**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

**Suggested Citation:**"Appendix F - Incident Probabilities Estimation for Freeway Scenario Generator." National Academies of Sciences, Engineering, and Medicine. 2014.

*Incorporating Travel Time Reliability into the Highway Capacity Manual*. Washington, DC: The National Academies Press. doi: 10.17226/22487.

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205 Incidents Defined and Classified An incident is an unplanned disruption to the capacity of the facility. Incidents do not need to block a travel lane to disrupt the capacity of the facility. They can be a simple distraction within the vehicle (e.g., spilling coffee) or on the side of the road or the reverse direction of the facility. Incidents can be classified according to the response resources and procedures required to clear the incident. This classifica- tion helps in identifying strategic options for improving inci- dent management. However, the 2010 Highway Capacity Manual (HCM2010) (Transportation Research Board of the National Academies 2010) classifies incidents on freeways only by number of lanes blocked, and if the incident is on the shoulder, by whether it is a collision or not. The HCM does not deal with incidents on urban streets. Section 6I.01 of the Manual on Uniform Traffic Control Devices (Federal Highway Administration 2009) classifies incidents according to their expected duration: â¢ Extended duration incidents are expected to persist for over 24 h and should be treated like work zones. â¢ Major incidents have expected durations of over 2 h. â¢ Intermediate incidents have expected durations of 0.5 h up to and including 2 h. â¢ Minor incidents are expected to persist for less than 30 min. Scenario Generation Fundamentals Estimating the probabilities of incidents is a key element in freeway travel time reliability analyses. Incident probabili- ties feed into the base-scenario generation procedure in order to enumerate and characterize the full variability of the operational status of the freeway facility. Once these opera- tional statuses are analyzed, the estimated travel time distribu- tion can be generated. The estimated travel time distribution, in turn, provides the primary basis for reliability performance assessment. In the SHRP 2 Project L08 analysis, three basic stochastic events affect travel time: variability in demand, weather, and incidents (Rouphail et al. 2012). The goal of this section is to stochastically model incidents on a freeway facility and characterize the properties that are capable of providing the required information for the reliability performance assess- ment. Specifically, this section provides the methodology for probability estimation of incident scenarios. Incidents are stochastic in nature in that their occurrence and duration are probabilistic with certain distributions and parameters. The location and start time are two other stochastic dimensions of incident occurrence. The freeway scenario generator (FSG) provides the analyst with multiple paths to estimate the required incident occur- rence probabilities. Analysts have the option of directly entering monthly incident probabilities, as well as the option of using national default values to generate the probabilities. In either case, the incident probability for a given time period is the fraction of the overall analysis time period or reliability reporting period that a specific incident type occurs on the facility. This section uses the incident attribute type to address the severity in terms of lateral lane closure. The process flow and theoretical background behind FSG are discussed later in this section. The default values pro- vided in the FSG are based on national data for incidents and crashes from nine freeway facilities. These default val- ues are provided for the analyst to use in the absence of local data. Appropriate mathematical models are required to account for the stochastic behavior of incidents on freeway facilities. The proposed mathematical model is a queuing theory approach that models the freeway as a queuing system in which A p p e n D I x F Incident Probabilities Estimation for Freeway Scenario Generator

