FE Review-Transportation-II. D e p a r t m e n t o f C i v i l E n g i n e e r i n g U n i v e r s i t y O f M e m p h i s

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1 FE Review-Transportation-II D e p a r t m e n t o f C i v i l E n g i n e e r i n g U n i v e r s i t y O f M e m p h i s

2 Learning Objectives Design, compute, and solve FE problems on Freeway level of service Vehicle signal change interval Stopping Sight Distance Traffic flow relationship Gravity model (Trip Distribution) Logit model (Mode Choice) Traffic Safety

3 Primary Types of Uninterrupted Flow Facilities Freeways Pure uninterrupted flow Multilane Highways Sections of multilane highways (four or six lane) that are more than two miles from the nearest point of fixed operation Rural Two-lane Highways Sections of two-lane highways (one lane in each direction) that are more than two miles from the nearest point of fixed operation

4 Capacity The capacity of a facility is the maximum hourly rate at which persons or vehicles reasonably can be expected to traverse a point or a uniform section of a lane or roadway during a given time period under prevailing roadway, traffic, and control conditions. (HCM 2000)

5 Capacity Under Ideal Conditions

6 Service Flow Rate Illustration

7 The Level of Service Concept A quality measure describing operational conditions within a traffic stream, generally in terms of such service measures as speed and travel time, freedom to maneuver, traffic interruptions, and comfort and convenience (HCM 2010). Rating scale A-F indicate best to worst operation

8

9 LOS Estimation: Freeways

10 Equations for LOS Estimation-Freeways

11 LOS Estimation: Multilane Highways

12 Maximum Service Flow Rate: Basic Freeway Sections

13 Factors Influencing LOS Volume Lane width Lateral obstructions Traffic composition Grade Speed

14 Types of Analysis Operational Analysis Service Flow Rate and Service Volume Analysis Design Analysis

15 Operational Analysis Flow Rate: Where: v p = v p = 15-minute passenger-car equivalent flow rate (pc/h/ln) V = hourly volume in the given direction of flow (vph) PHF = peak-hour factor N = number of lanes in the given direction of flow f HV = an adjustment factor for th presence of heavy vehicles f p = an adjustment factor to account for the fact that all drivers of the facility may not be commuters or regular users. *Basis for analysis is peak 15 min flow rate. V PHF N f HV f p

16 Example: Graphical Solution Speed: 62 mph Density: 29 pc/mi/lane LOS: D S = ( ) 2 = 62.7 mi/h

17 Design Analysis N i = DDHV MSF i PHF f HV f p Where: Ni = number of lanes required (in one direction) to provide LOS i DDHV = directional design hour volume, veh/h

18 Basic Freeway Segment Characteristics Ideal conditions for maximum service flow rate: Minimum interchange spacing 2 miles Only passenger cars Lane widths 12 feet Lateral obstructions 6 ft from roadway edge Level terrain (grades < 2%) Drivers typical of weekday (regular) traffic 10 or more lanes in urban areas **removed in HCM2010

19 Free Flow Speed: Basic Freeway Segments FFS = 75.4 f LW f LC 3.22TRD 0.84 *HCM2010 Where: FFS = estimated free flow speed in mph. BFFS = estimated base free flow speed in mph (75 mph for rural freeways, 70 mph for urban based on HCM recommendations). f LW = adjustment for lane width (if less than 12 ft), mph. f LC = adjustment for right side lateral clearance ( if less than 6 ft), mph. f N = adjustment for # of lanes (if less than 5 in one direction), mph. f ID = adjustment for interchange density if < 2 mi, mph. TRD = total ramp density (ramps/mi)

20 Adjustment for Lane Width: Freeway

21 Adjustment for Lateral Clearance : Freeway

22 Total Ramp Density Total number of on-ramps and off-ramps within 3 miles of the mid-point of the study segment divided by 6 miles Ramp density is a surrogate measure that relates to the intensity of land use activity in the vicinity of study segment

23 Multilane Highway Characteristics Ideal conditions for maximum service flow rate: Lane widths 12 feet Total lateral clearance 12 feet Divided highway No access points Only passenger cars in traffic stream Regular roadway users

24 Heavy Vehicle Effects: f HV 1 P T ( E T 1 1) P R ( E R 1) P T, P R = proportion of trucks and buses, and RV s E T, E R = PCEs for trucks and buses, and RV s ¼

25 Table Passenger-Car Equivalents for Trucks and Buses on Upgrades

26 Table (continued) Passenger-Car Equivalents for Trucks and Buses on Upgrades

27 Table Passenger-Car Equivalents for RVs on Upgrades

28 Table Passenger-Car Equivalents for Trucks and Buses on Downgrades

29 HCM2010

30 Example: FFS on Freeway Given: Six-lane urban freeway (3 in each direction) Lane width = 11 ft Right-side lateral clearance = 2 ft from the pavement edge Commuter traffic (regular users) Find FFS

