Signalized Intersection Analysis
Signalized Intersection Analysis with D/D/1 Queuing The assumption of D/D/1 queuing (as discussed in Chapter 5) provides a strong intuitive appeal that helps in understanding the analytical fundamentals underlying traffic analysis at signalized intersections. To begin applying D/D/1 queuing to signalized intersections, we consider the case where the approach capacity exceeds the approach arrivals. Under these conditions, and the assumption of uniform arrivals throughout the cycle and uniform departures during green, a D/D/1 queuing system.
Note that this chapter will use the variables v (for arrival rate) and s (for departure/saturation flow rate), rather than the variables λ and μ, as these variables are more commonly used in signalized intersection analyses.
The “Arrivals v×t” line gives the total number of vehicle arrivals at time t, and the “Departures s×t” line gives the slope of vehicle departures (number of vehicles that depart) during the effective greens. Note that the per-cycle approach arrivals will be vC and the corresponding approach capacity (maximum departures) per cycle will be sg. predicated on the assumption that sg exceeds vC for all cycles (no queues exist at the beginning or end of a cycle).
D/D/1 signalized intersection queuing with approach capacity (sg) exceeding arrivals (vC) for all cycles.
v = arrival rate, typically in veh/s, r = effective red time in seconds,
s = departure rate, typically in veh/s, g = effective green time in seconds, and
t = elapsed time since a reference time, typically the start of green or red, in seconds,
C = cycle length in seconds.
tc = time from the start of the effective green until queue clearance in seconds,