206 incidents represent the service provided for vehicles. The inci- dent occurrence rate and its duration are fed into the model to fully characterize the problem. In this study, the I-40 freeway in North Carolina was selected to demonstrate the application of the FSG in esti- mating monthly incident probabilities. A 12.5-mi section of the facility was analyzed in the Research Triangle Park area near Raleigh. Incident data logs (albeit incomplete) were made available to the research team from the North Carolina Department of Transportation (NCDOT) for the year 2010. The estimated probabilities based on the developed mathe- matical models were compared with incident data extracted from the logs. The FSG uses a deterministic approach for creating and characterizing the operational scenarios for a specific facility in a specified reliability reporting period. This deterministic methodology categorizes factors that affect travel time distri- bution. An important limitation of the methodology is the assumption of independence between the various contribut- ing factors. This assumption simplifies the estimation of joint probabilities by simply multiplying the individual factor probabilities. Each unique combination of demand level, weather effect, and incident type is termed a base scenario in the FSG. The incorporation of incident impacts includes one addi- tional step, namely modeling the incident effect within the study period, using the HCM freeway facilities model FREEVAL to estimate the resulting travel time. Incident modeling is done by inserting appropriate capacity adjustment factors (CAFs), free-flow speed adjustment factors (SAFs), and the number of open lanes associated with the incident. This section focuses on incident probability estimation. Table F.1 presents the inci- dent probability table in the FSG used to generate the base scenarios. For example, the probability of having a two-lane closure incident in April is 1.94%. This means that if a study period in April were selected at random, about 1.94% of the duration of that study period (on average) would involve a two-lane closure incident. There are other ways to categorize incidents on freeway facilities. FSG uses the categorization based on incident sever- ity (lane or shoulder closure) and calls those incident types. More detailed information and categorizations are provided in the project teamâs incident white paper. The categories used in the FSG methodology are no incident, shoulder clo- sure, one-lane closure, two-lane closure, three-lane closure, and four-lane closure. It is assumed that this categorization best describes different impacts of incidents on the facility travel time distribution. Data Requirements Implementing agencies that have access to high-quality incident-log data are in a data-rich environment. By high quality, the authors mean precise designation of the sequence of events around the incident, including start time, duration, number of lane closures, clearance time, mileposts affected, and so forth. If such data are not available (which is the majority of cases), then the analyst is advised to use national default values along with certain mathematical models for estimating study period monthly incident probabilities. The second condition is called a data-poor or semi-data-poor environment. Estimating Incident Probabilities in a Data-Rich Environment In data-rich environments, agencies can directly estimate the probabilities for different incident types by analyzing their entries in the incident logs. The data logs should have the Table F.1. Monthly Probabilities for Different Incident Types: I-40 Eastbound

207 incidents recorded and categorized as defined in a previous section of this appendix, along with their durations. Study period monthly probabilities of different incident types are computed from Equation F.1. The study period represents the number of hours in a given scenario in which the facilityâs operations are analyzed. i j j i j { } = Prob incident type in a SP in month Sum of minutes in all SPs in month that incident type is present Sum of all SP minutes in month (F.1) where SP is study period. Equation F.1 gives the fraction of time that incident type i is present on the facility, which is equal to the probability of having an incident at any time instance during the study periods in month j. Specifically, the probabilities required in the FSG are the time-wise probabilities of the presence of certain incident conditions. Conversely, the probabilities do not indicate the frequency or the chance of occurrence of an incident. In a data-rich environment, the monthly incident proba- bilities computed from data logs are inserted in the FSG directly. The quality of data is paramount in this case as there could be some cases of unreported incidents, which could introduce bias and errors into the travel time distribution. The example illustrated in this appendix pertains to I-40 eastbound (EB) in Raleigh in 2010. NCDOT compiled inci- dent data logs for I-40 based on reported incidents. The Traf- fic Management Center is in charge of incident data gathering based on phone calls and reports for incidents. According to the incident data logs, the incidentâs causes are not clear in the majority of cases. However, based on sensor readings from traffic.com, some accurate information is inserted into the database, such as speed of vehicles at the incident time. The I-40 facility incident database contains several attri- butes: freeway name, mile marker, county, city name, start time, end time, and reason/description. The first step is to select the appropriate records from this database. For this pur- pose, all incidents from Mile Marker 279 to 293 of I-40 were filtered and extracted. In 2010, according to crash reports, approximately 90 collisions occurred on the facility; however, the incident log maintained by North Carolinaâs Transporta- tion Information Management System reported only 32 col- lisions. During the peak period, 142 incidents were reported, but 29 of those reports stated âTraffic traveling at 0 mph at Xâ location instead of reporting a lane blockage or the actual location of the incident. The remaining reports were the only ones reporting lane blockages, and of those, only four shoul- der incidents were reported. The distribution of incidents by lane blockage shown in Table F.2 is significantly different from the national urban defaults. The incidents reported do not have enough infor- mation to be modeled at the level of detail required by the FREEVAL model. The research team thus concluded that data in the incident logs were not of sufficient quality for the purpose of this study, given that the generated incident probabilities are uncharacteristically low. This led the SHRP 2 L08 project research team to use a semi-data-poor approach for generating the incident probabilities for the I-40 EB case study. Estimating Incident Probabilities in Data-Poor or Semi-Data Poor Environments Figure F.1 shows the data structure proposed for the predic- tive methodology. The data required in each purple and green box in Figure F.1 can be estimated based on available local data or substituted with national default values. Table F.2. Incident Probabilities for I-40 EB Based on Analysis of Data Logs

