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169 This appendix discusses freeway demand estimation for the scenario generators. Demand Variability Categorization of demand is done by defining demand patterns in the reliability reporting period (RRP). Specific days with similar demand level are put into one demand pattern. The basis of defining demand pattern consists of two dimensions that account for the monthly and weekly variability of demand in the RRP. Monthly variability usually highlights seasonal demand effect, and the weekly dimension shows the effect of daily variation in demand levels. Demand level should be studied for the facility where the reli- ability analysis is performed. As one of the requirements, agen- cies or analysts should compile demand multipliers for each weekday for all months in the RRP. These demand multi pliers give the ratio of demand for a day-month combination to the annual average daily traffic (AADT) and are used to generate demand values for later FREEVAL-RL (FREeway EVALuationâ Reliability) runs. In the absence of facility-specific demand multipliers or local multipliers from nearby automated traffic recorders, the freeway scenario generator (FSG) can use its own embedded urban or rural default values. Table C.1 shows the demand multipliers for the I-40 eastbound (EB) case study. The text colors in Appendix C tables reflect the collection of pat- terns. The shading of cells provides conditional formatting on a green-to-red color scale, with lower-demand multipliers given a green shading and higher-demand multipliers, a red shading. Demand patterns are defined on the basis of the demand multiplier distribution across the months and weekdays. This task is done by the analyst, although the user can select the FSG default demand pattern. For example, the demand pat- tern for I-40 EB case study was found to be seasonal across the monthly dimension; demand on Monday, Tuesday, and Wednesday fit in one group, and Thursdays and Fridays were in two additional separate groups as shown in Figure C.1. The demand pattern definition for I-40 EB is based on demand level comparison and categorization of days of week and months of year based on the demand level shown in Figure C.1. Table C.2 shows the demand pattern configuration across weekdays and months for the I-40 EB case study. To estimate the probability of each demand pattern, RRP duration (in minutes) with a certain demand pattern is divided by the total RRP duration. Table C.3 presents a schematic of FSG demand patterns configuration for the I-40 EB case study. The demand pattern number is simply an indicator of each level of demand. It begins on the first day of the calendar, and a demand pattern number is assigned to each day inside the RRP. Define pDP(Z) as the probability of Demand Pattern Z, which is computed using Equation C.1: Sum of SP minutes within Demand Pattern Sum of SP minutes in RRP (C.1)DPp Z Z( ) = where SP is study period. For example, the probability of occurrence of Demand Pattern 5 at any time in the RRP is shown in Equation C.2: 5 13 6 60 261 6 60 4.98% (C.2)DPp ( ) = Ã Ã Ã Ã = where the number of SPs (or days) with Demand Pattern 5 is 13, SP is equal to 6 h, and the total number of SPs in the RRP (or days in analysis) is 261. There are two approaches in the FSG to generate the demand data required for FREEVAL: demand data poor and demand data rich. Demand from AADT When agencies do not have access to detailed demand infor- mation for a freeway facility, demand information is A p p e n D i x C Recurring Demand for Freeway Scenario Generator (text continues on page 172)
170 Table C.1. Demand Multipliers for I-40 EB Case Study Day of Week Month Monday Tuesday Wednesday Thursday Friday January 0.996623 1.027775 1.040394 1.052601 1.081612 February 0.939253 1.010728 1.039214 1.092029 1.140072 March 1.043305 1.069335 1.063524 1.110921 1.171121 April 1.073578 1.087455 1.098238 1.161974 1.215002 May 1.076331 1.106182 1.113955 1.157717 1.210434 June 1.078043 1.085853 1.067470 1.138720 1.180327 July 1.082580 1.070993 1.102512 1.147279 1.184981 August 1.046045 1.052146 1.060371 1.093243 1.164901 September 1.016023 1.024051 1.023625 1.074782 1.152946 October 1.048981 1.045723 1.066986 1.107044 1.160954 November 0.974044 0.999947 1.041211 1.081541 1.070354 December 0.974785 0.956475 0.987019 0.916107 1.007695 Figure C.1. Facility average ADT (average daily traffic) per lane by month and day of the week.
