Civil 303 Semester 2 2024 Lecture Notes PDF

Monday 15th July Semester 2, 2024 Dr. Prakash Ranjitkar Department of Civil & Environmental Engineering Room 401.1210, Tel. 923 3513...

Monday 15th July Semester 2, 2024 Dr. Prakash Ranjitkar Department of Civil & Environmental Engineering Room 401.1210, Tel. 923 3513 Email: [email protected] Consultation hours: 12 noon to 1 pm (after class on Monday/Tuesday) Click to edit Master title style Click to edit Master subtitle style 7/14/2024 ‹#› 1 Contents Learning Objectives 1. Traffic Studies [1-2] 1. Summarise and communicate key concepts regarding traffic data Volume, speed, density, and travel time 2. Understand how to collect traffic data and analyse traffic flow variables studies 3. Describe different types of traffic models and their applications. 2. Traffic Flow Theory [3-7] 4. Illustrate and describe relationships between the primary traffic flow Model traffic variables using distribution variables. functions 5. Analyse traffic data and model traffic flow variables (e.g., vehicle arrival, Microscopic and macroscopic traffic accident/delay probability, headway) flow models and their relationships 6. Demonstrate relationship between micro and macroscopic traffic models Operational analysis of unsignalized intersections 7. Analyse traffic operations at un-signalized (priority-controlled) intersections including pedestrian crossings 3. Multilane Highway Capacity [8-9] 8. Describe HCM 2016 concepts and methodology  Mobility dimensions, road types and operating conditions to conduct Level-of-service (LOS)  HCM terminologies, LOS concept and service measures analysis for multilane highway 9. Implement highway capacity methodology to analyse operational 4. Intelligent Transportation Systems performance of multi-lane highways. [10-11] 10.Understand the benefits of ITS and summarise the common ITS Benefits and common architectures architectures Applicability for traffic issues in NZ 11.Evaluate the applicability of ITS solutions for NZ traffic issues 2  Test (15% weightage) – 50% covering Traffic Studies / Traffic Flow Theory  Project (30% weightage) – 40% covering Traffic Studies  Final Exam (55% weightage) ~ 55% covering Traffic Flow Theory / Multilane Highway Capacity / Intelligent Transportation System 3 Semester 2, 2024 Dr. Prakash Ranjitkar Department of Civil & Environmental Engineering Room 401.1210, Tel. 923 3513 Email: [email protected] Click to edit Master title style Click to edit Master subtitle style 7/14/2024 ‹#› 4  Traffic congestion  Accidents  Air pollution Causes Urbanization Economic growth Demand > Supply Incidents, weather, road works Land use distribution, public transport patronage Source: Deloitte Touche Tohmatsu, 2016 5 Collection and analysis of measurable factual data relating to traffic and its characteristics. Why do we need traffic data?  Manage the physical systems (road network, traffic control devices) e.g., operate, maintain, repair  Investigate trends over time e.g., forecast future mobility needs  Access potential impacts of road improvement measures e.g., Before & After studies, or Cost-Benefits Analysis Measurement Traffic Applications device variables Point Volume/ To determine traffic demand and capacity of road (supply) Location Flow Short To determine speed limit, a key factor to influence road Traffic Speed safety Distance Studies An important measure of effectiveness for motorway, Density multi-lane highway Long Distance Travel An important measure of effectiveness to evaluate road Time performance 6 Lecture I end here Tuesday 16th July Manually with human surveyors Traffic Monitoring and Data Collection Costly and inefficient but flexible o To support decision making (e.g., improve performance of road network) o Feed into transport planning models (e.g., for calibration and validation) o Typically collect data of number of vehicles (by segregated classes (e.g., light-duty (cars, mini vans), medium-duty (mini-bus, small trucks), heavy-duty (bus, trucks) vehicles), pedestrians, cyclists Automatically using road tubes Traffic Volume (V in veh/day) refers to the total number of vehicles that pass over a given point or section during a period (usually in a day). Annual Average Daily Traffic (AADT) refers to the average number of vehicles per day on a road over the year. Average Daily Traffic (ADT) refers to the average number of vehicles per day on a road over a week. 7 Leiture 2 ended here 22nd July Flow (q in veh/h) is the equivalent Automatically using computer vision hourly rate at which vehicles pass a Efficient and economical point on a highway. But still quite early so might not be that reliable (yet) 𝑁 𝑞 𝑇 where, N = the number of vehicles passing a point in the roadway in T (in hours) time duration Time Headway or Headway (h in sec) is the time interval (in sec) between successive vehicles in a traffic stream measured at a point. 1 𝑇 1 ℎ ℎ 𝑁 𝑁 𝑞 8  CCTV footage of SH16 Peak Hourly Volume is the maximum flow observed over ANY one-hour period. In urban areas where tidal flows are common, it is usual to have two PHV’s, one for the A.M. and other for P.M. In rural areas, it is sufficient to use only one PHV. Peak Hour Factor (PHF) is a measure of variations in flow rate during the peak hour. 𝑉 𝑃𝐻𝐹 4𝑥𝑣 1000 Where, Vehicle count 710 750 720 740 800 630 660 650 670 700 690 650 600 640 V = Total hourly volume (in veh/h) 600 520 610 590 v15m = Volume during the peak 15 minutes of the 400 analysis hour (in veh/15-minute) 200 Peak hour: 7:45 to 8:45am 0 9:45-10:00 6:00-6:15 6:15-6:30 6:30-6:45 6:45-7:00 7:00-7:15 7:15-7:30 7:30-7:45 7:45-8:00 8:00-8:15 8:15-8:30 8:30-8:45 8:45-9:00 9:00-9:15 9:15-9:30 9:30-9:45 V = 670+700+690+720 = 2780 veh/h 𝑃𝐻𝐹 = =0.965 Time 9 Traffic Monitoring using Mobile Data Huge volume of detailed data but has privacy concerns or coarse resolution 10  11 Magnetic Fields of Different Vehicle Types 12 Spot speed (𝑣 in km/h) is the instantaneous speed of a vehicle at any specified point, which is the distance travelled by a vehicle during a unit time. Distance ∆𝑥 𝑣 ∆𝑡 85th Percentile Speed o Drivers exceeding 85th percentile speed are usually considered to be driving faster than is safe. o Establish “maximum speed limit”. L x 15th Percentile Speed t1 t2 ti o Vehicles travelling below this value tend to obstruct the flow of traffic, thereby increasing the accident hazard. o Establish “minimum speed limit”. Time occupancy (𝑂𝑡) is the proportion of time a detector is occupied by a vehicle in a specified duration. Time T ∑ ∆t O T 13 Time Mean Speed (𝑣 in km/h) is arithmetic average of speeds of vehicles observed passing a point on a highway; also referred to as the average spot speed. ∑ 𝑣 𝑣 Arithmetic Mean 𝑁 Space Mean Speed (𝑣 in km/h) is an average speed based on the average travel time of vehicles to traverse a length of roadway. ∆𝑥 ∆𝑥 𝑁 ∆𝑥 𝑁 𝑣 Harmonic Mean ∆𝑡 ∑ ∆𝑡 ∆𝑥 1 ∑ ∑ 𝑁 𝑣 𝑣 What if we have a lot of spot speeds that are similar? ∑ 𝑓𝑣 𝑁 𝑣 𝑣 𝑁 𝑓 ∑ 𝑣 Where 𝑓 is the frequency or the number of vehicles with the same spot speeds. 