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

2. 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”

3. 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

4. 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

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

6. 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

7. 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

8. 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?

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

10. 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:

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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.

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

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

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

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

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

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

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

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

26. 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

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

28. 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.

29. 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:

30. 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)

31. 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.

32. 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?

33. 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?

34. 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?

35. 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!

36. 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?

37. 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?

38. 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?

39. 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!

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

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

42. t1t1

43. t1t1 t2t2

44. t1t1 t2t2 t3t3

45. t1t1 t2t2 t3t3 t4t4

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

52. 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

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

54. 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

55. 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

56. 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

57. 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

58. 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

59. 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

60. Time-Space Diagram Point Measures

61. Time-Space Diagram Spatial Measures

62. 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

63. 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 t4t4 1 2 3 4 j=A(t) Time, t @ x

64. 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 t4t4 1 2 3 4 j=A(t) Time, t @ x

65. Queueing Theory Departure Process  Observer records times of departure for corresponding objects to construct D(t). Time, t @ x N(x,t) t1t1 t2t2 t3t3 t4t4 1 2 3 4 A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t)

66. 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, t @ x N(x,t) t1t1 t2t2 t3t3 t4t4 1 2 3 4 A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) Q(t) WjWj

67. Queueing Theory Analysis  Horizontal strip of unit height, width W j Time, t @ x N(x,t) t1t1 t2t2 t3t3 t4t4 1 2 3 4 A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) W2W2

68. Queueing Theory Analysis  Add up horizontal strips  total delay  Total time spent in system by some number of vehicles (horizontal strips) Time, t @ x N(x,t) t1t1 t2t2 t3t3 t4t4 1 2 3 4 A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) Total Delay=Area

69. 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, t @ x N(x,t) t1t1 t2t2 t3t3 t4t4 1 2 3 4 A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t) Total Delay=Area

70. 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, t @ x N(x,t) t1t1 t2t2 t3t3 t4t4 1 2 3 4 A(t) t1t1 ′ t2t2 ′ t3t3 ′ t4t4 ′ D(t)

71. 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!

72. 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.

73. 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.

74. 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.

75. 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.

76. Combination

77. Inductive loop detectors. Basic introduction.

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

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

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

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

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

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

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

86. 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

87. 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

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

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

90. 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

91. 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

92. 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

93. 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

94. 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

95. Freeway bottlenecks. Definition and previous studies.

96. 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.

97. Speed contour plot. Provides temporal and spatial resolution.

98. Previous studies. Bivariate plot—little information.

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

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

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

102. 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.

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

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

105. 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

106. Proposed method. Oblique plotting technique for two hours’ data. N(x,t)-q 0 t´ -1,000 0 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

107. 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

108. 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 -300 -250 -200 -150 -100 -50 0 N(x,t)-q 0 t´

109. 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 -300 -250 -200 -150 -100 -50 0 N(x,t)-q 0 t´

110. 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

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

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

113. Proposed method. Plot sensor data cumulatively at one point. x Time, t @ 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

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

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

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

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

118. 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)

119. 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)

120. 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)

121. 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)

122. 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)

123. 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

124. 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

125. 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. 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. 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. 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. 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. 130 Speeds Northbound A9 June 27, 2002 630

131. 131 Speeds Northbound A9 June 27, 2002 1

132. 132 Bottleneck Activation June 27, 2002 Station 380 N(x,t)-q 0 t′, q 0 =5170 veh/hr Station 380 + Off Ramp -50 50 150 250 350 450 14:4514:5014:5515:0015:0515:1015:1515:2015:2515:3015:3515:4015:4515:50 Time 420 390 380off 630

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

134. 134 N(x,t)-q 0 t′, q 0 =5170 veh/hr 15:21@ Station 390 15:21@ Station 380 Flow Reduction @380 Bottleneck Activation June 27, 2002 Stations 380–390–420 Time 630

