At a specified point on a bicycle path, bicycles are assumed to arrive according to a Poisson probability distribution. Bicycles are counted in 15 second intervals for a period of 30 minutes. It is noted that no bicycles arrived in 18 of those 120 intervals. Out of these 120 intervals, how many of these have exactly two bicycles arriving?

Round your answers to the nearest 2 decimal points. Note: Only include the numerical value (e.g. 51.36)

A section of an arterial road has been found to have a speed-density relationship that was modelled using the following form:

where v is the space-mean speed in kilometres per hour (km/h), and k is the density in vehicles per kilometres (veh/km).

The relationship was found to have the best fit to the data by using the following coefficients:

a = 3.5

k_m = 126 veh/km

Which is the critical density (ie the density at which the capacity is obtained) of the above arterial road?

The fundamental diagram for a road section can be modelled using a triangular flow-density relationship, having a capacity (maximum flow) of 2000 vehicles per hour (veh/h), a free-flow speed of 80 kilometres per hour (km/h), and a jam density of 125 vehicles per kilometre (veh/km). 

In the peak hour, the congested traffic condition is observed with a speed of 42km/h. What is the density during this peak hour?

A linear regression fit to real traffic data speed (v) and density (k) data has the following relationship: v= 83 –0.5*k, where v is measured in kilometres per hour (km/h) and k is measured in vehicles per kilometre (veh/km). What is the maximum flow of this fundamental diagram?

Round your answers to the nearest 2 decimal points in veh/h. Note: Only include the numerical value (e.g. 51.36)

If only the flow

of vehicles passing by a fixed location on a section of roadway is known then

which of the option(s) below can be determined:

Four vehicles are traveling on a 4-kilometer circular track. The four vehicles are traveling at constant speeds of 46 km/h, 61 km/hr, 62 km/hr, and 70 km/hr, respectively. Assume you are an observer standing at a point on the track for a period of 30 minutes and are recording the instantaneous speed of each vehicle as it crosses your point.  What is the space-mean speed for this stream of traffic?

Round your answers to the nearest 2 decimal points in km/h. Note: Only include the numerical value (e.g. 51.36)

The speeds of six vehicles collected at a fixed location on a long straight road section were 73 km/h, 81 km/h, 61 km/h, 77 km/h, 79 km/h and 79 km/h. What is the space-mean speed for this stream of traffic? 

Round your answers to the nearest 2 decimal points in km/h. Note: Only include the numerical value (e.g. 51.36)

The average headway of traffic on a single lane road has been measured as 8 seconds. What is the flow on the road?

Round your answers to the nearest 2 decimal points in veh/hr. Note: Only include the numerical value (e.g. 51.36)