208 Incident Rates Estimation in the Study Periods in a Month All subsequent discussions in this section refer to items num- bered 1, 2, and 4 in Figure F.1. Two possible approaches for incident rate estimation can be carried out. The first is by directly estimating the rates from the incident data logs. Alternatively, one can use the prevailing crash rate and apply a local or default crash-to-incident (CTI) factor to compute the incident rate. In the project teamâs incident white paper, the national default value for the CTI rate is 4.9. In the FSG the analyst may also specify a local CTI. Table F.3 presents CTI factors for freeway facilities. For the I-40 EB case study, and based on a study by Khattak and Rouphail (2005), CTI is esti- mated at 7.2. In the current FSG implementation a rounded value of 7.0 has been entered. Factors in this table were developed based on data sets from Washington, Virginia, Florida, Georgia, Maryland, and Cali- fornia for freeways and from Oregon, California, and Illinois for arterials. If the local crash rate is unavailable, or for future scenario analyses (Use Case 2), the HERS model (Federal Highway Administration 2005) is used in the FSG to estimate monthly crash rates on the facility. Agencies may use other predictive models, such as those in the Highway Safety Manual (Ameri- can Association of State Highway and Transportation Offi- cials 2010), to estimate the monthly crash rate for the facility. The crash or incident rate is estimated per 100 million vehicle miles traveled (VMT). The HERS model uses Equation F.2 to estimate the crash rate per 100 million VMT based on a few facility attributes: ( )[ ] = Ã + Ã Ã ï£«ï£ ï£¶ï£¸ Ã Ã CR 154.0 â1.203 ACR 0.258 ACR â 0.00000524 ACR exp 0.0082 12 â LW (F.2) 2 5 where CR = crash rate; ACR = facility annual average daily traffic (AADT) divided by two-way hourly capacity; and LW = lane width, ft. ACR is estimated to be 7.9 h per lane for the I-40 EB case study, which yields a crash rate equal to 159 crashes per 100 mil- lion VMT. The L08 project research team decided to use its own estimate, starting with a local crash rate of 164.5 for urban freeways in Wake County, North Carolina, where the facility resides. Incident Severity This section demonstrates the procedure related to Item 3 (inci- dent severity distribution) in Figure F.1. The distribution of incident severity must be known a priori for incorporation in the methodology. This distribution is defined by G(i), which is assumed to be homogeneous across the facility and demand levels. Agencies can estimate this distribution by analyzing the incident logs or by using the national default values provided Figure F.1. Proposed data structure for estimating incident probabilities in a data-poor environment. Table F.3. Crash- to-Incident (CTI) Factors for Freeway Facilities Statistic CTI Factor Range 2.4â15.4 Average 4.9 Median 6.5

