Unlocking Some Mysteries of Traffic Flow Theory Robert L. Bertini Portland State University University of Idaho, February 22, 2005

Introduction  Objective: learn how to think (avoid recipes) and visualize.  Tools of the trade:  Time space diagram  Input output diagram  Spreadsheets, probability, statistics, simulation, optimization  Transportation operations  Multimodal  Fleets: control routes and schedules  Flows: streams whose routes and schedules are beyond our control  Transportation Systems  Moving parts: containers, vehicles, trains  Fixed parts: networks, links, nodes, terminals  Intangibles: “software”

Focus  Travel time  Component of transportation cost  Measure delays  Prediction desirable  Facilitates cost minimization/optimization  Cost effectiveness: trade off travel time vs. construction + operating cost  Common elements in transportation  Rush hours/peaking  Seasonal variation  Long run trends in demand

Two tools  Peak demand  Can’t accommodate  Zero benefit for investment in last increment of capacity  A model  Transportation system as a network of channels connected by bottlenecks (flow restrictions)  The time space plane  Study how vehicles overcome distance  Study vehicular movement between bottlenecks  Queueing theory  Estimate delays at facilities when demand exceeds capacity  Study bottlenecks  Impacts to non-users  Safety  Noise  Energy consumption  Air pollution

Some Reminders Dimensional Analysis Triangles Rise Run Slope=Rise/Run

Some basic meaurements. Consider a single vehicle at one point.  Stand at a point.  Establish a line across road.  Record passage time of each vehicle.  Do this over a specific time interval (15 min, 1 hour, 1 day, 1 year) VehicleTime 19:02:09 29:04:34 39:06:44 49:08:12 59:09:37 69:11:22 79:12:49 89:13:33 99:14:20

Some basic meaurements. Consider a single vehicle at one point.  Stand at a point.  Establish a line across road.  Record passage time of each vehicle.  Do this over a specific time interval (15 min, 1 hour, 1 day, 1 year) VehicleTime 19:02:09 29:04:34 39:06:44 49:08:12 59:09:37 69:11:22 79:12:49 89:13:33 99:14:20

Some basic meaurements. Consider a single vehicle at one point.  Still standing at one point.  Imagine you are at a bus stop.  Count number of buses per unit time = Frequency  We might be interested in the actual or average time between buses – WHY?

Some basic meaurements. Consider a single vehicle at one point. ParameterUnits Flowqvehicles/time#/time Frequency buses/time #/time Headway htime/vehicle time/#

Some basic meaurements. Consider a single vehicle at one point. You can also measure the point speed of a vehicle, for example using a radar gun. ParameterUnits Speedv t distance/timemi/hr If you collect a set of vehicle speeds over a time interval and compute the arithmetic mean of these speeds, you have measured the Time Mean Speed for one point and over one time interval:

Some basic meaurements. Consider a section of straight road.  Imagine an aerial photograph.  If road section is one mile long, we can count the number of vehicles on the segment at one instant in time. 1 mi

Some basic meaurements. Consider a section of straight road.  Imagine an aerial photograph.  If road section is one mile long, we can count the number of vehicles on the segment at one instant in time:  We can now think about the average distance between vehicles on this segment at one instant in time: 1 mi

Some basic meaurements. Consider a section of straight road.  Now imagine two aerial photographs, taken at two times t 1 and t 2. 1 mi t1t1 t2t2 1 1 x1x1 x2x2 t1t1 t2t2

Some basic meaurements. Consider a section of straight road.  Now imagine two aerial photographs, taken at two times t 1 and t 2.  If you collect a set of vehicle speeds measured over space and compute the mean, you have measured the Space Mean Speed for this segment over a time interval: 1 mi t1t1 t2t2 1 1 x1x1 x2x2 t1t1 t2t2

Some basic meaurements. Time mean vs. Space mean speed  Time mean speed: speeds measured at one point averaged over time.  Space mean speed: speeds measured over a segment averaged over space.  The inverse of speed is known as Pace

Putting together some parameters Consider dimensional analysis. ParameterUnits Flowqvehicles/time#/t Frequency buses/time #/t Headway htime/vehicle t/# Densitykvehicles/distance#/x Spacingsdistance/vehiclex/# Speedvdistance/timex/t Paceptime/distancet/x

ParameterUnits Flowqvehicles/time#/t Frequency buses/time #/t Headway htime/vehicle t/# Densitykvehicles/distance#/x Spacingsdistance/vehiclex/# Speedvdistance/timex/t Paceptime/distancet/x Putting together some parameters Consider dimensional analysis.