14 Relationship between Time (𝒗𝒕 ) and Space Mean Speed (𝒗𝒔 ) 𝜎𝑠 ∑ 𝑓 𝑣 𝑣 𝑣 𝑣 always 𝜎𝑠 𝑣 𝑁 1 positive 𝑣 𝑣 𝜎𝑡 ∑ 𝑓 𝑣 𝑣 𝑣 ≅𝑣 whenvariance 𝜎𝑡 𝑣 iszero when 𝑁 1 all vehiclesaredriving atthesame speed Where 𝜎 is the variance of speed (𝜎𝑠 is the variance of space-mean-speed and 𝜎𝑡 is the variance of time-mean-speed), which measures the extent to which spot speeds is spread out from their average value. 15 Free Flow Speed (FFS) is the average speed of vehicles under low-flow conditions, i.e., when drivers are free to drive at their desired speed and are not constrained by the presence of other vehicles or downstream traffic control devices (i.e., traffic signals, or STOP signs). Average Running Speed is the length of the segment divided by the average running time of vehicles that traverse the segment. Running time includes only time during which vehicles are in motion. Average Travel Speed is the length of the segment divided by the average travel time of vehicles traversing the segment, including all stopped delay times. Space mean speed represents average travel speed. 16  Automatic, and can provide data in real-time once the infrastructure is in place. High maintenance cost Single Loop Detector 𝐸𝑉𝐿 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑠 𝑠𝑝𝑒𝑒𝑑, 𝑣 𝑂𝑖 where, EVL (effective vehicle length) = C + L C = Detector length L = Vehicle length Oi = Time occupancy vehicle i Oi Dual Loop Detector 𝑙𝑑𝑖𝑠𝑡 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑠 𝑠𝑝𝑒𝑒𝑑, 𝑣 𝑡 𝑡 where, ldist = distance between starting points of the first and second detector (see figure) tj = Time the vehicle entered jth detector 17 Density (k in veh/km) is the number of vehicles occupying a unit length of highway or lane. The unit length is usually one kilometre (km). 𝑁 𝑘 𝐿 where N is number of vehicles and L is the total length of the highway section. Space Headway or spacing (si in m) is the distance difference between successive vehicles in a traffic stream measured at an instant. ∑ 𝑠 𝐿 1 𝑠̅ 𝑁 𝑁 𝑘 Space Occupancy (Os) is the proportion of length of highway occupied with vehicles. ∑ 𝑙 𝑂 𝐿 where li is the length of vehicle i. 18  During a 60-sec period a single-loop detector is occupied by vehicles for the following occupancy times: 0.34, 0.38, 0.40, 0.32, and 0.52 sec. Assuming that the loop detector length = 4 m and that the average length of vehicles = 6 m, estimate flow (q), density (k) and space mean speed (vs). Hint: Use, EVL = C + L and 𝑣𝑖 C Given c 4m L 6m EVL 4 6 10 t L measy t 60sec N 5 9 veh see 60 60 300veh h Oi 9 Kx O Iff ME IF v 988 ms 64 3.6 105.9km hr 2 3 38 44.7km h V3 90km h V4 3 42.5km h 32 V5 3 2 692kmh 19 0 0544 I 9 KxVs K s 8 544 3.27veh km From a traffic video covering 1 km long section, an observer finds two groups of cars travelling along a road. Group A consists of 20 cars travelling at a speed of 10km/h; Group B consists of 40 cars travelling at a speed of 20 km/h. Determine the time mean speed and space mean speeds of the traffic. 10km h Group A 20caus 20km h Group B 40cars WE Efj 16.7km h III IF 15mn 20 Four vehicles, 6, 7, 8, and 9 m long, are distributed over a length of a freeway lane 200 m long. What is the space occupancy and density? 200m 0.2km 6m 12 7m 8m Ly 9m K 9 0s 9 K 20veh km 0s 6 9 or is 2 o.is 21  Time-space diagram illustrates the spatial-temporal trajectory of each vehicle.  Each line represents the trajectory of a vehicle.  The time difference between two vehicles at the same position (horizontal in the figure) represents the time headway (h).  The distance between two vehicles at the same time (vertical in the figure) represents the space headway or spacing (s). 22  The figure below shows a time-space (trajectory) diagram of vehicles on a road segment. A speed trap (Δx = 70 meter) recorded the times when vehicles passed two points, A–A′ and B–B′ as shown in the figure and the table below. Based on the given information determine the following. a) The flow (in veh/h) and individual headways of vehicles at location A-A’. b) The spot speed of each vehicle (3, 4, 5, 6, 7, and 8). c) The time mean speed, space mean speed. Solution T 4osec qN 6N q 6 xEven 3600 see 540 veh/h an T 40 9 3600 Individual vehn syoven headways n 7.5, 6.7 and 4.6 sec for vehicles 4, 5, 6, 7, are 8, 6.6, and 8 while headway for vehicle 3 can not be estimated. b Ax 70m Oi 4 70 70 3600 v x 57.3 km/h v x 3.6 53.6 km/h 7 29 24.3 3 6.6 4 2.2 3.6 1000 474 57.3 am n vy 70 70 v x 3.6 52.5 km/h v x 3.6 50.4 km/h fI 15 10.2s25kmlnr 36 31 70 70 Time of Time of v Vs 48.5km h 48.5 km/h x 3.6 v x 3.6 60 km/h Veh. Passing A-A' Passing B-B' 22 16.8 39.8 35.6 # (sec) (sec) ∑𝑣 57.3 h52.5 53.6km 48.5 53.6 50.4 60 3 2.2 fadway 6.6 v 53.7 km/h f N 6 4 10.2 15.0 v 7 N 7 504kmh 6 53.4 km/h 5 6 16.8 24.3 22.0 29.0 vs ∑ 𝑣1 1 60kmh 1 57.3 52.5 1 1 48.5 53.6 1 50.4 1 60 7 31.0 36.0 8 35.6 39.8 23 I s7.3 52st48 5 tss ve.ee 6tsoI s3tiam h us t 53.4kmh EE 4 Travel time is the total time (including stops, moving time and delay) to travel from one point to another. Free-flow travel time is the time it should take if we can always travel at the maximum possible speed, usually the speed limit. We often can calculate this by using a certain distance divide by the speed limit Delay is the time difference between the actual travel time and the travel time given no impedances (free-flow travel time). Delay = Actual travel time - Free-flow travel time 24 Floating or Probe Vehicle Method FHWA's Travel Time Data Collection Handbook 25 License Plate Method Travel time Origin/Destination 26 Video Processing 27 Crowd sourcing method e.g., Google travel time How do you think Google can estimate travel time so accurately? 