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Chapter 20 1 Chapter 20: Basic principles of intersection signalization Explain the meanings of the terms related to signalized intersections Explain the relationship among discharge headway, saturation flow, lost times, and capacity Explain the “critical lane” and “time budget” concepts Model left-turn vehicles in signal timing State the definitions of various delays taking place at signalized intersections Graph the relation between delay, waiting time, and queue length Explain three delay scenarios (uniform) Explain the components of Webster’s delay model and use it to estimate delay Explain the concept behind the modeling of random and overflow delay Know inconsistencies existing between stochastic and overflow delay models Chapter objectives: By the end of this chapter the student will be able to:

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Chapter 20 2 Four critical aspects of signalized intersection operation discussed in this chapter 1. Discharge headways, saturation flow rates, and lost times 2. Allocation of time and the critical lane concept 3. The concept of left-turn equivalency 4. Delay as a measure of service quality

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Chapter Components of a Signal Cycle Cycle length Phase Interval Change interval All-red interval (clearance interval) Controller

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Chapter 20 4 Signal timing with a pedestrian signal: Example IntervalPine St.Oak St.% Veh.Ped.Veh.Ped. 1G-26W-20R-31DW FDW Y-3.5DW R-25.5AR 2.7 5G-19W FDW Y-3DW R-2AR 3.6 Cycle length = 55 seconds

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Chapter Signal operation modes and left-turn treatments & Left-turn treatments Operation modes: Pretimed (fixed) operation Semi-actuated operation Full-actuated operation Master controller, computer control, adaptive traffic control systems for coordinated systems Left-turn treatments: Permitted left turns Protected left turns Protected/permitted (compound) or permitted/protected left turns

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Chapter 20 6 Factors affecting the permitted LT movement LT flow rate Opposing flow rate Number of opposing lanes Whether LTs flow from an exclusive LT lane or from a shared lane Details of the signal timing

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Chapter 20 7 CFI (Continuous Flow Intersection) Bangerter Highway & 3500 South

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Chapter 20 8 DDI (Diverging Diamond Interchange)

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Chapter 20 9 Four basic mechanisms for building an analytic model or description of a signalized intersection Discharge headways at a signalized intersection The “critical lane” and “time budget” concepts The effects of LT vehicles Delay and other MOEs (like queue size and the number of stops)

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Chapter Discharge headways, saturation flow, lost times, and capacity h Vehicles in queue Δ(i) Start-up lost time Saturation flow rate Capacity Cycle length Effective green Startup lost time Clearance lost time Total lost time Extension of green e GiGi yiyi ar i

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Sample problem, p. 467 Chapter First approach: Second approach: Eq. 20-6

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Saturation flow rates from a nationwide survey Chapter 20 12

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Chapter The “critical lane” and “time budget” concepts Each phase has one and only one critical lane (the most intense traffic demand). If you have a 2-phase signal, then you have two critical lanes Total loss in one hour Total effective green in one hour Max. sum of critical traffic demand; this is the total demand that the intersection can handle. N = No. of phases; t L = Lost time in seconds per phase; C = Cycle length, sec; h = saturation headway, sec/veh

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Chapter Finding an Appropriate Cycle Length Desirable cycle length, incorporating PHF and the desired level of v/c The benefit of longer cycle length tapers around 90 to 100 seconds. This is one reason why shorter cycle lengths are better. N = # of phases. Larger N, more lost time, lower V c. Doesn’t this look like the Webster model? Eq Eq

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Chapter Webster’s optimal cycle length model C 0 = 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.

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Chapter Finding an Appropriate Cycle Length (Review the sample problem on page 473) Marginal gain in V c decreases as the cycle length increases. Desirable cycle length, C des Cycle length 100% increase V c 8% increase Fig. 20.4

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A sample problem, p.473 Chapter 20 17

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Chapter The Concept of Left-Turn (and Right- Turn) Equivalency In the same amount of time, the left lane discharges 5 through vehicles and 2 left-turning vehicles, while the right lane discharges 11 through vehicles.

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Chapter Left-turn vehicles are affected by opposing vehicles and number of opposing lanes. The LT equivalent increases as the opposing flow increases. For any given opposing flow, however, the equivalent decreases as the number of opposing lanes is increased

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Chapter Left-turn consideration: 2 methods Given conditions: 2-lane approach Permitted LT 10% LT, TVE (E LT ) =5 h = 2 sec for through Solution 1: Each LT consumes 5 times more effective green time. Solution 2: Calibrate a factor that would multiply the saturation flow rate for through vehicles to produce the actual saturation flow rate.

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Chapter Delay as an MOE Common MOEs: Delay Queuing No. of stops (or percent stops) 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. Control delay: time-in-queue delay + acceleration/deceleration delay)

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Chapter Basic theoretical models of delay At saturation flow rate, s 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. The area of the triangle is the aggregate delay. Figure 20.10

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Chapter Three delay scenarios This is great. This is acceptable. If this is the case, we have to do something about this signal. A(t) = arrival function D(t) = discharge function UD = uniform delay OD = overflow delay due to randomness (“random delay”). Overall v/c < 1.0 OD = overflow delay due to prolonged demand > supply (Overall v/c > 1.0)

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Chapter Arrival patterns compared HCM uses the Arrival Type factor to adjust the delay computed as an isolated intersection to reflect the platoon effect on delay. Isolated intersections Signalized arterials

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Chapter Webster’s uniform delay model, p480 The area of the triangle is the aggregated delay, “Uniform Delay (UD)”. UD a Total approach delay To get average approach delay/vehicle, divide this by vC

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Chapter Modeling for random delay, p.481 UD = uniform delay OD = overflow delay due to randomness (in reality “random delay”). Overall v/c < 1.0 Adjustment term for overestimation (between 5% and 15%) Analytical model for random delay D = 0.90[UD + RD]

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Random delay derivation Chapter Chapter 20.

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Chapter Modeling overflow delay because c = s (g/C), divide both sides by v and you get (g/C)(v/c) = (v/s). And v/c = 1.0. The aggregate overflow delay is: Because the total vehicle discharged during T is cT, See the right column of p.482 for the characteristics of this model.

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Average overflow delay between T 1 and T 2 Chapter Average delay/vehicle = (Area of trapezoid)/(No. vehicles within T 2 -T 1 ). Derive it by yourself. Hint: the denominator is c(T 2 -T 1 ).

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Chapter Inconsistencies in random and overflow 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 =1.0. The real overflow delay is somewhere between these two models.

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Chapter Comparison of various overflow delay model Delay model in the HCM 2000 The 4 th edition dropped the HCM 2000 model (I don’t know why…). It looks like Akcelik’s model that you see in p. 484 (eq ). These models try to address delays for 0.85

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Chapter Sample delay computations We will walk through sample problems (pages ). This will review all delay models we studied in this chapter. Start reading Synchro 9.0 User Manual and SimTraffic 9.0 User Manual. We will use these software programs starting Mon, October 20, 2014.

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