209 in Appendix D and depicted in Table F.4. Equation F.3 gives a definition of G(i) as a discrete distribution, where i denotes the incident type (e.g., i = 1 is equal to shoulder closure and i = 5 is a four-lane closure). 1 2 3 4 5 (F.3) 1 2 3 4 5 i z z z z z g g g g g ( ) = = = = = = ï£± ï£² ï£´ï£´ ï£³ ï£´ï£´ Incident Mean Duration The incident mean duration is naturally required to estimate monthly incidents probabilities based on the formulation in Equation F.1. Although the duration of incidents are proba- bilistic and generally follow a lognormal distribution, in the proposed methodology only the mean value of durations is required for each incident type. Agencies could either enter local mean duration values for the facility or use the national default duration values provided in Table F.4. The duration of incidents is denoted by D(i), and the mean duration of an incident with severity i is expressed by E[D(i)], where i represents the severity of the incident. D(i) follows a discrete distribution of mean duration of incidents. For the I-40 case study, national default durations were incorporated in evaluating monthly incident probabilities. Demand Level The proposed methodology requires the demand level to be known in order to estimate the number and probability of incidents. Specifically, the crash or incident rate is estimated per 100 million VMT, which means that to yield the expected number of incidents, demand and facility length must be known. The demand is characterized based on AADT across the facility, along with a set of demand multipliers that vary the demand levels across the week and between months. In a data-rich environment in which agencies have access to demand data for a specific study period (also called a seed file), VMT can be directly calculated for each 15-min period. Adding these 15-min VMTs yields total VMT for the study period. Demand multipliers are used to adjust the demand for each demand pattern based on the seed file data. Thus, the VMT is divided by the demand multiplier associated with the seed fileâs date. Further dividing the resulting VMT by the fraction of demand in the study period (StâSPkt) produces a good estimate of the directional AADT for the facility. The main reason for estimating the AADT based on VMT is that the demand distribution across the facility is not nec- essarily uniform during each time period, since some ramps could have a different demand distribution (over time) com- pared with the mainline entry AADT. Equation F.4 shows the relationship between study period VMT, segment length, and demand on each facility segment: VMT 4 (F.4) Facility SegmentsSP L Dk k t kt ââ ( ) = Ã ââ where Lk represents the length of segment k, and D t k is the hourly demand on segment k in time period t. Equation F.5 shows how directional AADT can be com- puted when a demand seed file is available: k Ltt fâ( ) = Ã Ã â Directional Average AADT across the facility DAADT = VMT DM (F.5) Seed SP where (StâSPkt) represents the portion of daily demand occur- ring during the study period, and DMSeed is the demand multi- plier associated with the seed file. In cases for which only overall AADT data are available, the directional distribution along with the segments length is used to estimate the directional facility AADT according to Equation F.6: L L k kk kk â â ( ) ( ) ( ) = â â Directional AADT across the facility DAADT = DAADT (F.6) Facility Segments Facility Segments where DAADTk is the directional AADT on segment k. Table F.4. National Default Distribution of Incident Severity and Duration Severity Type of Closure Shoulder Single Lane Two Lanes Threeî± Lanes Mean and probability range 75.4% (28.8â96.3) 19.6% (3.0â65.6) 3.1% (0.5â7.5) 1.9% (0.6â4.3) Meana and duration range (min) 34.0 (8.7â58.0) 34.6 (16.0â58.2) 53.6 (30.5â66.9) 69.6 (36.0â93.3) a Durations are discretized to the nearest 15 min later on. Values are based on data from Washington, Virginia, Florida, Georgia, Maryland, and California.