28  Device Variables Unit Classification Formulae Definitions 𝑁 Number of vehicles passing a road location Short distance (loop Point location (count/watch) Flow (q) veh/h Macroscopic 𝑞 𝑇 per hour 1 𝑇 1 Time interval (in sec) between successive Time headway (hi) sec Microscopic ℎ ℎ 𝑁 𝑁 𝑞 vehicles in a traffic stream ∆𝑥 Spot speed (vi) km/h Microscopic 𝑣 Distance travelled by a vehicle per unit time ∆𝑡 detector) 1 Average speed of vehicles passing a point Time mean speed (vt) km/h Macroscopic 𝑣 𝑣 𝑁 over a specified duration ∑ ∆𝑡 Proportion of time a detector is occupied by a Time occupancy (Ot) % Macroscopic 𝑂 𝑇 vehicle in a specified duration 𝑁 Number of vehicles per unit length of road or Long distance (road segment) Density (k) veh/km Macroscopic 𝑘 𝐿 lane, also referred as “concentration” 1 𝐿 1 Distance between successive vehicles in a Spacing (si) meter Microscopic 𝑠̅ 𝑠 traffic stream, also referred as “space 𝑁 𝑁 𝑘 headway” 1 Proportion of road length occupied with Space occupancy (Os) % Macroscopic 𝑂 𝑙 𝐿 vehicles ∆𝑥 ∆𝑥 𝑁 𝑣 Average speed of traffic on a road section or Space mean speed (vs) km/h Macroscopic ∆𝑡 1 ∆𝑥 1 ∑ ∑ lane over a specified duration 𝑁 𝑣 𝑣 29 Problem 1-1 A loop detector having a length of 3 m was observed to have six vehicles cross over it in a period of 148 sec, for the following durations: 0.44, 0.48, 0.50, 0.41, 0.49, and 0.55s. Estimate the values of space-mean and time mean speed. The corresponding lengths of vehicles were 6, 7, 6.5, 5, 7.5, and 5.5m. [Answers: q = 146 veh/h, vs = 69.2 km/h, k = 2.1 veh/km, vt = 70 km/h] Problem 1-2 At traffic count stations A and B, the ADT are collected in 6 months as shown in the table below. The AADT can be estimated as the average values of these ADT. Station B also has another modern way to count the vehicles from automatic video processing, which considered more accurate. This value is 8800 veh/day, and is considered as the ground-truth of the vehicle count. Assume that the ratio between the estimated AADT (using ADT) and the ground-truth value is the same in both stations. Calculate the ground-truth AADT for Station A? [Answers: 4093 veh/day] Month Station A Station B January 4300 9100 February 4100 8700 March 3900 8400 April 3800 8200 May 3900 8500 June 4000 8700 30 Problem 1-3 Speeds are measured at a fixed point along a road section as follows (in km/h): 52, 47, 50, 54, 59, 63, 67, 57, 55, 48, 44, 53, 54, 58, 49, 61, 55, 50, 47, 55. Determine the following: a) The time mean speed and variance b) The space mean speed and variance directly from the measurement data. c) The space mean speed using the results in (a). [Answers: a) vt = 53.9 kph, σt2 = 34.1, b) vs = 53.3 km/h, σs2 = 34.5, c) vs = 53.3 kph] Problem 1-4 Using an intersection traffic flow diagram, determine all the traffic flow movements at this intersection based on the data given in the table. Assume that the D to C left turn is 150 veh/h and the C to B left turn is 10 veh/h. Assuming the traffic flow pattern at this intersection can be classed as typically urban, estimate the ADT on each intersection leg. [Answers: a) xCD=20, xAD=20, xBC=130, A.M. Peak Hour Flow xDA=20, xAB=20, xBA=50, b) 19,100 Inbound Straight Inbound Outbound Intersection Leg veh/day] Through Total Total A (north) 650 690 360 B (west) 320 500 260 C (south) 290 320 930 D (east) 230 400 360 31 Monday 29th July Semester 2, 2024 Dr. Prakash Ranjitkar Department of Civil & Environmental Engineering Room 401.1210, Tel. 923 3513 Email: [email protected] Click to edit Master title style Click to edit Master subtitle style 7/14/2024 ‹#› 32 Traffic flow theory is the study of interactions between travellers (e.g., pedestrians, cyclists, drivers, and their vehicles) and infrastructure (e.g., highways, signage, and traffic control devices), with the aim of understanding and developing an optimal transport network for an efficient movement of people and goods with minimal traffic congestion. It involves the development of relationships between primary traffic stream variables i.e., flow, density and speed. To help traffic engineers in planning, design and operational evaluation of road networks e.g., to determine: o length of turning bays at intersections o delay experienced by travellers o changes in road networks’ performance due to road improvement measures 33 Macroscopic models o Traffic states are expressed using macroscopic variables e.g., flow, speed and density as traffic flow is treated in an aggregate manner o Interactions between elements of traffic flow are expressed at a low level of detail however they satisfy physical law o Macroscopic models are used where results are not sensitive to microscopic details, for large network, real-time simulation, and when model development time and resources are limited. Traffic Flow Modelling Compressive fluid Group of vehicles Individual vehicle 1 sec 1 min Time Scale One lane Isolated intersection Large network Network Scale 34 Microscopic models o Traffic states are expressed using microscopic variables for individual vehicles e.g., car-following and lane changing models o describe both the system entities and their interactions at a high level of detail and hence have the potential to be more accurate than macroscopic models. o Requires significant high-resolution data to calibrate and validate hence are costly to develop, execute and maintain compared to macroscopic models. Mesoscopic models o Most entities are generally represented at a high level of detail but describes their activities and interactions at a much lower level of detail than would a microscopic model 35  Stochastic versus Deterministic Models: Stochastic models capture variations in e.g., reaction time, arrival processes, route choice. Every simulation run results in different outcome. Deterministic models represent average conditions only and ignore variance.  Time Step versus Event Based Models: Time-step based models calculate the changes in the system for every finite time steps (e.g., 1 second) while Event based models calculate changes in the system when some event happens.  