ParameterUnits Flowqvehicles/time#/t Densitykvehicles/distance#/x Speedvdistance/timex/t

q#/t k#/x vx/t Putting together some parameters Consider dimensional analysis.

q=#/t k=#/x v=x/t Putting together some parameters Consider dimensional analysis.

q=#/t k=#/x v=x/t Putting together some parameters Consider dimensional analysis.

q=#/t k=#/x v=x/t

Putting together some parameters Consider dimensional analysis. q=#/t k=#/x v=x/t q=kv

Putting together some parameters. Consider dimensional analysis. q=#/t k=#/x q max k max

Putting together some parameters. Consider dimensional analysis. q=#/t k=#/x q max k max Traffic state 1 (k 1,q 1 ) k1k1 q1q1

Putting together some parameters. Consider dimensional analysis. q=#/t k=#/x q max k max Traffic state 1 (k 1,q 1 ) Slope = rise/run = q 1 /k 1 = (#/t)/(#/x) = x/t = v k1k1 q1q1

A straight highway Some basic traffic flow principles  Consider a 22’ vehicle traveling at 30 mph

A straight highway Some basic traffic flow principles  Consider a 22’ vehicle traveling at 30 mph  How “close together” might we expect two vehicles to travel comfortably?  Maybe 3 vehicle lengths spacing (66 ft) is comfortable.

A straight highway Some basic traffic flow principles  Consider a 22’ vehicle traveling at 30 mph  How “close together” might we expect two vehicles to travel comfortably?  Maybe 3 vehicle lengths spacing (66 ft) is comfortable.  What is the headway (a point measurement)?  First what are headway units? seconds/vehicle passing a point  Time to travel 4 vehicle lengths:

An intersection Add a cross street  Now add a cross street.  Two interrupted traffic streams must now share the right-of-way.  Assume a simple 60 sec cycle with 30 sec phases for each approach.  What is the capacity of the approach now?  1/2*1800 vph = 900 vph  Compare to a freeway lane (>2400 vhp observed)

A straight highway Some basic traffic flow principles  Think about the value 1800 veh/hr  Based on a “minimum” spacing?  Is this value useful for anything?  Minimum spacing  Maximum density?  Minimum headway  Maximum flow?  It might be useful to think about what the word “capacity” means in this context.  Applicable at a signalized intersection when we are trying to pump through a tightly packed platoon.  Maybe applicable on a freeway if conditions downstream are unconstrained.

An Example Consider a 1-mile long elliptical racetrack, with five fast cars that always travel at 80 mph and four slow trucks that always travel at 50 mph. What is the proportion of slow vehicles as seen from an aerial photograph (in percent)? What is the space mean speed (mph) on the track, as seen from a series of aerial photographs? Will the proportion of slow vehicles that would be seen by a stationary observer over time who is positioned somewhere along the track be higher or lower than that observed from an aerial photo?

An Example Consider a 1-mile long elliptical racetrack, with five fast cars that always travel at 80 mph and four slow trucks that always travel at 50 mph. What is the proportion of slow vehicles as seen from an aerial photograph (in percent)? What is the space mean speed (mph) on the track, as seen from a series of aerial photographs? Will the proportion of slow vehicles that would be seen by a stationary observer over time who is positioned somewhere along the track be higher or lower than that observed from an aerial photo?

An Example Consider a 1-mile long elliptical racetrack, with five fast cars that always travel at 80 mph and four slow trucks that always travel at 50 mph. What is the proportion of slow vehicles as seen from an aerial photograph (in percent)? What is the space mean speed (mph) on the track, as seen from a series of aerial photographs? Will the proportion of slow vehicles that would be seen by a stationary observer over time who is positioned somewhere along the track be higher or lower than that observed from an aerial photo?

An Example Consider a 1-mile long elliptical racetrack, with five fast cars that always travel at 80 mph and four slow trucks that always travel at 50 mph. What is the proportion of slow vehicles as seen from an aerial photograph (in percent)? What is the space mean speed (mph) on the track, as seen from a series of aerial photographs? Will the proportion of slow vehicles that would be seen by a stationary observer over time who is positioned somewhere along the track be higher or lower than that observed from an aerial photo? Lower!