210 Core Incident Methodology Model This model begins with the widely used assumption that the number of incidents in a given study period is Poisson dis- tributed (Skabardonis et al. 1997). The first step is to compute the expected number of incidents on the freeway facility dur- ing the study period by using Equation F.7: n k Lj j j s f= Ã Ã Ã ÃIR DAADT DM (F.7) where nj = expected number of incidents in a study period (only) in month j; IRj = incident rate per 100 million VMT in month j; DMj = weighted average demand multiplier for month j; ks = fraction of daily demand that occurs during the study period; and Lf = length of facility (mi). Note that DAADT is the directional AADT and could be sub- stituted by AADT Ã DD, where DD is directional distribution. IRj is either known or is estimated from Equation F.8 from CRj, which is the crash rate in month j: = ÃIR CR CTI (F.8)j j M/G/î Queuing Modeling of Incidents on a Freeway Facility A stochastic queuing model is used for modeling incidents in the freeway facility. Table F.5 presents the definition of the queuing model used for computing the probability of incidents. The arrival of vehicles involved in an incident follows the Poisson distribution, because the incident occurrence follows a Poisson distribution with mean nj in month j. The probabil- ity of having x incidents in the SP in month j is computed from Equation F.9. In the queuing systems, this arrival distri- bution is denoted by M (Markovian). P ! (F.9)x n x ej j x nj( ) = â where Pj(x) is the probability of having x incidents in a study period in month j, and nj is the expected number of incidents in the study period for the same month. The service rate has an unknown distribution, where in the queuing systems it is denoted by G (general distribution). Since any lane of any segment of the freeway is operating as a server in the queuing system, the number of servers is infinite in this queuing model. Thus, the queuing model used for modeling incidents in the freeway facility is M/G/â. For the queuing model considered, the probability of hav- ing no incident on the freeway facility is first calculated, and then subtracted from one to yield the incident probability. Because there could be more than one incident, the team rec- ommends the use of complementary probabilities. Equa- tion F.10 shows this computation: i P { } { } { } = â = â = â Prob having one or more type incident 1 Prob having no incidents 1 Prob having no customers in system 1 (F.10)0 Based on Equation F.11, which is founded on the steady state (long-run) probability of having no customers in the queuing system, the probability of having no incident in the freeway facility is defined (Adan and Resting 2001): (F.11)0P e n E ij i= ( )[ ]( )â Ã Ã ; Because the probability of each incident type needs to be estimated separately in the FSG, the incident occurrence rate should multiplied by ;i, because the occurrence of dif- ferent incident types is independent, and ;i is considered homogeneous in time. The occurrence of each incident type Table F.5. Definition of Incidentâs Queuing Model for a Freeway Facility Queuing System Concept Transportation Equivalent Description Arrival rate Incidentâs occurrence rate nj is the arrival rate per SP in month j. Service rate Incidentâs clearance rate 1 E i[ ]( ) is the service rate per SP for incident type i. Service duration Incidentâs duration E i[ ]( ) is the incidentâs mean duration; the unit is the SP. Server Any lane of any segment of the facility There are infinite such servers where the incident can occur on the facility.

211 is also Poisson with the rate nj Ã ;i. Thus, the probability of incident type i in month j is computed using Equation F.12: Prob incident type in an SP in month 1 1 (F.12) 0i j P e n E ij i { } = â = â ( )[ ]( )â Ã Ã ; Thus, the probability of having any incident is set to be equal to the probability of having at least one incident in the system. Equation F.13 is thus the estimation alternative to Equation F.12 when data are not available. The probability of having no incident in the system is equal to one minus the probability of having any incident type (i), with i = 1, 2, . . . , 5. Prob No incident in the system 1 Prob Any type of incident 1 1 (F.13) incident types e n E i i j iâ { } { }= â = â â ( )[ ]( )â Ã Ã â ; Recommended Process Flow Since there could be many paths for agencies to compute the incident probabilities, this section presents a process flow that is compatible with the theoretical aspects of the paper. Table F.6 describes the process flow steps depicted in Figure F.2 and Figure F.3. Figures F.2 and F.3 present the flowchart of the process flow for agencies to follow while completing the Incidents worksheet in the FSG. numerical example for I-40 eB Case Study In this section, a numerical example is provided to demonstrate the detailed calculations executed in the FSG to estimate the incident probabilities per study period in any given month. This example focuses on the probability of a one-lane closure inci- dent to occur in a study period in May 2010 for the I-40 EB case study. The local crash rate used for I-40 EB is 164.5 crashes per Table F.6. Description of Process Flowchart Step Label Description 1 Are incident data logs available for the facility? If an agency has no access to incident data logs, select NO; otherwise select YES. 2 Is quality of data excellent? This step assesses the quality of incident-log data; if minimum quality thresholds are not met, select NO; otherwise select YES. 3 Use Equation F.1 to compute the monthly incident probabilities. Directly estimate the monthly incident probabilities. Equation F.1 can be used for this purpose. 4 Is incident rate available? This step attempts to estimate incident rates based on local data. If those data are available, select YES; otherwise select NO. 5 Use Figure F.3 process for estimating incident rate. Instructions to estimate incident rate are provided in the flowchart in Figure F.3. 5.1 Is crash rate available? If local crash rate (per 100 million VMT) for the facility is available, select YES; otherwise select NO. 5.2 Use HERS model to estimate the crash rate. If local crash rate is unavailable, or for future-year predictions, HERS model is recommended to estimate crash rate for the facility. 5.3 Is crash-to-incident rate available? If CTI factor for the facility is known, select YES; otherwise select NO. 5.4 Use default crash-to-incident rate. CTI = 4.9 should be used in the analysis. 5.5 Use Equation F.8 to compute the incident rate per study period in month. Equation F.8 is used to compute the incident rate. 6 Is incidents severity distribution known? If incident type distribution for facility is known, select YES; otherwise select NO. 7 Use national default values. Use national defaults for distribution of incident types in incident paper. 8 Is duration of incident types known? If mean duration for each incident type is known, select YES; otherwise select NO. 9 Use national default values. Use national defaults for the mean duration of each incident types in incident paper. 10 Using core computational procedure, estimate the monthly incident probabilities per study period. Equations F.7 through F.13 are used to estimate study period incident probabilities for each month.