Static versus Dynamic Models: Static models give an average steady-state traffic situation e.g., EMME 3. While Static dynamic models represent dynamic changes over time. Models, software packages and real-world Dynamic Models 7:00 10:00 15:00 18:00 Analytical/ Deterministic/ Stochastic Abstract Programming formulation Validation Validation Calibration / Validation Software Real world Situation Packages Output results 36  Speed 100 (km/h) Freetlow 80 Speed-Flow always 60  Linear relationship in free-flow state got 40  Unstable near the capacity q = qm 20 w 00 500 main 1000 1500 2000 Flow Flow (ver/hr) (veh/hr) either 2400 Flow-Density 1600  q = 0 at k = 0 and k = kj 800  q is maximum at a critical density, k = km  Unstable in congested region 0  Two densities for each value of q 0 30 60 90 120 150 Density (veh/km) 37 always x axis q=kv  Traffic stream models (TSM) provide relationships between flow (q), average speed (v) and density(k) for uninterrupted Uncongested state vf : Free flow speed flow situations. Congested state kj : Jam density km : Critical density vm: Optimum speed q qm: Maximum flow Key Properties qm  Space mean speed (v) represents the average speed of a traffic stream.  Density or speed describes a unique traffic condition while v km kj k flow doesn’t as each value of flow represents two different v conditions one for uncongested and the other for congested. vf vf v zero, the flow is also min  When density is min zero while speed is free flow speed (vf). maximium  As density increases, speed decreases while flow increases up to the maximum flow (qm), which represents capacity. Any further increases in density beyond that point result in km kj k qm q reductions of flow. 𝑞 𝑣 𝑣 𝑞𝑠̅ 𝑠̅ 𝑣ℎ  At maximum density termed as jam density (kj), flow is zero. 𝑘 𝑞 38  Civil 735  Micro-simulation – high resolution traffic simulation e.g., AIMSUN, VISSIM, PARAMICS, CORSIM, INTEGRATION, SUMO  Macro-simulation – AIMSUN, VISUM  Meso-simulation – AIMSUN, CONTRAM, DYNAMIT, DYNEMO, Civil 762 DYNASMART  Online adaptive traffic control system– SCATS, SCOOT  Traffic signal timing – TRANSYT  Intersection LOS and capacity analysis – SIDRA INTERSECTION, ARCADY, OSCADY, PICADY, HCS  Regional transportation planning – EMME, TRIPS  Traffic assignment - SATURN  Parking analysis - PARKSIM  Pavement design - CIRCLY  CAS - NZ database of road crashes  RAMM – NZ database of transport assets  dTIMS – NZ pavement asset management Civil 762 39 i 40 Discrete distributions an  Are applicable to situations in which the item of interest can take only integer values, for example, the number of vehicles that will enter a car park through a particular gate during the next 5 minutes.  Examples: binomial distribution (e.g., probability of accident), Poisson’s distribution (e.g., number of vehicles arrive during a specified duration) Continuous distributions  The item of interest can take both integer and non-integer values, for example, the time a particular vehicle will spend in the queue waiting to enter the car park via that gate.  Examples: negative exponential distribution (e.g., delay at unsignalized intersection), normal distribution (e.g., time headway during peak period, speed) 41 The probability of exactly ‘x’ successes in ‘n’ trials is expressed as follows: 𝑛! 𝑏 𝑥 𝑝 1 𝑝 𝑥! 𝑛 𝑥 ! where, b(x) = the probability of exactly x successes in n trials (x  n) p = the probability of a success in any one trial The binomial distribution is discrete, n and x can take only integer values. Mean, μ = n p and Variance,  2 = n p (1 - p) Note:  < μ In traffic applications, the cumulative form of the binomial distribution is often useful. This can be written as: 𝐵 𝑋 𝑏 𝑥 where, B(X) is the probability of X or less successes in n trials, and b(x) is the binomial frequency distribution function. 42 Assume that, at a certain time of day, a car park is being accessed by 300 veh/h and that 35% of these, on average, use Gate A. Determine the probability of more than 6 vehicles using Gate A over a two minutes period. Solution: Number of vehicles arriving at the car park in 2 minutes = 10 vehicles, i.e., n = 10 Given Flow q 300veh n Suchmin P 0.35 n The probability of using Gate A, p = 0.35 ftp blxprobability of pxli The 𝑛! xi Ei more than 6 vehicles using Gate A in 2 minutes, p(x>6) = b(7) + b(8) + b(9) + b(10) pgn sx veh'per 2minutes 𝑏 𝑥 𝑝 1 𝑝 x 6 𝑏 7 𝑥! 𝑛 𝑥 ! !7 b8 b9 b 0.35 1 0.35 if = 0.0212 0 00428 0.000512 0.0000270 0.026 ! ! 2.61.1 ! fbIIItf 𝑏 8 0.35 0.65 = 4.28 x 10 ! ! 𝑏 9 ! ! ! 0.350.65 = 5.12 x 10 0 357!0.653 0.0212 btbtbs.be Ii In Eve b7 1 𝑏 10 0.35 0.65 = 2.76 x 10 ! ! 8 0.3580.652 0 00428 bystep step 8 p(x>6) = 0.0212 + 4.28 x 10 + 5.12 x 10 + 2.76 x 10 0.026 or 2.6% onen.mmJ 43 a 03590.6s 0.000s b110 0.35 0.650 00000276 f foublyj.gg 357 10.6513 I The probability that an event occurs exactly 'n' times in a time duration ‘t’ can be expressed as follows: 1 3600 9 𝜆𝑡 𝑒 venin very 𝑃 𝑡 𝑛! where, P(n) = probability of having n vehicles arrive during a time interval t,  = average vehicle arrival rate in vehicles per unit time (veh/s), ( = q/3600) where q is flow in veh/h. t = duration of the time interval over which vehicles are counted, and e = base of the natural logarithm (e = 2.718) The Poisson distribution is discrete, n can take only integer values. However, λt is not restricted to integer values. Mean, μ  λ t Variance, σ2  λ t if mandO areclosethen Poissondis if u use binomial distribution 𝜆𝑡 𝜆𝑡 𝑒 𝜆𝑡 𝑃 𝑡 𝑃 𝑛 1 𝑛 𝑛 1 ! 𝑛 The cumulative Poisson distribution is often useful in traffic theory and analysis. This cumulative form is: 𝑃 𝑁 𝑃 𝑛 where P(N) is the probability of n or less occurrences of an event and P(n) is Poisson’s distribution function. 