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