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## Traffic Flow Characteristics

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**Traffic Streams**• Traffic streams are made up of individual drivers and vehicles, interacting in unique ways with each other and with elements of the roadway and general environment. • Because the judgments and abilities of individual drivers come into play, vehicles in the traffic stream do not and cannot behave uniformly. • Further, no two similar traffic streams will behave alike, even under equivalent circumstances, as driver behavior varies with local characteristics and driving habits. • Traffic streams, however, can be described in quantitative terms with the use of some key parameters like volume, speed and density.**Traffic Streams**• Traffic facilities are broadly separated into two principal categories: • Uninterrupted flow facilities, and • Interrupted flow facilities • Uninterrupted Flow Facilities are those on which noexternal factors cause periodic interruption to the traffic stream. Example: Freeway • Interrupted Flow Facilities are those having external devices that periodically interrupt traffic flow. Example: Urban Roadways. • The principal devices creating interrupted flow are primarily traffic signal and also STOP and YIELD signs, etc.**Traffic Streams**• Uninterrupted and Interrupted Flow are terms that describe the facility and not the quality of flow. • A congested freeway where traffic is almost coming to a halt is still classified as uninterrupted flow facility, because the reason for congestion is internal to the traffic stream. • A well-timed signaling system on an arterial may result in almost uninterrupted traffic flow, but still is classified as interrupted flow facility.**Traffic Stream Parameters**• Traffic Stream Parameters fall into two broad categories: • Macroscopic parameters, and • Microscopic parameters. • Macroscopic parameters characterize the traffic stream as a whole • Microscopic parameters characterize the behavior of individual vehicles in the traffic stream with respect to each other.**Traffic Stream Parameters**• Macroscopic flow • traffic in the aggregate. • overall speeds, traffic flows, densities, etc. • Microscopic flow • traffic at the level of the individual vehicle • observe the particular behaviors of drivers, and of individual vehicles in the traffic stream. • vehicle headways & lane-changing behavior (merging, diverging, weaving, passing, etc.) critical @ microscopic level.**Traffic Stream Parameters**• A traffic stream may be described macroscopically by three parameters: • Volume or Rate of Flow • Speed • Density**Traffic Stream Parameters**• Volume and Flow • Volume is defined as the number of vehicles that pass a point on a highway, or a given lane or direction of a highway, during a specified time interval. • Usually expressed as vehicles per unit time, for example, vehicles per hour or vph. • Rate of Flow is the equivalent hourly rate at which vehicles pass a point on a highway lane during a time period less than 1 hour.**Traffic Stream Parameters**• Volume and Rate of Flow are two different measures. • Volume is the actual number of vehicles observed or predicted to be passing a point during a given time interval. • Rate of flow represents the number of vehicles passing a point during a time interval less than 1 hour, but expressed as an equivalent hourly rate.**Traffic Stream Parameters**• A volume of 200 vehicles observed in a 10-minute period implies a rate of flow of (200 x 60)/10 = 1200 veh/hr. • Note that 1200 vehicles do not pass the point of observation during the study hour, but they do pass the point at that rate for 10 minutes.**Traffic Stream Parameters**• Capacity : The maximum number of vehicles per unit time that a particular transportation facility may accommodate (veh/h).**Traffic Stream Parameters**• Daily Volumes and Their Use • A common time interval for volumes is a day. • Daily volumes are frequently used as the basis for highway planning and general observations of trends. • Traffic volume projections are often based on measured daily volumes.**Traffic Stream Parameters**• Daily Volumes and Their Use (Contd..) • There are four commonly used daily volume parameters: • Average Annual Daily Traffic (AADT): is the average 24-hr traffic volume at a given location over a full 365-day year. • Average Annual Weekday Traffic (AAWT): is the average 24-hr traffic volume occurring on weekdays over a full 365-day year. • Average Daily Traffic (ADT): is an average 24-hr volume at a given location for some period of time less than a year, but more than one day. • Average Weekday Traffic (AWT): is an average 24-hr traffic volume occurring on weekdays for some period less than one year.