212 Figure F.2. Proposed process flow.

213 100 million VMT, and the CTI factor is 7 based on local data (Khattak and Rouphail 2005). Table F.7 shows the schematic of the incident data input file for the FSG with this specified con- figuration. The study period duration is 6 h, or 360 min. Table F.8 shows the demand multipliers for I-40 EB for all weekdays in May. The demand multiplier (DM) for May is calculated based on Equation F.14. j j j â ( ) = ï£«ï£ ï£¶ï£¸ Ã DM Number of days in each month with demand pattern DM Total number of days in demand pattern (F.14) for each month Based on Equation F.14, DM5 (i.e., the demand modifier for May, the fifth month) is calculated at 1.13 as shown below: = Ã + Ã + Ã + Ã + Ã = DM 5 1.076 4 1.106 4 1.114 4 1.158 4 1.210 21 1.13 5 The overall incident rate is computed from Equation F.15: j j= Ã = Ã = IR CR CTI 164.5 7 1,151.5 per 100 million VMT (F.15) The 6-h study period overall directional demand factor is 0.3884, and the facility length is 12.5 mi. The average AADT for I-40 is estimated from Equation F.16 and Equa- tion F.17. L Dk ktk t ââ ( )= Ã = â â VMT 4 330,006 vehicle miles (F.16) Facility Segments SP â( ) = = Ã = Ã Ã = â Directional AADT across the facility DAADT VMT DM 330,006 1 0.3884 12.5 67,972 veh (F.17) Seed SP K Ltt f The frequency of incidents in the study period is computed from Equation F.18: = Ã Ã Ã Ã Ã = Ã Ã Ã Ã Ã = â IR AADT DD DM 1,151.5 10 67,972 1.13 0.3884 12.5 4.294 incidents per study period in May (F.18) 5 5 5 8 n k Ls f Using the duration of a one-lane closure incident (34 min based on national default data), then E[D(One lane closure in units of a study period)] = Ã 34 60 6 = 0.0944 study periods. Alternatively, it can be shown that the expected number of incidents in month May (n5) is the incident rate multiplied by the adjusted VMT, as shown by Equation F.19: ( )= Ã Ã = Ã Ã = IR VMT DM 1,151.5 330,006 1.13 4.294 incidents SP (F.19) 5 5 5n The factor g(i) is also based on the use of national default values. Therefore, the portion of all incident times that inci- dents with one lane closure occur is 19.6%. The final prob- ability of one lane closure in a study period in May can be Figure F.3. Proposed process flow for incident rate estimation.