An Example Now, what is the proportion (in percent) of slow vehicles seen by a stationary observer who is positioned somewhere along the track? Will the time means speed on the track (the arithmetic average of the speeds that would be measured by the stationary observer) be higher or lower than that observed from a series of aerial photos?

An Example Now, what is the proportion (in percent) of slow vehicles seen by a stationary observer who is positioned somewhere along the track? Will the time means speed on the track (the arithmetic average of the speeds that would be measured by the stationary observer) be higher or lower than that observed from a series of aerial photos?

An Example Now, what is the proportion (in percent) of slow vehicles seen by a stationary observer who is positioned somewhere along the track? Will the time means speed on the track (the arithmetic average of the speeds that would be measured by the stationary observer) be higher or lower than that observed from a series of aerial photos?

An Example Now, what is the proportion (in percent) of slow vehicles seen by a stationary observer who is positioned somewhere along the track? Will the time means speed on the track (the arithmetic average of the speeds that would be measured by the stationary observer) be higher or lower than that observed from a series of aerial photos? Higher!

An Example Now, what is the time mean speed (in mph) on the track?

Some basic meaurements. Consider a series of aerial photographs. t1t1

t1t1

t1t1 t2t2

t1t1 t2t2 t3t3

t1t1 t2t2 t3t3 t4t4

Time-Space Diagram Fundamental tool for transportation evaluation x t Distance Time

Time-Space Diagram Fundamental tool for transportation evaluation  Construct from aerial photos.  Study movement and interaction from point to point.  One vehicle: plot trajectory, one x for every t  Speed = dx/dt (slope), acceleration = d 2 x/dt 2 (curvature)  Several vehicles: vehicle interactions  Intersecting trajectories: passing

Time-Space Diagram Fundamental tool for transportation evaluation x t Distance Time

Time-Space Diagram Fundamental tool for transportation evaluation  Headway: time between vehicles passing a point.  Spacing: front to front distance at a given time. x t Distance Time Spacing Headway

Time-Space Diagram Fundamental tool for transportation evaluation  Headway: time between vehicles passing a point.  Spacing: front to front distance at a given time.  Flow (q): number observed at a point divided by time interval.  q=N/T (horizontal slice) x t Distance Time Spacing Headway T x0x0

Time-Space Diagram Fundamental tool for transportation evaluation  Headway: time between vehicles passing a point.  Spacing: front to front distance at a given time.  Flow (q): number observed at a point divided by time interval.  q=N/T (horizontal slice) x t Distance Time Spacing Headway T x0x0 q at x 0 =2/T

Time-Space Diagram Fundamental tool for transportation evaluation  Headway: time between vehicles passing a point.  Spacing: front to front distance at a given time.  Flow (q): number observed at a point divided by time interval.  q=N/T (horizontal slice)  Density (k): number observed on a segment at a given time divided by the segment length.  k=N/L (vertical slice) x t Distance Time Spacing Headway L t0t0

Time-Space Diagram Fundamental tool for transportation evaluation  Headway: time between vehicles passing a point.  Spacing: front to front distance at a given time.  Flow (q): number observed at a point divided by time interval.  q=N/T (horizontal slice)  Density (k): number observed on a segment at a given time divided by the segment length.  k=N/L (vertical slice) x t Distance Time Spacing Headway L t0t0 k at t 0 =6/L

Time-Space Diagram Fundamental tool for transportation evaluation  Headway: time between vehicles passing a point.  Spacing: front to front distance at a given time.  Flow (q): number observed at a point divided by time interval.  q=N/T (horizontal slice)  Density (k): number observed on a segment at a given time divided by the segment length.  k=N/L (vertical slice)  N=qt=kL x t Distance Time Spacing Headway T L t0t0 x0x0

Time-Space Diagram Point Measures

Time-Space Diagram Spatial Measures

Queueing Theory Study of Congestion Phenomena  Objects passing through point with restriction on maximum rate of passage  Input + storage area (queue) + restriction + output  Customers, arrivals, arrival process, server, service mechanism, departures  Airplane takeoff, toll gate, wait for elevator, taxi stand, ships at a port, water storage in a reservoir, grocery store, telecommunications, circuits…  Interested in: maximum queue length, typical queueing times…. Input Storage Restriction Output

