Incorporating Travel Time Reliability into the Highway Capacity Manual (2014) / Chapter Skim
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37 C h a p t e r 5 This chapter discusses the development of scenario generators for freeway facilities and urban streets. It is divided into the following seven sections: 1.
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38 of time in the reliability reporting period (RRP) that the facility is expected to be operating under this condition.
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39 factors, such as demand, to vary by other factors, such as weather type. However, explicit consideration of factor interactions of this type must be handled during postprocessing of the automatically generated detailed scenarios.
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40 demand pattern for the I-40 EB case study was found to be seasonal across the monthly dimension. Furthermore, demand on Mondays, Tuesdays, and Wednesdays could be considered as one group, while Thursdays and Fridays were unique and classified as two additional, separate groups.
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41 provides a VBA module and weather database for computing the probability of different weather types as a function of the facility's geographic location, and time of day coincident with the SP. The weather database includes 10-year averages of hourly logs for 101 metropolitan areas in the United States.
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42 probability of incident type i in month j is computed from Equation 5.3: p i j j i j ( )
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43 Prob Demand Level , Weather Type , Incident Type Prob Demand Level Prob Weather Type Prob Incident Type (5.4) i j k i j k { } { } { } { }= × × Note that some dependencies between event occurrences are inherent through the use of the calendar.
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44 In fact, the base scenarios describe the operational condition of the freeway facility and the probability associated with it. The probability of a base scenario specifies the expected portion of time that the freeway facility is subject to operating at the scenario-specified conditions.
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45 a period of time equal to its probability times the study period duration. The term time-wise distinguishes this probability from other types of probabilities, such as VMT-wise, countwise, or length-wise probabilities.
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46 the events and the study period, what should the study period scenario probability values p1, p2, p3, and p4 be to provide consistent time-based probabilities throughout? The study period scenario probabilities should be selected in such a way that the likelihood of the conditions modeled is identical to the base scenario probabilities.
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47 Detailed scenario probability = π1 Detailed scenario probability = π2/2 Detailed scenario probability = π3/18 Detailed scenario probability = π4/18 Demand Demand and weather Demand and incident Demand, weather, and incident Figure 5.4. Event occurring during each analysis period of selected detailed scenarios.
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48 allowing the resulting travel time distribution to be properly aggregated. The final results of applying the adjusted probabilities for the I-40 EB case study are shown in Table 5.8.
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49 the three possible incident durations are selected to be at, below, and above the originally assumed mean duration. • Modeling in FREEVAL requires all events to be rounded to the nearest 15-min increment, to be consistent with HCM analysis period durations.
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50 Table 5.10. Subset of Base Scenarios Associated with Demand Pattern 1 Base Scenario No.
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51 Figure 5.6. Probability adjustment methodology for SP scenarios.
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52 weather and five incident categories. The incident categories are no incident, shoulder closure, one-lane closure, two-lane closure, and three-lane closure.
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53 Step 3: Calculate Category 4 SP Scenario Probability Denote pij and pij as the probabilities of base scenarios and SP scenarios, respectively. The duration of the study period is symbolized by SP.
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54 Step 4: Check the Necessity for Modeling More than One Event in Category 4 Scenarios The sum of all probabilities generated in Step 3 for Category 4 scenarios should be less than the total sum of the base scenario probabilities. Otherwise, the SP scenarios must model more than one event (or overall duration)
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55 Denote bij as an indicator variable, where 1, if the flag of scenario with weather type and incident type is ; 0, Otherwise.
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56 Note that after modeling two incidents in the Category 4 scenario associated with light snow and shoulder closure, the wij and Dij values should be updated for that specific scenario. Step 7: Calculate Remaining Probabilities of Category 2 and 3 Scenarios To model events in Category 2 and 3 scenarios, their base scenario remaining probabilities (in addition to the Category 4 residuals)
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57 generate SP scenario probabilities for Categories 2 and 3. Because pij is the remaining probability in Step 7, the probability of a Category 2 scenario is computed by using Equation 5.29.
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58 Category 3 (incident-only) scenarios are the targets.
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59 Weather events, however, are assumed to affect the entire facility at once. Thus, the two principal weather parameters in developing detailed scenarios are the event start time and duration.
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60 demand patterns, a maximum of 22,932 detailed scenarios can be generated.
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61 Figure 5.7. Operational number of lanes under detailed scenario 2117.
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62 Figure 5.9. CAF table for I-40 EB case study detailed scenario 2117.
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63 Freeway Summary and Conclusions The preceding sections of this chapter have presented the scenario generation process for evaluating travel time reliability on freeway facilities. In general, three factors affect travel time variability: traffic demand, weather, and incidents.
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64 Step 2: Precipitation Type If precipitation occurs, then Equation 5.37 is used to estimate the average temperature during the weather event for the subject day.
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66 reliability evaluation, total rainfall is assumed to be perfectly correlated with rainfall rate such that they share the same random number. This approach may result in slightly less variability in the estimated total rainfall; however, it precludes the occasional calculation of unrealistically long or short rain events.
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67 beyond midnight. To ensure this outcome, the duration computed from Equation 5.45 is compared with the time duration between the start of the rain event and midnight.
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68 order. Within a given day, the procedure considers only those hours that occur during the study period.
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69 Step 1: Compute the Equivalent Crash Frequency for Weather A review of the safety literature indicates that crash frequency increases when the road is wet, covered by snow, or covered by ice (Maze et al.
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70 and dry pavement, rt: rainfall, wp: wet pavement but not raining, sf: snowfall, sp: snow or ice on pavement but not snowing) for street location i of type str (str = int: intersection, seg: segment)
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71 provided by the analyst. Otherwise, CFAFstr and CFAFint equal 1.0.
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72 lan (lan = 1L: one lane, 2L: two or more lanes, sh: shoulder) , and severity sev (sev = pdo: property damage only, fi: fatal or injury, bkd: breakdown, oth: other)
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73 Step 5 is used to determine the incident location. For intersections, the location is determined to be one of the intersection legs.
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74 dvseg(i) , n = directional volume for the direction of travel served by NEMA Phase n on segment i, veh/h.
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75 = + + 1.0 1.0 0.48 R 0.39 R (5.59) rs,ap, r,ap, s,ap, f d d d where frs,ap,d = saturation flow adjustment factor for rainfall or snowfall rs, during analysis period ap and day d; Rr,ap,d = rainfall rate during analysis period ap and day d, in./h; and Rs,ap,d = precipitation rate when snow is falling during analysis period ap and day d, in./h.
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76 segments Perrin et al.
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77 adjusts the saturation flow rate on the basis of the number of lanes blocked by the incident. If the incident is located on the shoulder or in the lanes associated with another movement m (i.e., Nic = 0)
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78 develop the trend lines shown in this figure were based on simulated flow rates for 144 hours at each of seven average flow rates. The flow rate for each 15-min period in a given hour was computed using Monte Carlo methods with a gamma distribution, and a standard deviation that computed as factor f times the square root of the flow rate.
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79 Ifi, seg(i) , n, ap, d = indicator variable for fatal-or-injury crash in the direction of travel served by NEMA Phase n on segment i during analysis period ap and day d (= 1.0 if fatal-or-injury crash, 0.0 otherwise)
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