44  A traffic count on a motorway off-ramp is 600 veh/hr. Assuming the flow is random and free-flowing and the arrival rate follows a Poisson distribution, calculate: a) probability of there being no vehicles in a period of 3 secs. b) probability of there being one vehicle in a period of 3 secs. c) probability of there being two vehicles in a period of 3 secs. d) probability of there being three vehicles in a period of 3 secs. Solution: 𝜆  600 veh/h  1/6 veh/sec Firststepalways calculate lamdavalue R 𝜆 𝑡 = 3 x 600/3600 =0.5 veh/3-sec 600 A 93600 3600 fvensee 𝜆𝑡 𝑒 u At 𝑃3 𝑡0Sveh 6 3sec𝑛! (a) P0 = 0.61 Polt p.lt IÉ (b) P1 = 0.30 t Polt e (c)eP2 = a a0.08611 (d) P3 =0.01 f p.lt o.mx 031 31 P.CH 45 p.lt 0.31 0 078 781 Psp 5 our Variance/Mean Traffic Situation Distribution >1 Cyclic Negative Binomial =1 Low Flow Rate (Random) Poisson capacity  Minor disruptions may cause  Disruptions can not be easily serious local deterioration in dissipated and usually result in the service and queues may begin to formation of queues and the form deterioration of service 95 Volume - the total number of vehicles that pass over a given point or section of a lane or roadway during a given time interval; any time interval can be used, but volume are typically expressed in terms of annual, daily, hourly, or sub-hourly periods. Flow Rate (v) - the equivalent hourly rate at which vehicles pass over a given point or section of a lane or roadway during a given time interval of less than one hour, usually15 minutes. Peak Hourly Volume (PHV) - PHV is the maximum flow observed over ANY one-hour period. In urban areas where tidal flows are common, it is usual to have two PHV’s, one for the A.M. and other for P.M. In rural areas it is sufficient to use only one PHV. Peak Hour Factor (PHF) - PHF is used as a measure of variations over an hour and is calculated as, 𝐻𝑜𝑢𝑟𝑙𝑦 𝑣𝑜𝑙𝑢𝑚𝑒 𝑃𝐻𝐹 700 𝑃𝑒𝑎𝑘 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑤𝑖𝑡ℎ 𝑖𝑛 𝑡ℎ𝑒 ℎ𝑜𝑢𝑟 15 Minute Traffic Volume 600 Hourly traffic volume, V = 1800 veh/h 𝑉 𝑃𝐻𝐹 500 4𝑥𝑣 400 Where, 300 PHF = peak-hour factor 200 V = hourly volume (in veh) 100 vm15 = volume during the peak 15 minutes of the analysis 0 hour 0.75 0.82 0.90 0.95 1.00 Peak Hour Factor 96 Speed is a rate of motion expressed as distance per unit of time and generally expressed in km/h. Average Travel Speed (S) is the length of the segment divided by the average travel time of vehicles traversing the segment, including all stopped delay times. Space Mean Speed represents the average travel speed (S). Average Running Speed is the length of the segment divided by the average running time of vehicles that traverse the segment. Running time includes only time during which vehicles are in motion. Free Flow Speed (FFS) is the average speed of vehicles on a given segment, measured under low-volume conditions. Density (D) is the number of vehicles occupying a given length of a lane or roadway at a particular instant. Measuring density directly in the field is difficult. However, it can be computed from the average travel speed (S) and flow rate (vp), which are measured more easily. For under-saturated traffic conditions, density (D) can be computed as follows: v D S Where, D = density (veh/km), vp = flow rate (veh/h), and S = average travel speed (km/h). Density is a critical parameter for uninterrupted-flow facilities because it characterizes the quality of traffic operations. It describes the proximity of vehicles to one another and reflects the freedom to manoeuvre within the traffic stream. 97 Service measures are performance measures used to define LOS for transportation facilities. Ideally, service measures should exhibit the following characteristics:  should reflect travellers' perceptions  should be useful to operating agencies  should be directly measurable in the field  should be estimable given a set of known or forecast conditions Service measure for motorways and multilane highways Travel speed is a major concern of drivers that relates to service quality. However, freedom to manoeuvre with in the traffic stream and proximity to other vehicles are equally noticeable concerns. These qualities are related to the density of the traffic stream.  Density increases as flow increases up to capacity, resulting in a service measure that is both perceivable by motorists and is sensitive to a broad range of flows. While speed is relatively less sensitive under low to intermediate flow conditions.  Hence, density is used as the service measure for motorway facilities, basic segments, ramp junctions, weaving segments, and multilane highway. 98 On two-lane highways traffic flow in one direction influences traffic flow in the other direction.  Motorists must adjust their travel speeds as volume increases and the ability to lane change/overtake other vehicles declines.  Three service measures are used for two-lane highways: average travel speed, percent time-spent- following, and percent free-flow speed. Service measures for different types of facilities Type of Facility Service Measures Uninterrupted  Freeway or Motorway Flow  Basic sections Density (pcu/km/ln)  Weaving Sections Speed (kph)  Ramps Flow rates (pcu/hr/ln)  Multilane Highways Density (pcu/km/ln)  Two-lane Highways Average travel speed, percent time-spent-following, and percent free-flow speed Interrupted Intersections Average delay, reserve capacity Flow Arterial roads Average travel speed 99 Chapter 13 of HCM 2016 addresses capacity and LOS analysis for uninterrupted-flow segments of rural and suburban multilane highways.  In general, uninterrupted flow may exist on a multilane highway if there are 2 mile (approx. 3.2 km) or more between traffic signals.  Where signals are more closely spaced, the facility should be analysed as an urban street.  Isolated signalized intersections should be analysed as signalized intersections.  This lecture covers only methodologies for automobiles and does not include methodologies for bicycle. (Source: HCM 2010) 100  Step 1: Input Data For Automobile Geometric data Demand volume Step 1: Input Data Measured FFS (if available) Measured FFS is not available  Demand volume; Step 2: Compute FFS Lane width adjustment  Number/width of lanes; Lateral clearance adjustment Measured FFS Median type adjustment available  Left-side and median lateral clearance; Access point adjustment  Type of median; Step 3: Select FFS Curve  Roadside access points per km; Step 4: Adjust Demand Volume  Percent of heavy vehicles (trucks, buses and RVs); PHF Number of lanes (one direction)  Terrain/grades; Heavy vehicle adjustment Driver population adjustment  Directional distribution; and Compare adjusted demand flow rates to base capacity  Driver population factor. Demand flow rate > base capacity Demand flow rate LOS = F < base capacity Step 5: Estimate Speed and Density Step 6: Determine LOS (Source: HCM 2010) 101 Step 2: Computer FFS FFS can be determined directly from field measurements or can