171 Table C.2. Demand Pattern Configuration for I-40 EB Case Study Monday Tuesday Wednesday Thursday Friday January 1 1 1 2 3 February 1 1 1 2 3 March 4 4 4 5 6 April 4 4 4 5 6 May 4 4 4 5 6 June 7 7 7 8 9 July 7 7 7 8 9 August 7 7 7 8 9 September 10 11 11 12 12 October 10 11 11 12 12 November 10 11 11 12 12 December 1 1 1 2 3 Table C.3. Partial Listing of Demand Patterns Associated with I-40 EB Case Study Week # January Monday Tuesday Wednesday Thursday Friday Week 1 January na na na na 1/1/2010 (3) Week 2 January 1/4/2010 (1) 1/5/2010 (1) 1/6/2010 (1) 1/7/2010 (2) 1/8/2010 (3) Week 3 January 1/11/2010 (1) 1/12/2010 (1) 1/13/2010 (1) 1/14/2010 (2) 1/15/2010 (3) Week 4 January 1/18/2010 (1) 1/19/2010 (1) 1/20/2010 (1) 1/21/2010 (2) 1/22/2010 (3) Week 5 January 1/25/2010 (1) 1/26/2010 (1) 1/27/2010 (1) 1/28/2010 (2) 1/29/2010 (3) Week 6 February 2/1/2010 (1) 2/2/2010 (1) 2/3/2010 (1) 2/4/2010 (2) 2/5/2010 (3) Week 7 February 2/8/2010 (1) 2/9/2010 (1) 2/10/2010 (1) 2/11/2010 (2) 2/12/2010 (3) Week 8 February 2/15/2010 (1) 2/16/2010 (1) 2/17/2010 (1) 2/18/2010 (2) 2/19/2010 (3) Week 9 February 2/22/2010 (1) 2/23/2010 (1) 2/24/2010 (1) 2/25/2010 (2) 2/26/2010 (3) Week 10 March 3/1/2010 (4) 3/2/2010 (4) 3/3/2010 (4) 3/4/2010 (5) 3/5/2010 (6) Week 11 March 3/8/2010 (4) 3/9/2010 (4) 3/10/2010 (4) 3/11/2010 (5) 3/12/2010 (6) Week 12 March 3/15/2010 (4) 3/16/2010 (4) 3/17/2010 (4) 3/18/2010 (5) 3/19/2010 (6) Week 13 March 3/22/2010 (4) 3/23/2010 (4) 3/24/2010 (4) 3/25/2010 (5) 3/26/2010 (6) Week 14 April 3/29/2010 (4) 3/30/2010 (4) 3/31/2010 (4) 4/1/2010 (5) 4/2/2010 (6) Week 15 April 4/5/2010 (4) 4/6/2010 (4) 4/7/2010 (4) 4/8/2010 (5) 4/9/2010 (6) Week 16 April 4/12/2010 (4) 4/13/2010 (4) 4/14/2010 (4) 4/15/2010 (5) 4/16/2010 (6) Week 17 April 4/19/2010 (4) 4/20/2010 (4) 4/21/2010 (4) 4/22/2010 (5) 4/23/2010 (6) Week 18 May 4/26/2010 (4) 4/27/2010 (4) 4/28/2010 (4) 4/29/2010 (5) 4/30/2010 (6) Week 19 May 5/3/2010 (4) 5/4/2010 (4) 5/5/2010 (4) 5/6/2010 (5) 5/7/2010 (6) Week 20 May 5/10/2010 (4) 5/11/2010 (4) 5/12/2010 (4) 5/13/2010 (5) 5/14/2010 (6) Week 21 May 5/17/2010 (4) 5/18/2010 (4) 5/19/2010 (4) 5/20/2010 (5) 5/21/2010 (6) Week 22 May 5/24/2010 (4) 5/25/2010 (4) 5/26/2010 (4) 5/27/2010 (5) 5/28/2010 (6) Week 23 June 5/31/2010 (4) 6/1/2010 (7) 6/2/2010 (7) 6/3/2010 (8) 6/4/2010 (9) Week 24 June 6/7/2010 (7) 6/8/2010 (7) 6/9/2010 (7) 6/10/2010 (8) 6/11/2010 (9) Note: N/A = not applicable.