Queueing Theory Conservation Principle  Customers don’t disappear  Arrival times of customers completely characterizes arrival process.  Time/accumulation axes N(x,t) t1t1 t2t2 t3t3 t4t j=A(t) Time, x

Queueing Theory Arrival Process  j=A(t) increases by 1 at each t j  Observer can record arrival times  Inverse t=A -1 (j) is time jth object arrives (integers)  If large numbers, can draw curve through midpoints of stair steps….continuous curves (differentiable). N(x,t) t1t1 t2t2 t3t3 t4t j=A(t) Time, x

Queueing Theory Departure Process  Observer records times of departure for corresponding objects to construct D(t). Time, x N(x,t) t1t1 t2t2 t3t3 t4t A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t)

Queueing Theory Analysis  If system empty at t=0:  Vertical distance is queue length at time t: Q(t)=A(t)-D(t)  A(t) and D(t) can never cross!  For FIFO horizontal distance is waiting time for jth customer. Time, x N(x,t) t1t1 t2t2 t3t3 t4t A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) Q(t) WjWj

Queueing Theory Analysis  Horizontal strip of unit height, width W j Time, x N(x,t) t1t1 t2t2 t3t3 t4t A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) W2W2

Queueing Theory Analysis  Add up horizontal strips  total delay  Total time spent in system by some number of vehicles (horizontal strips) Time, x N(x,t) t1t1 t2t2 t3t3 t4t A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) Total Delay=Area

Queueing Theory Analysis  Add up horizontal strips  total delay  Total time spent in system by some number of vehicles (horizontal strips)  Total time spent by all objects during some specific time period (vertical strips) Time, x N(x,t) t1t1 t2t2 t3t3 t4t A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) Total Delay=Area

Queueing Theory  Total delay = W  Average time in queue: w = W/n  Average number in queue: Q = W/T  W = QT = wn  Q = wn/T  say n/T = arrival rate λ  Q = λw  Average queue length = avg. wait time  avg. arrival rate Time, x N(x,t) t1t1 t2t2 t3t3 t4t A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t)

Combination  Time space diagram looks at one or more objects, many points  Queueing theory looks at one point many objects.  Combining the two results in a three-dimensional surface  Use care when distinguishing between queuing diagrams and time space diagrams!

Combination  Take vertical “slices” at t 1 and t 2  Construct vehicle counting functions N(x,t 1 ) and N(x,t 2 )  Can observe distances traveled and numbers passing a particular point.

Combination  Take vertical “slices” at t 1 and t 2  Construct vehicle counting functions N(x,t 1 ) and N(x,t 2 )  Can observe distances traveled and numbers passing a particular point.

Combination  Take horizontal “slices” at x 1 and x 2  Construct vehicle counting functions N(t,x 1 ) and N(t,x 2 )  Can observe accumulations and trip times between points.

Combination  Take horizontal “slices” at x 1 and x 2  Construct vehicle counting functions N(t,x 1 ) and N(t,x 2 )  Can observe accumulations and trip times between points.

Combination

Inductive loop detectors. Basic introduction.

Meaurements over space. Consider a single vehicle on a straight road.

Measurement over space. Represent on time-space plane. x t Distance Time

Measurements over space. Vehicle trajectory on time-space plane. x t

Vehicle trajectory. Slope at any time is vehicle velocity. Slope = distance/time = VELOCITY x t

Vehicle trajectory. Represent front and rear of vehicle. x t L veh

Vehicle trajectory. Single inductive loop detector of fixed length. x t L loop

Single inductive loop detector. Sends binary on/off signal to controller. x t t t on t off

Single inductive loop detector. Counting function via arrival time record. x t t t on t off Individual vehicle arrival time can be plotted. i

Single inductive loop detector. Speed estimation possible with vehicle length. x t t t off L loop L veh vivi i t on t off

Single inductive loop detector. Measurement of other parameters. x t t i j k l m n o p

Single inductive loop detector. Usually pre-defined time intervals. x t t i 1 min j k l m n o p

Single inductive loop detector. Interval count – number of rising edges. x t t i 1 min n=2 j k l m n o p