31 Example: LOS of Basic Freeway (1) Given: Four-lane freeway (2 in each direction) Lane width = 11 ft Right-side lateral clearnece = 2 ft Commuter traffic (regular users) Peak-hour, peak-direction demand volume = 2,000 veh/h 5% trucks, 0% RVs PHF = 0.92 TRD = 4 ramps/mile Rolling terrain Find: LOS

32 Example: LOS of Basic Freeway (2) Step-1: Input Data All the input data is given in the previous slide Step-2: Compute FFS FFS = 75.4-f lw -f lc -3.22(TRD) 0.84 FFS = (4) 0.84 FFS = 60.8 mi/hr Step-3: Select FFS Curve FFS>57.5 and less than 62.5, so 60 mi/h curve will be used

33 Example: LOS of Basic Freeway (3) Step-4: Adjust Demand Volume V = 2000 veh/hr PHF = 0.92 f p = 1.0 (commuter traffic) N = 2 v p = V PHF N f HV f p f HV = 1/[1+0.05(2.5-1)+0] = 0.93 Vp = 1,169 pc/h/lane. f HV 1 P T ( E T 1 1) P R ( E R 1)

34 Step-5: Estimate Speed and Density Density = 1169/60 = 19.5 pc/mi/lane Determine LOS Operates at LOS C Though close to B No improvement is needed

35 Vehicle Signal Change Interval Change Interval (Yellow) This interval allows that is one safe stopping distance away from the STOP line when GREEN is withdrawn to continue at the approach speed and enter the intersection legally on yellow. y = t + v 2a + (64.4 G) Where, y-> length of the yellow interval t-> driver reaction time, s v -> 85 th percentile speed of approaching vehicles or speed limit in ft/sec a-> decelleration rate of vehicles, ft/sec 2 G-> Grade of approach, %

36 Vehicle Signal Clearance Interval Assuming that a vehicle has just entered the intersection legally on yellow, the all-red must provide sufficient time for the vehicle to cross the intersection and clear its back bumper past the far curb line (crosswalk line) before conflicting vehicles that are given GREEN. All Red = AR = w + L v L = length of the clearing vehicle, normally 20 feet W = width of the intersection in feet, measured from the upstream stop bar to the downstream extended edge of pavement w P

37 Stopping Sight Distance Stopping sight distance is composed of how many distances? What are they? Distance traveled during perception/reaction time Distance required to physically brake vehicle Reaction time distance Braking distance SSD = 1.47Vt + V 2 30({a/32.2} ± G) V is in mph

38 Example :Stopping sight distance A section of highway with 1.5% down grade, and design speed of 70 mph. Find the stopping sight distance when the driver reaction time is 2sec, driver eye height is 4ft, and object height is 6 inches.

39 Flow(veh/hr) Speed (miles/hr) Speed (miles/hr) V Traffic Flow Relationship V Density (veh/mi) K Q K Flow (veh/hr) Q Macroscopic: Speed (V): mi/hr Density (K): veh/mi/lane Flow (Q): veh/hr/lane Q= KV

40 Flow(veh/hr) Speed (miles/hr) Speed (miles/hr) V Traffic Flow Relationship (2) V f V f V 0 V 0 Q 0 K j Density (veh/mi) K Q Q m V 0 Macroscopic: Speed (V) Q m Flow (veh/hr) Q Density (K) K 0 K j K Flow (Q) Qm= V f K j /4

41 Question: Traffic Flow Speed on a road is given by S = D 1. If mean speed is 45mph find density 2. Find maximum capacity

42 4-Step Transportation Planning Trip generation is the process of determining the number of trips that will begin or end in each traffic zone within a study area. Trip distribution is the process by which trips generated in one zone are allocated to other zones in the study area. Mode choice determines the number of trips between zones that are made by different modes (such as highway and transit). Traffic Assignment is used to obtain expected traffic volume on the network is known as trip assignment.

