Synchro 6 introduces a new series of traffic analysis called Queue Interactions. Queue Interactions look at how queues can reduce capacity through spillback, starvation, and storage blocking between lane groups.
Spillback is caused when a queue from a downstream intersection uses up all the space on a link and prevents vehicles from entering the upstream intersection on green. (See Figure 1)
Figure 1, Spillback
Starvation occurs when a downstream signal is green, but the signal can not service at full capacity efficiency because the upstream signals is red, see Figure 2.
Figure 2, Starvation
Storage Blocking occurs when queues extend past the opening of the storage bay. Through traffic can block access to the left or right storage bay, or turning traffic can use up the bay space and block through traffic. Figure 3 illustrates storage blocking of left traffic by through traffic.
Figure 3, Storage Blocking
The left turning vehicle is blocked from the left storage bay by through traffic. The signal shows a green left arrow, but no left traffic can reach the stop bar. Storage blocking is a combination of spillback and starvation. In this case the through traffic is causing spillback. The left movement is experiencing starvation because of the spillback.
Queue Interactions have the potential to not just increase delay, but also reduce capacity, even on movements that normally are under capacity. With movements at or above capacity, queue interactions become even more critical because they have the potential to reduce capacity even further.
Historically Synchro has modeled how good coordination can reduce delay. With Queue Interaction modeling, Synchro is modeling how bad coordination or no coordination can exponentially increase delays and reduce capacity.
Queue Interactions look at queues on short links and short turning bays. Less storage space than one full cycle of traffic causes higher delays along with a reduction in capacity. It is not just a bad problem, it is a terrible problem. in addition to the problems previously notes, it is also a safety problem. Vehicles holding at a green light can get rear ended. Vehicles stuck within intersection can get into right angle collision.
Spillback and starvation are tightly interrelated. It is possible to initially have one and not the other; depending on which intersection is more capacity constrained. The reduction in capacity due to starvation will eventually lead to spillback upstream. Spillback and starvation are caused by no coordination or bad coordination in conjunction with short block spacing.
To reduce spillback and starvation; all major movements for a direction need to be green at the same time. Using shorter cycle lengths and/or longer block distances can also reduce queue interaction problems.
The Queue Interaction calculations are used throughout Synchro 6; including the following areas:
A new queue delay term is introduced. All displays and reports that show a percentile delay now have an additional term called Queue Delay. This delay measures the additional delay incurred by the capacity reduction of queues on short links.
Queue delay is part of the objective function used for optimizations. Optimized timing plans will now take into account the affects of queue interactions. This will tend to favor timing plans that hold all movements green simultaneously on short links; and to favor shorter cycle lengths.
The Time-Space Diagrams can now show times where queue interactions occur. Starvation, spillback, and storage blocking times are shown at the stop bar with colored rectangles.
The Coding Error Check feature now looks for queue interaction problems. Any significant problems are reported in detail as a warning.
The Queue report now contains detailed information about the three types of queue interactions. The Queuing penalty is removed.
The queue interactions calculations generally have 3 steps:
1. Determine if the volume per cycle to distance ratio is critical.
2. Determine the capacity reduction, due to the amount of time per cycle that the movement is starved or blocked.
3. Determine the additional delay incurred by this capacity reduction.
The first step is to determine if the ratio of volume per cycle to distance is critical. Queue Interactions only cause a reduction in capacity when the storage space is less than one cycles worth of traffic.
If a movement is over capacity, it will cause spillback at any distance; but system capacity will not be reduced because there is enough storage space to accommodate an entire cycle of traffic.
A link is subject to spillback and starvation whenever:
Min(capDist, volDist) > Dist
capDist = L * [2 + C * c / (n * 3600)] = distance per lane used by one cycle of capacity
volDist = L * [2 + v90 * C / (n * 3600)] = distance per lane used by one cycle of 90th percentile volume
Dist = Internal Link Distance
c = lane group capacity
n = number of lanes
v90 = 90th percentile volume
C = cycle length
L = average vehicle length
The addition of 2 vehicles is to accommodate a possible truck.
A storage bay is subject to storage blocking whenever:
Min(capDist, volDist) > Store
Store = Storage Bay Distance
This test must be true for both the blocking and the blocked movement. Both movements need to have a queue extending past the storage bay opening for an interaction to occur.
These tests don’t actually determine if queue interactions are occurring, only if they have the potential to occur.
The next step is to determine the time that the movement is blocked or starved. For storage blocking and spillback, the capacity during this time will be zero. For starvation, the capacity during this time will be reduced to the upstream saturation flow rate active at the time.
The time-space diagram in Figure 4 illustrates a case of starvation.
Figure 4, Starvation in Time Space View
Note that at the beginning of green vehicles begin to clear the queue at point (1), the queue is drained at time (2) and the last queued vehicle clears the stop bar at time (3). From time (3) to time (4) the only vehicles that can be serviced are those that enter the intersection from times (2) to time (5). The storage space can not be used after time (3).
If the upstream signal is red between times (2) and (5), only vehicles using the intersection will be vehicles turning from side streets upstream or entering mid-block. The capacity of the downstream intersection is limited by the saturated flow rate of allowed movements upstream during this time.
For starvation analysis, the green time is divided into two portions. The beginning of green for Tq is able to clear vehicles stored on the link. After Tq, the capacity is limited to the upstream saturated flow rates of traffic given a green during that time.
Tq = queue clearance time = D/L/[s/(n*3600)]
D = link distance
s = saturated flow rate
Refer to Figure 5 for an example.