**Traffic Stream Parameters**• Hourly Volumes and Their Use • While daily volumes are useful in highway planning, they cannot be used alone for design or operational analysis purposes. • Traffic volume varies considerably during the course of a 24-hr day. • The single hour of the day that has the highest hourly volume is referred to as the “peak hour”. • Traffic volume within this hour is of greatest interest to traffic engineers in design or operational analysis.**Traffic Stream Parameters**• Sub-hourly Volumes and Rates of Flow • The variation within a given hour is also of considerable interest for traffic design and analysis. • The quality of traffic flow is often related to short-term fluctuations in traffic demand. • A facility may have capacity adequate to serve the peak-hour demand, but short-term peaks of flow within the peak hour may exceed capacity, thereby creating a breakdown.**Traffic Stream Parameters**• Sub-hourly Volumes and Rates of Flow**Traffic Stream Parameters**• Sub-hourly Volumes and Rates of Flow (contd..) • The relationship between hourly volume and the maximum rate of flow within the hour is defined by the Peak Hour Factor (PHF). • where, V = hourly volume, and V15 = maximum 15-minute volume within the hour.**Traffic Stream Parameters**• Sub-hourly Volumes and Rates of Flow (contd..) • The maximum value of PHF is 1.00, which occurs when the volume in each 15-min period is equal. • The minimum value is 0.25, which occurs when the entire hourly volume occurs in one 15-min interval. • The normal range of values is between 0.70 and 0.98, with lower values signifying a greater degree of variation in flow during the peak hour.**Traffic Stream Parameters**• Speed • Speed is the second principal parameter describing the state of a given traffic stream. • In a moving traffic stream, each vehicle travels at a different speed. • Thus, the traffic stream does not have a single characteristic speed but rather a distribution of individual vehicle speeds. • From the distribution of vehicle speeds, a number of “average” or “typical” values may be used to characterize the traffic stream as a whole.**Traffic Stream Parameters**• Speed (contd..) • Average or mean speeds can be computed in two different ways: • Time Mean Speed (TMS) is defined as the average speed of all vehicles passing a point on a highway over some specified time period. • Space Mean Speed (SMS) is defined as the average speed of all vehicles occupying a given section of a highway over some specified time period. • Time mean speed is a point measure, while space mean speed is a measure relating to a length of highway or lane.**Traffic Stream Parameters**• Speed (contd..) • where, d is the distance traversed, n is the number of travel times observed and ti is the travel time for i-th vehicle.**Traffic Stream Parameters**• Speed (contd..)**Traffic Stream Parameters**• Relationship between time mean speed and space mean speed • Time mean speed is greater to equal to space mean speed • The two speeds have the following relationship:**Traffic Stream Parameters**• Speed (contd..) • Average Travel Speed and Average Running Speed • They are two forms of space mean speed. • The Average Travel Speed computation uses total average travel time while Average Running Speed computation uses the average running time. • Running time is defined as the time during which the vehicle is in motion while traversing a given highway segment.**Traffic Stream Parameters**• Speed (contd..) Example • Consider the case of a 1-mile section of a roadway. On the average, it takes a vehicle 3 minutes to traverse the section, 1 minute of which is stopped time experienced at signalized intersections.**Traffic Stream Parameters**• Speed (contd..) • Operating Speed is defined as the maximum safe speed at which a vehicle can be conducted in a given traffic stream, without exceeding the design speed of the highway segment. • Operating speed is difficult to measure. It requires that a test car be driven through the traffic stream in a manner consistent with the definition. • As “maximum safe speed” is a judgmental matter, consistent measurements among test-car drivers are not often achieved.**Traffic Stream Parameters**• Density • Density, the third measure of traffic stream conditions, is defined as the number of vehicles occupying a given length of highway or lane. • Usually expressed as vehicles per mile (vpm) or vehicles per mile per lane (vpmpl). • Density is difficult to measure directly, as an elevated point is required.