43 Trip Distribution T ij = P i A j F ij K ij A j F ij K ij σn j=1 T ij = Trips Volume between i & j Pi = Total number of trips produced in zone i Aj = Total number of trips attracted to zone j F ij = Friction Factor (inverse function of travel time between i and j) K ij = Socioeconomic Adjustment Factor

44 Trip Distribution-Example Zone Total Production Attraction Zone

45 Fij Matrix (Inverse Square Fn) Zone Zone

46 Tij Matrix Zone Sum Target Sum

47 Balance Iteration#1 Iteration#1 Zone Sum Target Ratio Sum Target Ratio Iteration#1.1 Zone Sum Target Ratio Sum Target Ratio

48 Balance Iteration#2 Iteration#2 Zone Sum Target Ratio Sum Target Ratio Iteration#2.2 Zone Sum Target Ratio Sum Target Ratio

49 Mode Choice The choice of mode is a complex process that depends upon factors such as Income Availability of transit service Auto ownership Cost Comfort, convenience, and safety Relative advantage of one mode over other How do we quantify the attractiveness of a mode Utility

50 Utility Definition The attractiveness as a function of Attributes travel time, cost, and other mode specific parameters Characteristics Income, auto ownership or other user parameters Functional form of Utility Where Ux: Utility of mode x a i : Coefficient of attribute X i : Attribute or characteristic value n: Number of attributes n U x = a i X i i=1

51 Numerical Example-1 (1) Suppose that an individual can travel to work by driving alone, carpooling, or riding the bus. Assume that the relevant attributes of these modes are travel time travel cost income

52 Numerical Example-1 (2) Let T denote door-to-door travel time in hours, C denote travel cost in dollars, and Y denote annual income in thousands of dollars per year. Let the utility function be U(T,C,Y) = -T - 5C/Y

53 Numerical Example-1 (3) Suppose the values of travel time and cost for the available modes are: Time (T) Cost (C) Mode (hours) ($) Drive Alone are as following: Mode Time (T) (hours) Cost (C)($) Drive Alone Carpool Bus

54 Numerical Example-1 (4) If income is $40,000 per year, for example, the value of U for drive alone is (2.00)/40 = The following table shows the value of U corresponding to each mode for an individual whose income is $40,000 per year (Y = 40) and an individual whose income is $10,000 per year (Y = 10):

55 Numerical Example-1 (5) Mode Time (T) (hours) Cost (C)($) Drive Alone Carpool Bus U(T,C,Y) = -T - 5C/Y Mode Y = 40 Y = 10 Drive Alone Carpool Bus

56 Numerical Example-1 (6) The high-income individual chooses to drive alone (because drive alone has the highest utility for this individual), and the low-income individual chooses to carpool Mode Y = 40 Y = 10 Drive Alone Carpool Bus

57 Numerical Example-1 (7) Note that all utilities are negative because U consists of (generalized) costs of travel but excludes the value of reaching the destination. In this case, the highest value of U is the one that is least negative.

58 Probability of Choosing a Mode Probability of choosing a mode i Where Ui: Utility of mode i j: All available modes

59 Probability of Mode Choice Example If we have two modes then the probability of choosing each mode is given by Mode Y = 40 Y = 10 Prob (Y=40) Prob (Y=10) Drive Alone Carpool Bus

60 Crash Rate at Intersection Represented as Crash Rate per Million Entering Vehicles (RMEV) RMEV = A 1,000,000 V Where A: Number of crashes at a location in a given time period Total crash or by crash type V = ADT * 365 ADT: Average Daily Traffic at the intersection

61 Example: RMEV The number of crashes recorded at an intersection in a year was 23, and average 24 hour volume entering from all approaches was Determine Crash Rate per Million Entering Vehicles (RMEV) 23 1,000,000 RMEV = = 9.69 crashes/million entering vehicles

62 Crash Rate at Roadway Segments Represented as Crash Rate per hundred Million Vehicle Miles (RMVM) Where RMEV = A 1,000,000 VMT A: Number of crashes at a location in a given time period Total crash or by crash type V = ADT * 365 VMT: Vehicle Miles Travelled VMT = ADT*Length of the road*number of days ADT: Average Daily Traffic at the intersection

63 Example: RMVM It is observed that 40 traffic crashes occurred on a 17.5 mile long section of a highway in one year. The ADT on the section was 5000 vehicles. Determine the rate of crashes per 100 million vehicle-miles Determine the rate of fatal crashes per 100 million vehiclemiles if 5% of the crashes involved fatalities RMEV T = 40 1,00,000, = crashes per 100 million veh mi RMEV F = = 6.26 crashes per 100 million veh mi

64 Crash Reduction Crashes Prevented = N CR ADT After Improvement ADT Before Improvement Where N: Expected number of crashes if countermeasure is not implemented and if the traffic volume remains the same CR: Overall crash reduction factor for multiple mutually exclusive improvements CR = CR 1 + (1 CR 1 )*CR 2 +(1-CR 1 )(1-CR 2 ) CR 3 + +(1- CR 1 )* 1 CR m 1 CR m CRi: Crash Reduction Factor for a specific countermeasure i m: Number of countermeasures at the site.

65 Example Crash Reduction At a single location three countermeasures with CRs of 40%, 28%, and 20% are proposed. Determine the overall CR factor? CR = 0.4+(1-0.4)*0.28+(1-0.4)*(1-0.28)*0.2 = 0.66

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