214 shown to be 7.64%. All computations are shown in Equa- tion F.20: P e e n E ij i { } = â = â = â = ( ) ( )[ ]( )â Ã Ã â Ã Ã Ã Prob single-lane closure incident in a study period in May 1 1 1 7.64% (F.20) 0 4.294 0.196 34 60 6 This result is highlighted in Table F.9, where up to 60 such computations are made for each month and incident type combination. The probability balance is then assigned to the no-incident column. An interesting sidelight of the application of Equation F.20 highlights the beneficial effects of good incident management Table F.8. I-40 EB Demand Multipliers for Weekdays in May Number in May Demand Multiplier Monday 5 1.076 Tuesday 4 1.106 Wednesday 4 1.114 Thursday 4 1.158 Friday 4 1.210 Table F.7. Schematic of FSG for I-40 EB Case Study Showing the Monthly Crash Rates and CTI practice. For example, by reducing the incident clearance time say, from 34 to 20 min, the probability of a lane closure inci- dent decreases from 7.64% to 4.57%. Summary This section documents a detailed methodology for estimating study period incident probabilities adjusted on a monthly basis. This approach ensures that the probabilities are un biased and are founded on a definition that takes into account the number and expected duration of incidents, as well as the traffic demand. A key attribute of the method is its flexibility. It allows an agency to generate probability estimates consistent with their data availability, ranging from direct input of the probabilities from incident logs to estimation methods that use appropriate combinations of national and local defaults. Of course, a minimum amount of information about the facility geometry and AADTs is essential to applying the methodology. Application of the method to a 12.5-mi freeway facility in North Carolina indicates that for a study period of 6 h in the p.m. peak encompassing all weekdays in 2010, there was approximately a 33% chance of an incident occurring. About two-thirds of the predicted incidents involved shoulder clo- sures, and one-third involved lane closures. The impact of those incidents on travel time is documented elsewhere.

215 The methodology could benefit from a number of enhance- ments, notably in acknowledging the correlation between incidents and weather conditions. The team is aware of a parallel effort under the auspices of SHRP 2 Project L04 in which a model is being tested in the New York area that pro- vides conditional incident probabilities based on weather events. Another area of needed improvement is the correla- tion of (major) incidents and expected demand. These areas for improvement are recommended for future research and methodological development. References Adan, I., and J. Resting. Queueing Theory. Eindhoven University of Technology, Eindhoven, Netherlands, 2001. American Association of State Highway and Transportation Officials. Highway Safety Manual. Washington, D.C., 2010. Federal Highway Administration. Highway Economic Requirements System: State Version: Technical Report. Washington, D.C., August 2005. Federal Highway Administration. Manual on Uniform Traffic Control Devices. Washington, D.C., 2009. Highway Capacity Manual 2010. Transportation Research Board of the National Academies. TRB of the National Academies, Washington, D.C., 2010. Khattak, A. J., and N. M. Rouphail. Incident Management Assistance Patrols: Assessment of Investment Benefits and Costs. North Carolina Department of Transportation, Raleigh, 2005. Rouphail, N. M., B. J. Schroeder, and W. Kittelson. Freeway Reliability in the Context of the U.S. Highway Capacity Manual. Presented at 5th International Symposium on Transportation Network Reliabil- ity, Hong Kong, 2012. Skabardonis, A., K. F. Petty, R. L. Bertini, P. P. Varaiya, and D. Rydzewski. The I-880 Field Experiment: Analysis of the Incident Data. In Trans- portation Research Record 1603, TRB, National Research Council, Washington, D.C., 1997, pp. 72â79. Table F.9. Final Study Period Monthly Incident Probabilities Month Probability of Different Incident Types No Incident Shoulder Closure One-Lane Closure Two-Lane Closure Three-Lane Closure Four-Lane Closure January 66.42% 23.30% 7.06% 1.79% 1.43% 0.00% February 66.36% 23.34% 7.08% 1.79% 1.43% 0.00% March 65.10% 24.18% 7.36% 1.87% 1.49% 0.00% April 63.79% 25.05% 7.66% 1.94% 1.56% 0.00% May 63.87% 25.00% 7.64% 1.94% 1.55% 0.00% June 64.53% 24.56% 7.49% 1.90% 1.52% 0.00% July 64.10% 24.85% 7.59% 1.93% 1.54% 0.00% August 65.30% 24.04% 7.32% 1.86% 1.48% 0.00% September 65.97% 23.60% 7.17% 1.82% 1.45% 0.00% October 65.04% 24.22% 7.38% 1.87% 1.50% 0.00% November 66.79% 23.05% 6.98% 1.77% 1.41% 0.00% December 68.56% 21.86% 6.59% 1.67% 1.33% 0.00%