be estimated using the following equation. FFS = BFFS – fLW – fLC – fM – fA Exhibit 21-4. Adjustment for lane width Exhibit 21-5. Adjustment for lateral clearance where, Lane width Reduction in FFS Four-lane Six-lane FFS = FFS of the segment, km/h (m) (km/h) highways highways  3.6 0.0 TLC Reduction in TLC Reduction in BFFS = base FFS of multilane highway segment, km/h 3.5 1.0 (m) FFS (km/h) (m) FFS (km/h) fLW = adjustment for lane width, km/h m (Exhibit 21-4) 3.4 2.1 3.6 0.0 3.6 0.0 fLC = adjustment for total lateral clearance (TLC), km/h 3.3 3.1 3.0 0.6 3.0 0.6 3.2 5.6 2.4 1.5 2.4 1.5 (Exhibit 21-5) 3.1 8.1 1.8 2.1 1.8 2.1 fM = adjustment for median type, km/h (Exhibit 21-6) 3.0 10.6 1.2 3.0 1.2 2.7 fA = adjustment for access point density, km/h (Exhibit 21-7) 0.6 5.8 0.6 4.5 Exhibit 21-7. Access-point density adjustment 0.0 8.7 0.0 6.3 Adjustments for Lateral Clearance Access- Reduction in FFS points/km (km/h) TLC = LCL + LCR 0 0.0 Exhibit 21-6. Adjustment for median type Note: Total lateral clearance (TLC) is the sum 6 4.0 Reduction in 12 8.0 Median Type of the lateral clearances of the median (if greater FFS (km/h) 18 12.0 Undivided highways 2.6 than 1.8m, use 1.8m) and shoulder (if greater 24 16.0 Divided highways 0.0 than 1.8m, use 1.8m). Therefore, for purposes of analysis, TLC can not exceed 3.6m. 102 For undivided four lane highway For divided four lane highway TLC = LCL+1.8 m TLC = LCL+1.8 m (if no obstruction on the median) fM = 2.6 km/h TLC = LCL+ LCR fM = 0 km/h SHOULDER SHOULDER SHOULDER SHOULDER MEDIAN Lateral Lateral obstruction obstruction e.g. pillar e.g. pillar LCL LCR >1.8 m LCL LCR 103 Step 3: Select FFS Curve Once FFS is determined, one of the four base speed-flow curves from Exhibit 21-3 is selected for use in the analysis. Interpolating between curves is not recommended. 104  Step 4: Adjust Demand Volume Demand volumes expressed as vehicles per hour under prevailing conditions must be converted to flow rate expressed in equivalent passenger cars per hour per lane (pc/h/ln). The following equation is used for this adjustment. 1 𝑓 𝑉 1 𝑃 𝐸 1 𝑃 𝐸 1 𝑣 𝑁𝑥𝑃𝐻𝐹𝑥𝑓 𝑥𝑓 where, where, ET, ER are the passenger car equivalents for trucks/buses, vp= demand flow rate under equivalent base and RVs, respectively. conditions, pc/h/l PT, PR are the proportions (as decimals) of trucks/buses, and V = demand volume under prevailing conditions, RVs, respectively. veh/h PHF = peak hour factor N = number or lanes (in one direction) fHV = adjustment factor for presence of heavy vehicles in the traffic stream fp= adjustment factor for atypical driver populations 105 106 Step 5: Estimate Average Travel Speed and Density Determine, (a) the FFS and appropriate FFS curve for use in the analysis, and (b) the demand flow rate (vp) expressed in pcu/h/lane under equivalent base conditions. The expected average passenger-car speed (S) can be drawn from Exhibit 21-3. The following equation can be used to estimate the density of the traffic stream. 𝑣 𝐷 𝑆 Step 6: Determine LOS Use Exhibit 21-2 to determine the expected LOS under the prevailing conditions. 107 The methodology presented in this lecture does not consider the following conditions:  The negative impacts of poor weather conditions, traffic accidents or incidents, railroad crossings, or construction operations;  Interference cause by parking on the shoulders of the multilane highway;  The effect of lane drops and lane additions at the beginning or end of multilane highway segments;  Possible queuing impacts when a multilane highway segment transitions to a two-lane highway segment;  Differences between various types of median barriers and the difference between impacts of a median barrier and a two-way right turn lane;  FFS below 70 km/h or higher than 100 km/h;  Significant presence of on-street parking;  Presence of bus stops that have significant use; and  Significant pedestrian activity. 108 A four-lane divided suburban highway in a level terrain has the following characteristics: lane widths 3.7 m, 1.8 m shoulder widths (each side), 20% trucks. The free-flow speed is 100 km/h. During the peak hour the flow has a PHF of 0.95. Part A: Based on the given information determine the following: a) the capacity (in one direction) of the highway during the peak hour. b) the maximum flow (in veh/h) during the peak hour at a level of service B. c) the level of service during the peak hour if the peak hour volume (PHV) is 2500 veh/h. Part B: Re-determine (a) to (c) above BUT for a 1.5 km long section with 5% grade. Solution a) The given conditions are ideal - hence, no need to make any adjustments to the estimated FFS. However, adjustment are needed to the demand volume due to 20% trucks in the traffic stream. From Exhibit 21-8, ET = 1.5 1 1 𝑓 0.909 1 𝑃 𝐸 1 1 0.2 1.5 1 109 LOS E represents the capacity. The maximum service flow rate (vp) at LOS E is 2200 pc/h/ln (Exhibits 21-2). Hence, the capacity of the highway, VE = vp x N x PHF x fHV = 2200 x 2 x 0.95 x 0.909 = 3800 veh/h b) The maximum service flow rate (vp) at LOS B is 1100 pc/h/l (Exhibits 21-2, ). Hence, the maximum flow at LOS B, VB = vp x N x PHF x fHV = 1100 x 2 x 0.95 x 0.909 = 1900 veh/h c) The equivalent service flow rate during peak hour, F 𝑉 2500 𝑣 1447 𝑝𝑐/ℎ/𝑙 𝑃𝐻𝐹𝑥𝑁𝑥𝑓 𝑥𝑓 2𝑥0.95𝑥0.909 From Exhibits 21-3, S = 100 km/h 𝑣 1447 𝐷 14.5 𝑝𝑐/𝑘𝑚/𝑙 𝑆 100∗ From Exhibits 21-2, Los is C. 110  Part B: For upgrade ET = 3.0 (Exhibit 21-9) and for downgrade ET =1.5 (Exhibit 21-11) For the upgrade, 1 1 𝑓 0.714 1 𝑃 𝐸 1 1 0.2 3 1 a) The maximum service flow rate (vp) is 2200 pc/h/l (Exhibits 21-2). Hence, the capacity, VE = vp x N x PHF x fHV = 2200 x 2x0.95x0.714 = 2985 veh/h Sufficient capacity in peak hour as 2985 veh/ h > 2500 veh/h b) The maximum flow rate at LOS B, VB = vp x N x PHF x fHV = 1100x 2x0.95x0.714 = 1490 veh/h c) The equivalent service flow rate (vp) during peak hour, 𝑉 2500 𝑣 1842 𝑝𝑐/ℎ/𝑙 𝑃𝐻𝐹𝑥𝑁𝑥𝑓 𝑥𝑓 2𝑥0.95𝑥0.714 S = 95* km/h (*approximated from Exhibits 21-3) 𝑣 1842 𝐷 19.4 𝑝𝑐/𝑘𝑚/𝑙 From Exhibits 21-2, Los is D. 𝑆 95∗ For the downgrade, the results will be same as for the level terrain as ET remains as 1.5. 