172 computed based on the AADT estimated for the facility along with hourly and daily demand multipliers. Mainline and ramp AADTs are entered in the Facility-Basics worksheet of FSG. Each detailed scenario is associated with a base sce- nario. Each base scenario is a combination of a demand pattern, weather, and incident event. The demand associ- ated with each base scenario comes from the demand pattern for which that base scenario is generated. Thus, an aggregated demand multiplier for each demand pattern should be com- puted and applied for each detailed scenario to adjust the demand level. The hourly variation should be incorporated for generat- ing demand distributions for different 15-min time periods for FREEVAL-RL. Hourly demand distributions are entered in the Demand Hourly worksheet in FSG. Because FREEVAL- RL requires a 15-min demand distribution, 15-min demand distributions are estimated using linear interpolation. Define Kt15 minute as the portion of demand in the 15-min time period t, and (Dti)k as the hourly demand in segment i, time period t for detailed scenario k. Equation C.3 shows how (Dti)k is computed. DMDPk is the aggregated demand multiplier for scenario k across its defined demand pattern. This aggregation is done based on the num- ber of days that the demand pattern has. 4 DMDP DAADT 24 (C.3)15 minuteD Kit k t k i( )( ) ( ) ( )= à à à where DAADTi is directional AADT on segment i. Table C.4 presents the demand multipliers for each time period of detailed scenarios. Note that since the I-40 EB case study uses the data-rich approach, data presented in Table C.4 are just for illustrative purposes. Demand from Sensor Data In a data-rich environment, FSG has hourly demands for all time periods of an SP. A 15-min variation is already incorpo- rated in the seed file. The only adjustment that needs to be inserted for generating the demand for a detailed scenario is the daily demand multiplier for the seed SP, which is denoted by DMSeed. The hourly demand in segment i, time period t for detailed scenario k is then computed using Equation C.4: DM DMDP (C.4)Seed Seed D D i t k i t k( ) ( ) ( )= ï£ï£¬  In a data-rich approach, what passes to FREEVAL-RL is basically DMDP DMSeed kï£«ï£ ï£¶ï£¸. Table C.5 shows the demand multipliers for the I-40 EB case study scenario Number 2117. Demand Example: I-40 Study Site The freeways methodology was applied to a 12.5-mi freeway facility on I-40 EB between Mile Markers 278.5 and 291 near Raleigh, North Carolina. The case study facility has a speed limit of 65 mph and a free-flow speed of 70 mph. The RRP over which the analysis was carried included all weekdays of calendar year 2010 in a study period from 2:00 to 8:00 p.m. Figure C.2 shows the location of the study site. The facility is primarily a commuter route that connects Durham, North Carolina (Point A) to Raleigh (Point B) and passes through Research Triangle Park, a major employment center in the area. The two-way facility AADT was approximately 120,000 in 2010; the EB facility experiences recurring congestion in the p.m. peak period. Table C.4. Minute Demand Adjustment Factors
173 Table C.5. Demand Multipliers for I-40 EB Detailed Scenario Number 2117 Source: © 2013 Google. Figure C.2. I-40 facility location.
174 June to August; and September to November) were selected to group similar demand months, as well as months with similar weather conditions. This process resulted in the identification of 12 demand groups, or patterns. Daily and monthly demand factors were calculated from the ratio of ADT for each combination of month and day for 2010 to the AADT, as shown in Table C.6. These values were then averaged for each of the 12 demand patterns emerging from the data. These patterns are depicted in Table C.6 for each collection of contiguous cells with the same cell color background and border color. In the following calibration, the overall demand levels are adjusted to deter- mine the best demand level that recreates the observed operations. Traffic demand data were estimated from counts extracted from permanent side-fire radar sensors placed along the main- line of the facility, supplemented with temporary tube counters placed at the on- and off-ramps for a 2-week period (there are no permanent sensors on the ramps). Side-fire sensor data were collected for all of 2010 at the 15-min level, and daily per lane volumes were calculated at each sensor to determine combinations of days and months that operated similarly. Table C.6 shows the average daily traffic (ADT) per lane trends for 2010, when Mondays through Wednesdays experienced very similar demand levels. Thursday demand levels were more elevated, and Fridayâs were the highest. Although the seasonal variation was not as significant, four seasons, each encom- passing 3 months (December to February; March to May; Table C.6. Demand Factors: Ratio of ADT to AADT by Month and Day of Week SUN MON TUE WED THU FRI SAT Jan 0.617609 0.999005 1.030232 1.042881 1.055117 1.084198 0.662407 Feb 0.763747 0.941499 1.013144 1.041699 1.094640 1.142797 0.837179 Mar 0.794913 1.045799 1.071891 1.066066 1.113577 1.173921 0.940873 Apr 0.817347 1.076144 1.090055 1.100863 1.164751 1.217906 0.911421 May 0.815670 1.078904 1.108827 1.116618 1.160484 1.213328 0.933496 Jun 0.805796 1.080620 1.088449 1.070022 1.141443 1.183148 0.942226 Jul 0.764001 1.085168 1.073553 1.105148 1.150022 1.187813 0.933042 Aug 0.801063 1.048545 1.054661 1.062905 1.095856 1.167686 0.911527 Sep 0.768024 1.018452 1.026499 1.026072 1.077352 1.155702 0.893950 Oct 0.825240 1.051489 1.048223 1.069537 1.109691 1.163729 0.924886 Nov 0.756585 0.976373 1.002337 1.043700 1.084126 1.072912 0.829501 Dec 0.586780 0.977116 0.958762 0.989379 0.918297 1.010103 0.744283