Single inductive loop detector. Occupancy is percent of time interval “occupied.” x t t i 1 min n=2, occupancy (%)= /1 min j k l m n o p

Double inductive loop detector—speed trap. Directly measure speed—on times. x t t t on1 t off1 t on2 t off2 Loop 1 Loop 2 L veh L loop L int L loop v on t on1 t on2 L loop

Double inductive loop detector—speed trap. Directly measure speed—off times. x t t t on1 t off1 t on2 t off2 Loop 1 Loop 2 L veh L loop L int L loop v off t off1 t off2 L loop

Double inductive loop detector—speed trap. Directly measure vehicle length. x t t t on1 t off1 t on2 t off2 Loop 1 Loop 2 L veh L loop L int L loop v off t on2 t off2 L loop L veh

Freeway bottlenecks. Definition and previous studies.

Introduction. Bottleneck diagnosis.  An “active” bottleneck is a restriction that separates upstream queued traffic from downstream unqueued traffic.  An active bottleneck is deactivated when there is either a decrease in flow or when a queue spills back from a downstream bottleneck.

Speed contour plot. Provides temporal and spatial resolution.

Previous studies. Bivariate plot—little information.

Previous studies. Time series count data—1 min resolution.

Previous studies. Time series count data—5 min resolution.

Previous studies. Time series count data—15 min resolution.

Proposed innovative graphical method. Developed at U.C. Berkeley.  Takes advantage of ubiquitous sensor data to inform theoretical underpinning.  Process data without losing resolution.  Reveal parametric changes over time.  Can be used for count (flow), speed and other parameters.

Proposed method. Oblique plotting technique for two hours’ data. Motorway A9, Station 340, July 4, 2002 N(x,t)

Proposed method. Oblique plotting technique for two hours’ data. N(x,t) Motorway A9, Station 340, July 4, 2002 q 0 =5180 vph

Proposed method. Oblique plotting technique for two hours’ data. Motorway A9, Station 340, July 4, 2002 N(x,t)-q 0 t´ N(x,t) q 0 =5180 vph

Proposed method. Oblique plotting technique for two hours’ data. N(x,t)-q 0 t´ -1, ,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 14:0014:1514:3014:4515:0015:1515:3015:4516:00 Time N(x,t) Cumulative Count

Proposed method. Oblique plotting technique for two hours’ data. 14:0014:1514:3014:4515:0015:1515:3015:4516:00 Time N(x,t) Cumulative Count 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000

Proposed method. Oblique plotting technique for two hours’ data. 14:0014:1514:3014:4515:0015:1515:3015:4516:00 Time N(x,t) Cumulative Count N(x,t)-q 0 t´

Proposed method. Oblique plotting technique for two hours’ data. 14:0014:1514:3014:4515:0015:1515:3015:4516:00 Time N(x,t) Cumulative Count N(x,t)-q 0 t´

Proposed method. Plot sensor data cumulatively using oblique axis to reveal details in trends. N(x,t)-q 0 t’, q 0 =5180 vehicles/hour

Proposed method. Oblique plot reveals times at which pronounced flow changes occurred. N(x,t)-q 0 t’, q 0 =5180 vehicles/hour

Proposed method. Plot sensor data cumulatively at one point. x Time, x Travel Direction N(x,t) 6:306:316:326:336:346:356:366:376:386:396:40 6:41

Proposed method. Plot sensor data cumulatively at one point. x Time, x Travel Direction N(x,t) 6:306:316:326:336:346:356:366:376:386:396:40 6:41 Equal Time Intervals (1 min) Interval Count

Proposed method. Plot sensor data cumulatively at one point. x Travel Direction N(x,t) Time, x 6:306:316:326:336:346:356:366:376:386:396:40 6:41

Proposed method. Plot sensor data cumulatively at one point. x Travel Direction N(x,t) Time, x 6:306:316:326:336:346:356:366:376:386:396:40 6:41 Slope = number/time = FLOW

Proposed method. Plot sensor data cumulatively at one point. x Travel Direction N(x,t) Time, x 6:306:316:326:336:346:356:366:376:386:396:40 6:41 Slope = number/time = FLOW Flow Increase