111 For the four-lane divided highway in the Example 3-1, consider the combined effect of the following on the capacity: a) undivided, (was divided in Example 3-1) b) lanes 3.0 m, (was 3.7 m in Example 3-1) c) lateral clearance, 0.3 m, (was 1.8 m in Example 3-1) d) access point density, 6 per km Solution FFS = BFFS – fLW – fLC – fM – fA = 100 - 10.6 - 1.8 - 2.6 - 4 = 81 km/h For 81 kph FFS, vp = 2010 pc/h/ln (by interpolation using Exhibit 21-2). Capacity, VE = vp x N x PHF x fHV = 2010 x 2 x 0.95 x 0.909 = 3471 veh/h 112  Capacity is defined for prevailing roadway, traffic, and control conditions, which should be reasonably uniform for any section of facility analysed. Any change in the prevailing conditions will result in a change in the capacity of the facility. The time period used in most capacity analyses is 15 minutes, which is considered to be the shortest interval during which stable flow exists. 1. Roadway conditions refer to the geometric characteristics of the street or highway e.g. number of lanes, lane widths, shoulder widths and lateral clearance, design speed, horizontal and vertical alignment etc. 2. Traffic conditions refer to the composition of the traffic stream using the facility. 3. Control conditions refer to the types and specific design of control devices and traffic regulations present on a given facility e.g. signal, STOP, YIELD, Lane-use control. 113 Roadway conditions include all of the geometric parameters describing the roadway, including:  Number of lanes,  The type of facility and its development environment,  Lane widths,  Shoulder widths and lateral clearances,  Design speed,  Horizontal and vertical alignments, and  Availability of exclusive turn lanes at intersections. Type of facility and its development environment - Multi-lane facilities have higher capacities per lane than two-lane (two-way) facilities. Restricting access and parking also increases capacity. Lane width - Studies have shown that under uninterrupted flow conditions,the capacity of a traffic lane is maximum when it is 3.6 m wide. Shoulder widths and/or lateral clearances - Studies have shown that the lateral clearance (to obstructions such as retaining walls, abutments, lighting poles, and parked vehicles) significantly reduces capacity if they are located closer than 1.8 m from the edge of the traffic lane. As there is an inter-relationship between lane width and lateral clearance, the combined effects are used for highway capacity analysis. Design Speed - HCM 2000 offers analysis for a speed range from 70 km/hr to 100 km/hr. Horizontal and vertical alignment of a highway depend on the design speed and the land topography on which it is constructed. In general, as the severity of the terrain increases, capacity and service flow rate are reduced. This is significant for two-lane rural highways, where the severity of terrain can affect the operating capabilities of individual vehicles in the traffic stream and restrict opportunities for passing slow-moving vehicles. 114 The effect of gradients and alignment on a facility with design speed of 70 to 100 km/h is relatively low, if the traffic flow contains only passenger cars and the gradients are less than about 5%. However, the effect of gradients and alignment on heavy vehicles (i.e., vehicles with low power to weight ratios) can be very significant. The effect on heavy vehicles depends on the steepness and the length of the gradient as well as whether the gradient is up or down. If the up-gradients are more or less equivalent to the down-gradients over an extended length, then the effects can be determined on the basis of terrain (i.e., the topographical profile of the road) which is defined as follows: Level terrain - any combination of grades and horizontal and vertical alignment permitting heavy vehicles to maintain approximately the same speed as passenger cars; this generally includes short grades of no more than 1 to 2 percent. Rolling terrain - any combination of grades and horizontal or vertical alignment causing heavy vehicles to reduce their speeds substantially below those of passenger cars, but not causing heavy vehicles to operate at crawl speeds for any significant length of time. Mountainous terrain - any combination of grades and horizontal and vertical alignment causing heavy vehicles to operate at crawl speeds for significant distances or at frequent intervals. Crawl speed is the maximum sustained speed which heavy vehicles can maintain on an extended upgrade of a given percent. It is often not appropriate to analyse a section of highway/roadway as an extended general terrain segment. In these cases, the HCM 2000 provides guidelines and gives (more complicated) procedures to determine the effect of specific grades. 115 Traffic conditions that influence capacities and service levels include vehicle type, lane use or directional distribution and driver population. Vehicle Types - Vehicles which are larger or have operating capabilities poorer than passenger cars reduce highway capacity. Heavy vehicles are defined as having more than four tyres on the pavement. They are generally grouped into one of the three categories: Trucks - A truck is defined as a heavy vehicle involved primarily in the transport of goods, or in the delivery of a service (other than public transportation). Buses - A bus is a heavy vehicle involved in the transportation of groups of people (at least 16) on a for-hire, charter, or franchised transit basis. Buses can be further categorised as intercity or local transit buses. For analysis of multi-lane highways, buses are categorised as trucks. Recreational vehicles - A recreational vehicle (RV) is defined as a heavy vehicle, operated by a private motorist, and involved in the transport of recreational equipment or facilities. Lane Use and Directional Distribution - Although often significant, these factors are beyond the scope of this lecture note. Lane use is particularly significant on multi-lane facilities - typically, the shoulder lane which usually carries less traffic than the other lanes. Directional distribution is a critical factor on two-lane (two-way) highways - optimum conditions occur when there is 50% in each direction and capacity declines as the directional split becomes more unbalanced. Driver Population – Studies have noted that non-commuter driver populations do not display the same characteristics as do regular commuters. For example, for recreational traffic on a motorway segment, capacities have been observed to be as much as 10% to 15% lower than for commuter traffic travelling on the same segment. HCM methods include an adjustment for driver population, for system elements where driver population has made a difference in the observed capacity. 