Chapter 10: Speed, Travel Time, and Delay Studies10.1 Introduction10.2.2. Uses of spot speed dataSlide 4Slide 510.2 Spot Speed StudiesSpeed Sample SizeLocation, time of day, and duration…10.2.3 Analysis of Spot SpeedSlide 10Slide 11Chi-square (2-) test (So called “goodness-of-fit” test), p.143Steps of Chi-square (2-) testSteps of Chi-square (2-) test (cont)What’s the Chi-square (2-) test testing?p.207 Before and After Spot Speed StudiesSlide 1710.3 Travel-time (travel delay) studiesApplications of travel time and delay data (p.211)10.3.1 Field study techniquesSlide 21Slide 2210.3.2 TT along an arterial: An example of the statistics of TTWhat about travel times?, p.214, Fig 10.3Fig 10.3Slide 2610.4 Intersection Delay StudiesDelay Types4 assumptions made for control delay field measurements (p.219)Slide 30Delay data collection form (fig 10.9 & Handout)Average time-in-queue estimationAdjustments for accel/decel delaySlide 34Slide 35Chapter 10 1Chapter 10: Speed, Travel Time, and Delay StudiesExplain when speed, travel time, and delay studies are neededDetermine how many samples are neededCollect and reduce speed dataCompute descriptive statisticsApply a Chi-square test to speed dataConduct a before and after studyCollect and reduce travel time dataExplain the types of delays experienced at signalized intersectionsCollect and reduce intersection delay dataChapter objectives: By the end of these chapters the student will be able to (we spend 2 lectures for this chapter):Chapter 10 210.1 IntroductionThey are used to evaluate the performance of a traffic facility, like arterials and signalized intersections. “Speed” here is a so-called a spot speed measured by a radar gun, etc., at a point in the facility. If you determine travel time and compute speed for a relatively long section, then it is a space speed.Chapter 10 310.2.2. Uses of spot speed dataSpot speed studies are conducted to estimate the distribution of speeds of vehicles in a stream of traffic at a particular location on a highway.Used for: Establish the effectiveness of new or existing speed limits and/or enforcement practices Establish trends to assess the effectiveness of national policy on speed limits and enforcementSpecific design applications (like sight distance) Specific control applications (yellow/all red timing – the size of dilemma zone depends on speed) Investigation of high-accident locations at which speed is suspected to be a causative factorChapter 10 4Average speedSpeed data Grouped Not grouped Standard deviationSpeed data Grouped Not groupedVariance s2u = uj/Ns = f(ui – u)2N - 110.2.1 and 10.2.4 Speed definitions of interestChapter 10 5Median speedThe speed at the middle value in a series of spot speeds. Or, 50th-percentile speedModal speed The speed value that occurs most frequently in a sample of speedsith-percentile speedThe spot speed below which i percent of the vehicles travel, e.g. 85th-percentile speedPace The range of speed that has the greatest number of observations; usually 10-mph range50%85%See table 10.1.Chapter 10 610.2 Spot Speed StudiesOnce data are collected, the first thing you do is to compute several descriptive statistics to get some ideas about the distribution of the speed data. (Note that many statistical analyses used in traffic engineering assume data are normally distributed.  So, the goal is to check whether they are really normally distributed.)Typical descriptive statistics are: Average speed Variance and standard deviation Median speed Modal speed (or Modal speed range  Needs a histogram) The ith-percentile spot speed Pace  Usually a 10-mph interval that has the greatest number of observations.(These concepts appeared in chapter 7.)Speed Sample SizeChapter 107For percentile speed comparisonsThis table is for two-sided tests.K = z-scoreChapter 10 8Location, time of day, and duration…The objective and scope of the study dictate these.Basic data collectionLike deciding speed limits  Find locations where system characteristics change and TWThSpeed trend analysesAvoid external influences such as traffic lights, busy access roads; off-peak, TWTh  mid blocks of streets, straight,level sections of highwaysSpecific traffic engineering problemsAll other specific purposes  Conduct it at the location of interest and time of dayAt least 1 hour or at least 30 data (if you want to assume normal distribution, but usually you should collect at minimum 100 speeds.)10.2.3 Analysis of Spot SpeedChapter 10 9Chapter 10 10Chapter 10 11PaceChi-square (2-) test(So called “goodness-of-fit” test), p.143Example: Distribution of height data in Table 7-9. H0:The underlying distribution is uniform. H1: The underlying distribution is NOT uniform.The authors intentionally used the uniform distribution to make the computation simple. We will test a normal distribution in class using Excel.5.0-5.25.2-5.45.4-5.65.6-5.85.8-6.06.0-6.26.2-6.46.4-6.66.6-6.86.8-7.00510152025Observed Freq Theoretical FreqNiiiiffn122)(Steps of Chi-square (2-) test Define categories or ranges (or bins) and assign data to the categories and find ni = the number of observations in each category i. (At least 5 bins and each should have at least 5 observations.)Compute the expected number of samples for each category (theoretical frequency), using the assumed distribution. Define fi = the number of samples for each category i.Compute the quantity:Niiiiffn122)(Steps of Chi-square (2-) test (cont)2 is chi-square distributed (see Table 7-11, p.145). If this value is low if our hypothesis is correct. Usually we use  = 0.05 (5% significance level or 95% confidence level). When you look up the table, the degree of freedom is f = N – 1 – g where g is the number of parameters we use in the assumed distribution. For normal distribution g = 2 because we use µ and  to describe the shape of normal distribution.If the computed 2 value is smaller than the critical c2 value, we accept H0.Why g = 2 for normal distribution? See Eq. 7-7 in p.125.What’s the Chi-square (2-) test testing?Assumed distributionExpected distribution (or histogram)Actual histogramChi-square (2-) test tests this relationship.You need to know how to pull out values