Proposed method. Plot sensor data cumulatively at one point. x Travel Direction N(x,t) Time, x 6:306:316:326:336:346:356:366:376:386:396:40 6:41 Slope = number/time = FLOW Flow Increase Flow Decrease

Queueing diagram. Use two oblique plots in series to see queueing and resulting delay. x 1 Time, t Travel Direction N(x j,t) N(x 1,t)

Queueing diagram. Use two oblique plots in series to see queueing and resulting delay. x 1 x 2 Ref. Veh. Trip Time Time, t Travel Direction N(x j,t) N(x 1,t) N(x 2,t)

Queueing diagram. Use two oblique plots in series to see queueing and resulting delay. x 1 x 2 Ref. Veh. Trip Time Number Time, t t1t1 Travel Direction N(x j,t) N(x 1,t) N(x 2,t)

Queueing diagram. Use two oblique plots in series to see queueing and resulting delay. x 1 x 2 Ref. Veh. Trip Time Number Trip Time j Time, t j t1t1 Travel Direction N(x j,t) N(x 1,t) N(x 2,t)

Queueing diagram. Shift upstream curve to reveal... x 1 x 2 Time, t Travel Direction N(x j,t) N(x 1,t) N(x 2,t)

Queueing diagram. Shift upstream curve to reveal excess accumulation... Excess Accumulation x 1 x 2 Time, t Travel Direction N(x j,t) N(x 1,t) N(x 2,t) t2t2

Queueing diagram. Shift upstream curve to reveal excess accumulation and delay. Excess Accumulation x 1 x 2 Time, t Travel Direction N(x j,t) Excess Travel Time=Delay N(x 1,t) N(x 2,t) t2t2 k

Empirical Analysis of Traffic Sensor Data Surrounding a Bottleneck on a German Autobahn. Robert L. Bertini Steven Hansen Portland State University Klaus Bogenberger BMW Group TRB Annual Meeting January 10, 2005

126 Introduction. Objectives.  Empirical analysis of features of traffic dynamics and driver behavior on a German autobahn.  Understand details of bottleneck formation and dissipation.  Improved travel time estimation and forecasting:  Traffic management  Traveler information  Driver assistance systems.  Contribute to improved traffic flow models and freeway operational strategies.

127 Background.  Previous empirical research (U.S., Canada, Germany)  Active bottleneck definition:  Queue upstream  Unrestricted traffic downstream  Temporally and spatially variable, static and dynamic, merges and diverges.  Activation/deactivation times.  Bottleneck outflow features and possible triggers.  Opportunity to compare with previous findings using data from German freeways.

128 Study Area. Data.  14-km section of northbound A9, Munich  17 dual loop detector stations (labeled 280– 630)  One-minute counts & average speeds  Cars  Trucks  Six days in June–July 2002  Focus on June 27, 2002  Clear weather  Variable speed limits and traffic information (VMS) 630

129 Methodology. Analysis Tools.  Cumulative curves (Newell, Cassidy & Windover):  Vehicle count  Average speed  Transformations to heighten visual resolution:  Oblique axis  Horizontal shift with vehicle conservation  Retain lowest level of resolution (one-minute)  Identify bottleneck activations and deactivations.

130 Speeds Northbound A9 June 27,

131 Speeds Northbound A9 June 27,

132 Bottleneck Activation June 27, 2002 Station 380 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station Off Ramp :4514:5014:5515:0015:0515:1015:1515:2015:2515:3015:3515:4015:4515:50 Time off 630

133 Bottleneck Activation June 27, 2002 Stations 380–390–420 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station On Ramp Station 390 Station Off Ramp Time 630

134 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station 390 Station 380 Flow Bottleneck Activation June 27, 2002 Stations 380–390–420 Time 630

:1515:2015:2515:30 Time 15:21 89 km/h 70 km/h V(380,t)-b 0 t′, b 0 =3300 km/hr 2 Bottleneck Activation June 27, 2002 Station 380 Speed 630

136 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station 420 Station 390 Station 380 Flow :1515:2015:2515:30 Time 15: V(380,t)-b 0 t′, b 0 =3300 km/hr 2 V(390,t)-b 0 t′, b 0 =4335 km/hr :1515:2015:2515:30 Time 15: :1515:2015:2515:30 Time V(420,t)-b 0 t′, b 0 =4850 km/hr 2 15: Bottleneck Activation June 27, 2002 Stations 380–390–420 Time 630