116 Control Conditions These conditions refer principally to interrupted flow facilities such as urban arterials and consist of factors such as available green time, parking. Interrupted flow is far more complex than uninterrupted flow. It is beyond the scope of this lecture note. Technology ITS strategies aim to increase the safety and performance of roadway facilities. Motorway ITS strategy such as ramp signalling, has demonstrated improved mainline throughput and speed, while incident management techniques have reduced the time required to identify and clear incidents, thus minimizing the time during which capacity is reduced as well as the associated delay. Variable speed limits on motorway, combined with automated speed limit enforcement, also show promise but require additional study. Other ITS strategies seek to shift demand to alternative routes or times, thus making better use of available system capacity and reducing delay on individual vehicle facilities. 117  TRB Special Report (2001) Traffic Flow Theory, A State-of-the-Art Report, A revised version.  TRB Special Report 165 (1975) Traffic Flow Theory, A Monograph.  Mannering, F.L., Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis. 3rd Edition, Wiley.  Ogden K W and Taylor S Y (1996 and reprinted 1999) (Editors). Traffic Engineering and Management, Monash University, Melbourne, Australia.  Transportation Research Board (2016) Highway Capacity Manual 2016.  Transportation Research Board (2010) Highway Capacity Manual 2010.  Transportation Research Board (2000) Highway Capacity Manual 2000. 118 Problem 3-1 Counts Vehicle Count Variation 600 The figure for Problem 3-1 shows traffic count data collected from a highway during the morning peak hour from 8:00 am to 9:00 am. The 500 traffic volume is counted in each 5 minutes as shown in the figure. 400 Determine the peak hour factor (PHF) using: 300 (i) 5-minute observation time interval; and 200 (ii) 15-minute observation time interval. 100 [Answers: a) 0.53 b) 0.67] 0 Problem 3-2 Determine the maximum flow at LOS C and LOS E for a four-lane Figure for Problem 3-1 undivided suburban highway on level terrain with the following characteristics: Lane widths: 3.5 m Lateral obstructions: 1.2 m (from the outer lane edge) Design speed: 100 km/hr Access points: 12 per km Heavy vehicles (trucks): 10% PHF = 1.0 [Answers: 2668 veh/h and 3958 veh/h] 119 Problem 3-3 A six-lane suburban arterial with a design speed of 100 km/h has a 2.5 m paved shoulder, 3.7 m wide lanes and a 5.5 m median. The road alignment is level and ideal. Based on the given information determine the following: (i) the capacity of the arterial, with 12% trucks (ii) the volume-to-capacity ratio and the level of service during the peak hour, if the PHF is 0.92 and the flow is 4200 veh/hr (in one direction) of which 12% are trucks (iii) the capacity and the maximum flow at LOS D (in pc/h/l), if the lane widths are reduced to 3.5m and there are lateral obstructions in the median and on the shoulder, (say, a barrier plus street lighting) 1.2 m from the lane edges. [Answers: a) 6226 veh/h b) 0.73 and LOS D c) 5663 veh/h and 5146 veh/h] Problem 3-4 An undivided four-lane urban highway with a design speed of 100 km/h on a rolling terrain has 3.1 meters wide lanes, a 0.6m paved shoulder and frequent lateral obstructions at 1.2 meters distance from the edge of the shoulder that is, there is 8.0 meters of total width available (in one direction). It may take some time before finance is available to improve the lateral clearance. In the meantime, the following three options are being considered: Option 1: existing (status quo) Option 2: extend the pavement surface to have a lane width of 3.3 meters per lane, plus 0.2 m of shoulder Option 3: extend the pavement surface to have a lane width of 3.6 meters per lane (no shoulder) Determine the maximum capacity, which can be obtained from the three options assuming 8% trucks in the traffic stream, there are very few access points per km and the PHF is 1.0. [Answers: 3860 veh/h] 120 Problem 3-5 A four-lane divided rural multi-lane highway with a design speed of 100 km/h has an ideal cross-section and alignment except there is a 5% grade for 1.5 km. The peak hour flow is 2200 veh/hr with 10% trucks and the PHF is 0.95. For the upgrade and the downgrade section, determine the expected speed (in km/hr), the expected density (pc/km/l), and the expected level of service during the peak hour. [Answers: For upgrade: 100 kph, 13.9 pcu/km/ln and LOS C, For downgrade: 100 kph, 12.2 pcu/km/ln and LOS C] Problem 3-6 Re-evaluate Problem 3-5 using a grade of 4% (for 1.5 km), the PHF is 0.82 AND 5% recreational vehicles. [Answers: For upgrade: 97 kph, 17.0 pcu/km/l and LOS D, For downgrade: 100 kph, 14.2 pcu/km/l and LOS C] 121 Problem 3-7 A four-lane undivided suburban highway (with two lanes in each 700 600 Vehicle Count (veh) 550 570 direction) in a rolling terrain has the following characteristics: 600 530 500 500 450 450 Design speed: 100 km/hr 400 400 400 350 Lane width: 3.5 m 300 Lateral obstructions: 1.2 m (from the edge of the outer lane) 200 Number of access points: none 100 Percentage of trucks: 10% 0 6:45 7:00 7:15 7:30 7:45 8:00 8:15 8:30 8:45 9:00 Time Figure for Problem 3-7 The figure for Problem 3-7 presents traffic count data recorded using detector loops placed on the highway section (in one direction). Based on the given information, determine the following: a) The peak hour flow rate and peak hour factor. b) The expected free flow speed (in km/h) and service flow rate (in pcu/h/l) under the prevailing conditions. c) The expected average operating speed (in km/h), the expected density (in pcu/km/l), the level of service and the volume-to-capacity ratio during the peak hour. d) The capacity of the highway section and the expected average operating speed at the capacity (in km/h). [Answers: a) 2050 veh/h, 0.9, b) 95.8 km/h, 1310 pcu/h/l, c) 95.8 km/h, 13.7 pc/km/l, LOS C, 0.607, d) 2050 veh/h, 85 km/h] 122