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Lec 16, Ch16, pp.413-424: Intersection delay (Objectives) PowerPoint Presentation

Lec 16, Ch16, pp.413-424: Intersection delay (Objectives)

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Lec 16, Ch16, pp.413-424: Intersection delay (Objectives)

- Know the definitions of various delays taking place at signalized intersections
- Be able to graph the relation between delay, waiting time, and queue length
- Become familiar with three delay scenarios
- Understand the derivation of Webster’s delay model
- Understand the concept behind the modeling of overflow delay
- Know inconsistencies that exist between stochastic and overflow delay models

What we discuss today in class…

- Definition of various delays and a typical time-space diagram for signalized intersections
- 3 delay scenarios
- Webster’s delay model
- Overflow delay model (v/c > 1.0)
- Inconsistencies between stochastic and overflow delay models
- Introduction to the HCM delay model
- Theory vs. reality
- Sample delay computations

Delays

Stopped time delay: The time a vehicle is stopped while waiting to pass through the intersection

Approach delay: Includes stopped time, time lost for acceleration and deceleration from/to a stop

Travel time delay: the difference between the driver’s desired total time to traverse the intersection and the actual time required to traverse it.

Time-in-queue delay: the total time from a vehicle joining an intersection queue to its discharge across the stop-line or curb-line.

- Common MOEs:
- Delay
- Queuing
- No. of stops (or percent stops)

Time-space diagram to show approach delay

Uniform arrival rate assumed, v

Here we assume queued vehicles are completely released during the green.

Note that W(i) is approach delay in this model.

At saturation flow rate, s

Three delay scenarios

This is acceptable.

This is great.

UD = uniform delay

OD = overflow delay due to prolonged demand > supply (Overall v/c > 1.0)

OD = overflow delay due to randomness (“random delay”). Overall v/c < 1.0

A(t) = arrival function

D(t) = discharge function

You have to do something with this signal.

Webster’s intersection delay model (Analytic model) for uniform delay

UDa

Total approach delay

The area of the triangle is the total stopped delay, “Uniform Delay (UD)”.

To get average approach delay/vehicle, divide this by vC

Webster’s intersection delay model (Analytic model) for random delay

UD = uniform delay

Analytical model for random delay

Adjustment term for overestimation (between 5% and 15%)

OD = overflow delay due to randomness (in reality “random delay”). Overall v/c < 1.0

D = 0.90[UD + RD]

Webster’s optimal cycle length model random delay

C0 = optimal cycle length for minimum delay, sec

L = Total lost time per cycle, sec

Sum (v/s)i = Sum of v/s ratios for critical lanes

Delay is not so sensitive for a certain range of cycle length This is the reason why we can round up the cycle length to, say, a multiple of 5 seconds.

Modeling overflow delay when v/c>1.0 random delay

because c = s (g/C), (g/C)(v/c) = (v/s). And v/c = 1.0.

The aggregate overflow delay is:

Since the total vehicle discharged during T is cT,

See the right column of p.418 for the characteristics of this model.

Inconsistencies between stochastic and overflow delay models random delay

The stochastic model’s overflow delay is asymptotic to v/c = 1.0 and the overflow model’s delay is 0 at v/c =0. The real overflow delay is somewhere between these two models.

Comparison of various overflow delay model random delay

Eq. 16-26

Eq. 16-27

The HCM 1994 model looks like:

Eq. 16-25

Theory vs. reality random delay

Isolated intersections

Signalized arterials

HCM uses the Arrival Type factor to adjust the delay computed as an isolated intersection to reflect the platoon effect on delay.

Sample delay computations (p.421) random delay

- Sample computation A:
- Approach volume v = 1000 vph
- Saturation flow rate s = 2800 vphg (2 lanes?)
- g/C = 0.55
- Find average approach delay per vehicle

- Sample computation B:
- Chronic oversaturation
- Two-hour period T = 2 hours
- Approach volume v = 1100 vph
- Saturation flow rate s = 2000 vphg (2 lanes?)
- C = 120 sec
- g/C = 0.52
- Find the total average approach delay per vehicle for the 2 hour period and for the last 15 min

Sample computation C: Apply the HCM 1994 model to the condition described in Sample computation B. What is its implication?

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