**Traffic Stream Parameters**• Density (contd…) • It can, however, be computed from speed and flow rate using the relationship as follows: Where, q = flow rate (vph) vs = space mean speed (mph), and k = density (vpm).**Traffic Stream Parameters**• Spacing and Time Headway • Spacing and Time Headway are microscopic measures, because they apply to individual pairs of vehicles within the traffic stream. • Spacing is defined as the distance between successive vehicles in a traffic lane, measured from some common reference point on the vehicles, such as the front bumpers or front wheels. Spacing @ given point**Traffic Stream Parameters**• Spacing and Time Headway • Time Headway is the time between successive vehicles as they pass a point along the lane, also measured between common reference points on the vehicles. Particular location**Traffic Stream Parameters**• Clearance (ft) = (spacing) – (average vehicle length) • Gap (sec) = (headway) – (time equivalence of the average vehicle length)**Traffic Stream Parameters**• Spacing and Time Headway (contd..) • Average values of Spacing and Time Headway are related to the macroscopic parameters as follows: • where, k = density (vpmpl), vs = average speed (ft/sec), q = rate of flow (vphpl), da = average spacing (ft), and ha = average time headway (sec).**Traffic Stream Parameters**• Lane occupancy: measure used in freeway surveillance. • Ratio of the time that vehicles are present at a detection station in a traffic lane compared to the observation time.**Traffic Stream Parameters**• Lane occupancy • Time that the vehicle used to travel L+C:**Traffic Stream Parameters**• Lane occupancy • Assume k vehicles are evenly spread out on 1 mile highway at speed vs mile/hr • Total time needed to have all vehicles pass the detector is: (hrs) • Therefore:**Speed, Flow and Density Relationship**• Assume • We have**Properties of speed-density curve**• The product of the x-y coordinates of the point P is the flow associated with P • Max flow occurs at:**Properties of speed-flow curve**• The slope of the line connecting any point on the curve and the origin is the inverse of the density • Max flow occurred at:**Properties of flow-density curve**• The slope of the line connecting any point on the curve and the origin is the space mean speed**General properties for any traffic flow model**• Need to satisfy four boundary conditions • Flow is zero at zero density • Flow is zero at maximum density • Mean free-flow speed occurs at zero density • Flow-density curves are convex (i.e. there is a point of max flow)**Connections between speed, density and flow**• A: almost zero density, free-flow speed, very low volume • B: increased density, reduced speed, increased volume • C: increased density, reduced speed, max volume • D: jam density, min speed (crawling), very low volume**Traffic Stream Parameters**• Since a given flow may occur under two completely different operating conditions (stable and unstable), volume or rate of flow cannot be used as a measure describing the operational quality of the traffic stream. • Speed and density, however, are good measures of the quality of operations, as both uniquely describe the state of the traffic stream.**Macroscopic Models of Traffic Flow**• The two most commonly used macroscopic models are: • The Greenshields Model • The Greenberg Model**Macroscopic Models of Traffic FlowGreenshields’ Model**• The general model connecting speed, flow, and density discussed so far is a linear model proposed by Greenshield in 1935. • He suggested that the speed and density were linearly related as follows:**Macroscopic Models of Traffic FlowGreenshields’ Model**• It can be shown that: • The maximum flow (i.e., capacity) occurs when the speed of the traffic stream is half of the free-flow speed: • The maximum flow (i.e., capacity) occurs when the density is half of the jam density: • The maximum flow, qmax:**Macroscopic Models of Traffic FlowGreenberg’s Model**• Greenberg developed a model in 1959, taking speed, flow and density measurements in the Lincoln Tunnel. • Used a fluid-flow analogy concept. • The model is of the following form:**Macroscopic Models of Traffic FlowGreenberg’s Model**• It can be shown that: • The maximum flow occurs when speed • The maximum flow occurs when density (k) is related with jam density (kj) as follows: • Then, the maximum flow (qmax) is the product of the density (k) and speed (vs) at maximum flow.**Macroscopic Models of Traffic FlowLimitations of the Models**• The Greeshields Model can be used for light or heavy traffic conditions. • The Greenberg Model is useful only for heavy traffic conditions.