So flow = 13 veh/min = 780 veh/hour -------------------------------------------------------------------------------------------------------------------------- Space mean speed is calculated by the formula Space-Mean Speed, bar(v)_("SMS ")=(" distance traveled ")/(" avg. travel time ")=(d)/(sumt_(i)_)=(n xx d)/(sumt_(i))where:{:[d,=" distance traveled or length of roadway segment; "],[n,=" number of observations; "],[v_(i),=" speed of the "i" th vehicle; "],[t_(i),=" travel time of the "i" th vehicle; and "],[t_(ri),=" running time of the "i" th vehicle. "]:} So draw a horizontal line at x = 0.1 mile and then calculate it as follows So after drawing horizontal ... See the full answer