# John van Rijn INDEVELOPMENT ROAD CAPACITIES

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1 John van Rijn INDEVELOPMENT ROAD CAPACITIES

2 ROAD CAPACITIES Any part of this publication may be fully reproduced or translated provided that the source and author are fully acknowledged. Edition

4 1 INTRODUCTION This document provides information about a traffic flow theory and simulation models and it provides information about capacities of road networks. Capacity is usually defined as: The maximum hourly rate at which persons or vehicles can reasonably be expected to traverse a point or uniform section of a lane or roadway during a given time period under prevailing roadway, traffic and control conditions. 4

5 Road networks Traffic stream characteristics Intensity 2 MOTORWAYS Road networks are composed of intersections and links. If the links are long enough, the intersections will no longer have influence on the behaviour of the traffic on a link. The capacity of the road network is thus different near the intersection than on long links. This chapter will first discuss the capacities on the long links and subsequently the capacities of some types of intersections. The traffic stream has three main characteristics: Intensity Density And mean speed The intensity of a traffic flow is the number of vehicles passing a cross section of a road in a unit of time. The intensity is expressed with q. Thus in formula: q= n/t or Intensity = number of vehicles/unit of time Density The density of a traffic flow (k) is the number of vehicles (m) present on a unit of road length (X) at a given moment. Thus in formula: k= m/x If the traffic flow is in a stationary and homogeneous state, then the following relationship is valid: density multiplied with mean speed (u) equals the intensity. In formula: q=k*u Three fundamental diagrams In traffic flow theory there are three fundamental diagrams: Intensity-density q=q(k) Speed-density u=u(k) Speed-intensity u=u(q) 5

6 The relations in the diagrams tend to depend on characteristics of the road, drivers and their vehicles and conditions like lightning and weather. Eddie It is therefore common that the exact relationship differ from country to country but also varies over time. First of all the composition of the traffic changes but also traffic behaviour is totally different. In western world people tend to drive faster and keep less distance between the bumpers of each other cars. On their highways they separated slow from fast moving traffic and roads are usually lighted. In many low and middle-income countries traffic behaves in a less disciplined manner and that affects the average speed of the vehicles. Eddie was the first researcher to indicate the possibility of a discontinuity in the diagram around the capacity point. It was observed that an increasing traffic stream that moves in free flow reaches a higher capacity than a diminishing traffic stream moving from a congested situation into a free flow situation. 6

7 More lanes Overtaking vehicles Dominant traffic rules Keep your lane Fast lane If a road is composed of different lanes, it is not correct to add the diagrams of the different lanes to compile a diagram for the whole road. In particular the distribution of the traffic over the different lanes have major complications. It appears that the upper mean speed of a multilane highway almost remain constant until the road get congested. This phenomenon can be partly be explained due to changing lanes of overtaking vehicles and therefore changing intensities at the different lanes. This process depends also partly on the traffic rules on multi-lane roads. Basically there are two systems. 1. Keep your lane 2. Fast lane Keep your lane implies that traffic will stay in its lane until it wants to take over another vehicle. To take over the vehicle, it could either move to the left or right lane as it pleases. Fast lane system means that vehicles in principle will use the outer lane, until it wants to take over. After having taken over the vehicles in the inner lanes, it moves back to the outer lane. Thus the inner lane is used for taking over only. When the traffic intensity increases and reaches congestion, more and more vehicles will stay in the inner lanes, and traffic starts using the keep your lane system. With increasing intensity, that starts and still is in free flow situation, it is noticeable that traffic in the outer lanes are slowing down, while traffic in the inner (fast) lanes keep their high speed. But because more and more traffic is using the inner lanes, the average speed of all traffic tends to remain constant. 7

8 Maximum free flow Queue discharge To estimate the capacities of roads, it is necessary to take these aspects into account. It is possible to calculate the maximum free flow capacity by fitting a model of the function q(k) to data. The capacity is the maximum of q(k). To estimate the queue discharge capacity, it is necessary to set-up three measuring stations in and near the overloaded bottlenecks. 1. Upstream of the bottleneck 2. Downstream of the bottleneck, the traffic should move freely, thus there is no congestion 3. At the bottleneck At an overloaded bottleneck the intensities at the three stations are more or less the same. The station downstream is than used to measure the traffic flow, because it has the smoothest traffic flow. 8

9 Level of service 2.1 CAPACITY AND LEVEL OF SERVICE ANALYSIS An important question is how much traffic the road can carry. Current studies present the relationships between the capacity of the road link/node and the resulting level-of-service offered to the user of the road. LOS Flow conditions v/c limit Service volume Speed Density (veh/h/lane) (miles/h) (veh/mile) A Free > 60 < 12 B Stable > 57 < 20 C Stable > 54 <30 D High density : E Near capacity : F Breakdown Unstable < 30 > 67 Level of service for basic freeway sections for 70 km/h design speed Ideal conditions Highway Capacity Manual The above-presented table presents the capacities and service-levels for traffic in the US under ideal conditions. The ideal conditions relate to the lane width (3.5 meters) and to the fact that it is a motorway. Thus slow traffic does not interfere with fast traffic. The maximum capacity in the US is around 2000 vehicles per lane. The Highway Capacity Manual proposes using the following example relation to express the influence of non-ideal conditions c=cj N fw fhv fp where c = capacity (veh/h) Cj = lane capacity under ideal conditions with design speed of j N = number of lanes f w = lane width and lateral clearance factor f HV = heavy vehicle factor fp = driver population factor Effect of rain Several studies have shown that other factors (such a weather and ambient conditions) also influence the capacity significantly. For instance, the effect of rain on the capacity yields a factor of fweather = The capacity of the road is highly influenced by the behaviour of the drivers. In countries, with disciplined traffic behaviour the capacity seems to be considerable higher than in countries where traffic behaviour is less disciplined. Less disciplined traffic tend to block other traffic. Another factor are the headways that traffic is using. Headways is the distance between two vehicles in a row. In particular on motorways, it appears that the high-speed traffic with small headways, results in a high capacity of the road. 9

