Lec 16, Ch16, pp.413-424: Intersection delay (Objectives)What we discuss today in class…DelaysTime-space diagram to show approach delayThree delay scenariosWebster’s intersection delay model (Analytic model) for uniform delayWebster’s intersection delay model (Analytic model) for random delayWebster’s optimal cycle length modelModeling overflow delay when v/c>1.0Inconsistencies between stochastic and overflow delay modelsComparison of various overflow delay modelTheory vs. realitySample delay computations (p.421)Lec 16, Ch16, pp.413-424: Intersection delay (Objectives) Know the definitions of various delays taking place at Know the definitions of various delays taking place at signalized intersectionssignalized intersectionsBe able to graph the relation between delay, waiting Be able to graph the relation between delay, waiting time, and queue lengthtime, and queue lengthBecome familiar with three delay scenariosBecome familiar with three delay scenariosUnderstand the derivation of Webster’s delay modelUnderstand the derivation of Webster’s delay modelUnderstand the concept behind the modeling of Understand the concept behind the modeling of overflow delayoverflow delayKnow inconsistencies that exist between stochastic and Know inconsistencies that exist between stochastic and overflow delay modelsoverflow delay modelsWhat we discuss today in class…Definition of various delays and a typical time-space Definition of various delays and a typical time-space diagram for signalized intersectionsdiagram for signalized intersections3 delay scenarios3 delay scenariosWebster’s delay modelWebster’s delay modelOverflow delay model (v/c > 1.0)Overflow delay model (v/c > 1.0)Inconsistencies between stochastic and overflow delay Inconsistencies between stochastic and overflow delay modelsmodelsIntroduction to the HCM delay modelIntroduction to the HCM delay modelTheory vs. realityTheory vs. realitySample delay computationsSample delay computationsDelaysCommon MOEs:• Delay• Queuing• No. of stops (or percent stops)Stopped time delay: The time a vehicle is stopped while waiting to pass through the intersectionApproach delay: Includes stopped time, time lost for acceleration and deceleration from/to a stopTravel 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.Time-space diagram to show approach delayAt saturation flow rate, sUniform arrival rate assumed, vHere we assume queued vehicles are completely released during the green.Note that W(i) is approach delay in this model.Three delay scenariosThis is great.This is acceptable.You have to do something with this signal.A(t) = arrival functionD(t) = discharge functionUD = uniform delayOD = overflow delay due to randomness (“random delay”). Overall v/c < 1.0OD = overflow delay due to prolonged demand > supply (Overall v/c > 1.0)Webster’s intersection delay model (Analytic model) for uniform delay vsvsCgCVvsvRtsttRvVCgCRccc11The area of the triangle is the total stopped delay, “Uniform Delay (UD)”.vsvsCgCheightbaseUDa22121))((21UDaTotal approach delayTo get average approach delay/vehicle, divide this by vC    svCgCUD1122Webster’s intersection delay model (Analytic model) for random delayUD = uniform delayOD = overflow delay due to randomness (in reality “random delay”). Overall v/c < 1.0           CgcvvccvvcvsvCgCD23122265.0/12112Adjustment term for overestimation (between 5% and 15%)Analytical model for random delayD = 0.90[UD + RD]Webster’s optimal cycle length model 10155.1iisvLCC0 = optimal cycle length for minimum delay, secL = Total lost time per cycle, secSum (v/s)i = Sum of v/s ratios for critical lanesDelay 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     2)(11122CgCsvCgCUDobecause c = s (g/C), (g/C)(v/c) = (v/s). And v/c = 1.0.   cvTcTvTTODa2212The aggregate overflow delay is:Since the total vehicle discharged during T is cT,  12 cvTODSee the right column of p.418 for the characteristics of this model.  1221 cvTTODInconsistencies between stochastic and overflow delay models           CgcvvccvvcvsvCgCD23122265.0/12112  12 cvTODThe 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 modelEq. 16-25Eq. 16-26Eq. 16-27       cXXXXXCgCgCd16111731138.0222The HCM 1994 model looks like:Theory vs. realityIsolated intersectionsSignalized arterialsHCM 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)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 vehicleSample 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 minSample computation C: Apply the HCM 1994 model to the condition described in Sample computation B. What is its