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CEE 764 – Fall 2010CEE 764 – Fall 2010
Topic 6Topic 6
DelayDelay andand OffsetOffset
CEE 764 – Fall 2010CEE 764 – Fall 2010
DelayDelay
Delay:Delay: the most commonly used performance the most commonly used performance measure measure
Types of Intersection Types of Intersection DelaysDelays Stopped delayStopped delay Total delay (control delay)Total delay (control delay) Time in queue delayTime in queue delay
CEE 764 – Fall 2010CEE 764 – Fall 2010
Delay StudiesDelay Studies
Stopped Delay
Total Delay(Control Delay)
Deceleration Acceleration
Stop Line
Time
Distance
CEE 764 – Fall 2010CEE 764 – Fall 2010
Time in Queue DelayTime in Queue Delay
Stopped Delay
Time in Queue Delay
Stop Line
Time
Distance
CEE 764 – Fall 2010CEE 764 – Fall 2010
The HCM Delay EquationThe HCM Delay Equation
321 ddPFdd
CgX
CgCd
/),1min(1
/15.0 2
1
cT
klXXXTd
8)1()1(900 2
2
Uniform Delay
CEE 764 – Fall 2010CEE 764 – Fall 2010
Uniform DelayUniform Delay
Cumulative Departurer
Cum
ulat
ive
Arr
ival
CgX
CgCd
/),1min(1
/15.0 2
1
gg0
V
S
C
CEE 764 – Fall 2010CEE 764 – Fall 2010
Uniform DelayUniform Delay
Cumulative DepartureC
Cum
ulat
ive
Arr
ival V
S
C
S
CEE 764 – Fall 2010CEE 764 – Fall 2010
Random and Over-saturation DelayRandom and Over-saturation Delay
Cumulative DepartureC
Cum
ulat
ive
Arr
ival V
S
C
S
CEE 764 – Fall 2010CEE 764 – Fall 2010
Delay with Initial QueueDelay with Initial Queue
Cumulative DepartureC
Cum
ulat
ive
Arr
ival
V
S
C
S
CEE 764 – Fall 2010CEE 764 – Fall 2010
Uniform Delay with Platoon ArrivalUniform Delay with Platoon Arrival(Platoon on Red)(Platoon on Red)
Cumulative Departurer
Cum
ulat
ive
Arr
ival
g
V np
S
C
V p
N
CEE 764 – Fall 2010CEE 764 – Fall 2010
Uniform Delay with Platoon ArrivalUniform Delay with Platoon Arrival(Platoon on Green)(Platoon on Green)
Cumulative Departurer
Cum
ulat
ive
Arr
ival
g
V np
S
C
V p
N
CEE 764 – Fall 2010CEE 764 – Fall 2010
ExampleExample
Assume a two-lane one-way street links two Assume a two-lane one-way street links two intersections intersections ii and and jj, which is 800 feet apart. The one-, which is 800 feet apart. The one-way link flow is all through traffic and has a volume of way link flow is all through traffic and has a volume of 1000 vph. Saturation flow rate is all 1800 vphpl. 1000 vph. Saturation flow rate is all 1800 vphpl. Assume vehicle travel speed is 25 mph. The system Assume vehicle travel speed is 25 mph. The system cycle is 70 sec, and the effective arterial through greens cycle is 70 sec, and the effective arterial through greens for the upstream (for the upstream (ii) and downstream () and downstream (jj) intersections ) intersections are 35 sec and 30 sec, respectively. The offsets are 0 are 35 sec and 30 sec, respectively. The offsets are 0 and 20 sec for the two intersections, referencing to the and 20 sec for the two intersections, referencing to the start of green of the arterial phases (i.e., arterial phase start of green of the arterial phases (i.e., arterial phase green at green at jj starts 20 sec later after starts 20 sec later after ii). ).
Calculate the uniform delay at intersection Calculate the uniform delay at intersection jj considering considering (1) no platoon dispersion; (2) with platoon dispersion (1) no platoon dispersion; (2) with platoon dispersion ((αα=0.35, =0.35, ββ=0.80); (3) What if the offset is 40 sec?=0.80); (3) What if the offset is 40 sec?
CEE 764 – Fall 2010CEE 764 – Fall 2010
No Platoon DispersionNo Platoon Dispersion
Timet0
Flo
w R
ate
gu
C
s
v
ru
Timegd
C
s
v
rd
T.T
θ
CEE 764 – Fall 2010CEE 764 – Fall 2010
Offset - 20Offset - 20
Delay = 3.7 sec/veh
CEE 764 – Fall 2010CEE 764 – Fall 2010
Offset - 40Offset - 40
Delay = 13.6 sec/veh