10 Typical ramps Ramps Ramps are sections of roadway that provide connections from one motorway to another motorway or normal road. Entering and exiting traffic causes disturbances to the traffic on the motorway and can thus affect the capacity and level-of service of the motorway. There are basically two types of ramps: 1. Tapers 2. Parallel merger An example of a taper A parallel merger Weaving sections Weaving is the crossing of traffic streams moving in the same general direction. It is accomplished through merging and diverging movements. Traffic change lanes at the weaving sections. (Ramps are in a way weaving sections) There are several different kinds of weaving sections. The most common ones are: Simple weaving Multiple weaving One sided weaving Two-sided weaving Or a combination of the above mentioned 10

11 With the help of the graph below it is possible to calculate the maximum capacity of a multi lane weaving section. Note that it is necessary to change N and SV in the presented equations. 11

13 Stationary traffic lights Traffic situation Unlike stationary traffic lights do not react on the traffic situation. Regardless whether there are vehicles in one of the legs of the junction it will signal that vehicles may pass or have to stop. Dynamic traffic lights do react on the traffic situations and it will alter its green, yellow and red periods on basis of actual traffic demands. Most traffic lights in low-income countries are of the stationary type. The following formulas to calculate parameters of the traffic light, like delay, queue length and capacity are based for these kinds of junctions. Dynamic traffic lights are usually based on calculations with computer models. The traffic situation affects the parameters of interest considerable. The queue length, the average delay time etc are all considerable longer when the traffic is congested. Unless specified differently the formulas presented below are applicable under free-flow situations. The first parameter of interest the delay. The number of stops and the time a vehicle has to wait at a traffic light before it can pass a junction influences the delay. The average delay can be calculated with the following formulas: Extreme low traffic density (pedestriants and cycle lanes) D av =r 2 /(2*C) Where: D av = average delay per vehicle or pedestrian r= time of yellow and red period per cycle [seconds] C= cycle period [seconds] Normal circumstances D av =C(1-λ) 2 /[2*(1-y)] Where: λ= green time/cycle period ratio; g/c (g= green time [seconds]) y=i/k I= intensity K= capacity of leg Under optimal circumstances, maximum capacity and traffic is not congested Queue length D av =0.9*{ C(1-λ) 2 /[2*(1-y)] + x 2 /[2q(1-x)] } Where: x= saturation level; I*C/(K*g) q= number of arriving vehicles per second; I/3600 The queue length can be expressed in the number of vehicles or in meters. But most traffic engineers are interested to find out if the queue is blocking another intersection, and therefore the queue length is usually expressed in meters. The total length in meters depend on the 13

14 number and composition of vehicles and the average distance between two vehicles. When the composition of the vehicles is known it is relatively easy to determine the average vehicle length. N=q*r q the number of vehicles arriving at the junction per second N b = N/{1-(J/V)q} J average length of vehicle V Driving Speed [m/s] N m =1.4 N b /(1-y) Capacity Under normal circumstances (no congestion) the total number of vehicles in the queue (N) is equal to number of vehicles arriving during the yellow and red period [r (sec)]. Because the vehicles have a certain dimension, the location where the vehicles have to stop moves backwards. And therefore the vehicles have to stop earlier as the queue grows. Thus the number of vehicles arriving at the junction accelerates. It is therefore necessary to correct the number of vehicles in the queue. When the situation close to the saturation level, the queue will continue growing during the first part of the green light period. It is possible to include this behaviour to multiply N b with 1/(1-y). It is often assumed that the arrival of the vehicles follow the Poisson distribution and therefore N b is also multiplied with 1.4. The capacity of a single lane is the maximum number of vehicles that can pass the stop line of a lane. The basic saturation flow (S 0 ) is 1800 pce/h 1, PCE stands for passenger car equivalent. Since lorries, busses and vans need more time to pass the stop line, they have a higher PCE. Vehicle Category PCE value Passenger car 1 Lorry 1.5 Articulated Lorry 2.3 Bus 2 Motor cycle 0.4 Bicycle The basic saturation flow for separate bicycle lanes and pedestrian lanes are a lot higher; Lane width (m) Basic saturation flow per hour Bicycles Pedestriants

16 Table Adjustment factor for bus blockage Number of lanes in lane group Number of stopping busses per hour Table Adjustment factor for area type (HCM) Area type Central business district All other areas f area Table Adjustment factor for radius of turning movement Radius (m) f radius Table Adjustment factor for Composition of traffic movements Percentage of vehicles turning f comp Table adjustment factor for traffic situations in which traffic has to give way to pedestrians Number of pedestraints/hour f pp

18 With the help of the graph it is possible to estimate the value for α. 18

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