Figure 5, Starvation Capacity Reduction
Figure 5(a) shows the basic capacity for the downstream intersection versus time for one cycle. Figure 5(b) shows the upstream saturated flow rates for vehicles bound to the downstream intersection. The saturated flow rates are adjusted to account for the proportion of vehicles in that stream bound for this movement. Note that there is a big flow for the upstream through movement, and smaller flow on red for vehicles turning from side streets upstream. Figure 5(b) is time adjusted to account for the travel time between intersections.
Figure 5(c) shows the combination of the two flow profiles. The shaded area is the reduced starvation capacity. The difference between Figure 5(a) and Figure 5(c) is the reduction in capacity due to starvation.
In the case where the upstream intersection has a different cycle length, the average volume is used for the capacity during the Starvation time.
Figure 6, Reduced Starvation Capacity
Note that at some cycles the starvation time will be fully utilized and other cycles will be starved.
The link clearance time for a 300 ft link with sat flow of 2000 vphpl is:
tQ = 300ft / 25ft / (2000/3600) = 21.6 s
If the two intersections operate at different cycle lengths, starvation may occur on some cycles but not others. Over time the flow rate serviced after time tQ will be equal to the volume. During some cycles it will be greater and some cycles it will be less.
The capacity at the downstream intersection is reduced depending on the amount of vehicles that can be serviced after tQ.
If starvation is a potential problem, its essential to use good signal coordination and/or shorter cycle lengths.
For spillback analysis, the upstream capacity will be zero whenever the queue extends to the upstream link.
Refer to Figure 7. The first step is to simulate the traffic flow of the downstream movement. This will determine the queue time upstream. In Figure 7 this is from time (2) to (4). The capacity of the upstream movement(s) are reduced to zero during this time.
Figure 7, Spillback in Time Space View-2
Note that side street movements may also have their capacity reduced during the spillback time. If a side street lane group has two lanes of Thru and Thru-Right, its capacity will be reduced by ½ during the time the right movement is blocked.
In the case where the two intersections have different or variable cycle lengths, the calculations are performed multiple times. The upstream intersection’s departure and capacity profiles are rotated at 5 second increments over their entire cycle. At each 5 second increment, the profiles are truncated or extended to match the downstream cycle length and the spillback analysis is performed. The capacity reduction is averaged for all the 5 second offset rotations. This allows all offset combinations to be evaluated and considered. It is likely the spillback affects will vary greatly among offset rotations. It is necessary to test all offset rotations in order to determine whether there are damaging spillbacks with incompatible cycle lengths.
For half cycling or double cycling, offset rotation is not used; the analysis is performed using a double cycle.
For queue delay calculations the capacity reduction is calculated using both 50th percentile traffic and 90th percentile traffic with the 50th percentile traffic counting for 2/3 of the total.
crSB = (crSB50 * 2 + srSB90)/3 = capacity reduction due to spillback
crSB50 = capacity reduction due to spillback using 50th percentile traffic
crSB90 = capacity reduction due to spillback using 90th percentile traffic
Storage blocking combines a spillback and a starvation analysis. The first step is to determine the time that the entrance to the storage bay is blocked by the blocking movement.
Refer to Figure 8. In this example through traffic is simulated for a cycle to determine the queue time at the top of the storage bay. In Figure 8 this is from time (1) to (2).
Figure 8, Storage Blocking in Time Space View (Through Traffic)-2
Refer to Figure 9 , this shows left traffic on the same link.
Figure 9, Storage Blocking in Time Space View (Left Turn Traffic)
Next the storage clearance time is determined:
tS = storage clearance time = St/L/[s/(n*3600)]
St = storage distance
The time from (3) to (5) is the storage clearance time. From time (5) to (6), the capacity will be zero if the storage entrance is blocked.
Figure 10(a) shows the basic capacity for the blocked movement versus time for one cycle. Figure 10(b) shows the time the entrance to the storage bay is blocked. Figure 10(b) is time adjusted to account for travel time.
Figure 10, Storage Blocking Capacity Reduction
Figure 10(c) shows the combination of the two flow profiles. The capacity is reduced after ts whenever the storage bay is blocked. The shaded area is the reduced storage blocking capacity. The difference between Figure 10(a) and Figure 10(c) is the reduction in capacity due to storage blocking.
crB = (crB50 * 2 + crB90)/3 = capacity reduction due to storage blocking
crB50 = capacity reduction due to storage blocking using 50th percentile traffic
crB90 = capacity reduction due to storage blocking using 90th percentile traffic
Queue delay is the additional delay associated with the capacity reduction of queue interactions. It is calculated using the incremental delay formula with and without the capacity reduction.
The purpose is to penalize queue interactions that increase v/c above 1, but not penalize queue interactions that keep v/c < 1. This delay also penalizes interactions in proportion to the amount they increase delay by reducing capacity on the critical links.
d2 = incremental delay = 900*T*[(X – 1) + sqrt(( X – 1)^2 + (8*k*I*X / (c*T)) ) ]
T = duration of analysis period (hours)
X = v/c = volume to capacity ratio
c = capacity
k = incremental delay factor, 0.50 is used here because these movements are at capacity
I = upstream filtering, 0.3 is used here, because these movements are metered
qd = queue delay = d2’ – d2
d2’ = incremental delay using c – cr instead of c
cr = capacity reduction due to queue interactions = max(crB, crSB, crS)
crB = capacity reduction due to storage blocking
crSB = capacity reduction due to spillback
crS = capacity reduction due to starvation.
Here are some examples of how capacity reduction affects queue delay:
v
c
cr
X
X'
qd
800
1000
100
0.80
0.89
2.3
900
0.90
1.00
12.0
1.11
martinibb