137 Bottleneck Activation June 27,

138 Bottleneck Activation June 27, :21 15:24 15:34 15:41 15:42 15:47 15:

139 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station 350 Station Off-Ramp Station 340 Station On-Ramp station 380 Bottleneck Activation June 27, 2002 Stations 320–340–350–380 Time 630

140 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station 380 Flow station 380 Bottleneck Activation June 27, 2002 Stations 320–340–350–380 Time 630

141 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station 350 Station 320 Station 340 Station 380 Flow station :1515:2015:2515:30 Time 15:23 84 V(350,t)-b 0 t′, b 0 =4200 km/hr :1515:2015:2515:3015:3515:4015:45 Time 15: V(340,t)-b 0 t′, b 0 =5600 km/hr :1515:2015:2515:3015:3515:4015:45 Time 15: V(320,t)-b 0 t′, b 0 =6000 km/hr 2 Bottleneck Activation June 27, 2002 Stations 320–340–350–380 Time 630

142  Active bottleneck located between detectors 380 and 390.  Activated at 15:21.  Queue propagated as far as detector 630.  Unrestricted traffic downstream. Bottleneck Activation June 27,

143 Bottleneck Activation June 27, 2002 Direction of Travel 15:21 19:40 17:40 18:44 17:28 17:35 17:38 15:24 15:34 15:41 15:42 15:47 15:58 19:

144 Bottleneck Activation June 27, 2002 Direction of Travel 15:21 19:40 17:40 18:44 17:28 17:35 17:38 15:24 15:34 15:41 15:42 15:47 15:58 19:

145 Direction of Travel 15:21 19:40 17:40 18:44 17:28 17:35 17:38 15:24 15:34 15:41 15:42 15:47 15:58 19:18 Bottleneck Activation June 27,

146 Direction of Travel 15:21 19:40 17:40 18:44 17:28 17:35 17:38 15:24 15:34 15:41 15:42 15:47 15:58 19:18 Bottleneck Activation June 27,

147 Bottleneck Activation June 27, 2002 Stations 380–390–420 N(420,t) N(390,t) N(380,t) :0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 630

148 Bottleneck Activation June 27, 2002 N(420,t) N(390,t) N(380,t) :0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19:

149 Bottleneck Activation June 27, 2002 N(380,t) :0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19:

150 Bottleneck Activation June 27, 2002 N(380,t) :0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19: vph 5370 vph 1 630

151 Bottleneck Activation June 27, 2002 N(380,t) :0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19: vph 5370 vph 5410 vph

152 Bottleneck Activation Northbound A9 Outflow Summary at

153 Bottleneck Activation Northbound A9 On-Ramp Dynamics June 27, 2002 Station veh/hour (+12%) :16 15: :3014:4515:0015:1515:3015:4516:00 Time N(420 on ramp,t) - q 0 t' 630

154 Bottleneck Activation Northbound A9 Station 420 Truck Flow Dynamics June 27, 2002 Ramp Right q 0 =385 veh/hour 400 veh/hour 750 (+190%) Mainline Right q 0 =220 veh/hour Ramp Left q 0 =15 veh/hour Mainline Left q 0 =22 veh/hour (+120%) (9 trucks in 2 minutes) Trucks Only N(x,t)-q 0 t 630

155 Bottleneck 1 Activation Northbound A9 Station 390 Truck Flow Dynamics June 27, 2002 N(x,t)-q 0 t Shoulder q 0 =560 veh/hour Center q 0 =65 veh/hour Median q 0 =15 veh/hour 630 veh/hour (+95%) (+120%) (6 trucks in 2 minutes, +680%) Trucks Only 630

156 Conclusion.  Method for diagnosing active bottlenecks.  11 bottleneck activations on 6 days at one location.  Measured bottleneck outflows appear stable:  Day to day (contrary to other research)  Preceded by queueing or not  Pre-queue flows measurably higher than bottleneck outflow.  Precursors to queue formation some distance downstream of merge:  Rise in on-ramp flow (total)  Surges in truck counts  Research continuing at this and other sites in Germany.

157 Thank you for your attention. Acknowledgements BMW Group Oregon Engineering Technology Industry Council Portland State University Steven Boice