135. 135 380 15:1515:2015:2515:30 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. 136 N(x,t)-q 0 t′, q 0 =5170 veh/hr 15:24@ Station 420 15:21@ Station 390 15:21@ Station 380 Flow Reduction @380 380 55200 55400 55600 15:1515:2015:2515:30 Time 15:21 89 70 V(380,t)-b 0 t′, b 0 =3300 km/hr 2 V(390,t)-b 0 t′, b 0 =4335 km/hr 2 390 98120 98170 98220 15:1515:2015:2515:30 Time 15:21 80 41 420 95010 95060 95110 15:1515:2015:2515:30 Time V(420,t)-b 0 t′, b 0 =4850 km/hr 2 15:24 92 65 Bottleneck Activation June 27, 2002 Stations 380–390–420 Time 630

137. 137 Bottleneck Activation June 27, 2002 630

138. 138 Bottleneck Activation June 27, 2002 15:21 15:24 15:34 15:41 15:42 15:47 15:58 630 1

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

140. 140 N(x,t)-q 0 t′, q 0 =5170 veh/hr 15:21@ Station 380 Flow Reduction @380 Time @ station 380 Bottleneck Activation June 27, 2002 Stations 320–340–350–380 Time 630

141. 141 N(x,t)-q 0 t′, q 0 =5170 veh/hr 15:23@ Station 350 15:27@ Station 320 15:26@ Station 340 15:21@ Station 380 Flow Reduction @380 Time @ station 380 350 40500 40600 40700 15:1515:2015:2515:30 Time 15:23 84 V(350,t)-b 0 t′, b 0 =4200 km/hr 2 340 22320 22370 22420 15:1515:2015:2515:3015:3515:4015:45 Time 15:26 99 97 V(340,t)-b 0 t′, b 0 =5600 km/hr 2 320 19690 19740 19790 15:1515:2015:2515:3015:3515:4015:45 Time 15:27 105 104 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. 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, 2002 630

143. 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 19:18 1 630

144. 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 19:18 1 2 630

145. 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, 2002 1 2 3 630

146. 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, 2002 1 2 3 4 630

147. 147 Bottleneck Activation June 27, 2002 Stations 380–390–420 N(420,t) N(390,t) N(380,t) 0 100 15:0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 630

148. 148 Bottleneck Activation June 27, 2002 N(420,t) N(390,t) N(380,t) 0 100 15:0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19:18 1 630

149. 149 Bottleneck Activation June 27, 2002 N(380,t) 0 100 15:0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19:18 1 630

150. 150 Bottleneck Activation June 27, 2002 N(380,t) 0 100 15:0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19:18 5510 vph 5370 vph 1 630

151. 151 Bottleneck Activation June 27, 2002 N(380,t) 0 100 15:0016:0017:0018:0019:00 Time N(x,t)-q 0 t, q 0 =5178 veh/hr 15:21 17:35 17:40 18:45 19:18 5510 vph 5370 vph 5410 vph 1 4 630

152. 152 Bottleneck Activation Northbound A9 Outflow Summary at 380 630

153. 153 Bottleneck Activation Northbound A9 On-Ramp Dynamics June 27, 2002 Station 420 2280 veh/hour 2630 1830 2370 2660 (+12%) 1850 2330 2630 15:16 15:20 15:21 @390 0 100 200 300 400 500 600 14:3014:4515:0015:1515:3015:4516:00 Time N(420 on ramp,t) - q 0 t' 630

154. 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%) 15:21 @390 Mainline Right q 0 =220 veh/hour Ramp Left q 0 =15 veh/hour Mainline Left q 0 =22 veh/hour 550 320 580 320 530 260 490 330 510 230 390 240 170 330 160 350 (+120%) 230 50 100 50 270 (9 trucks in 2 minutes) 24 20 30 40 Trucks Only N(x,t)-q 0 t 630

155. 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 400 740 470 670 770 420 820 (+95%) 570 740 220 20 200 80 210 100 210 (+120%) 15:21 @390 140 80 180 20 70 20 180 (6 trucks in 2 minutes, +680%) 70 30 Trucks Only 630

156. 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. 157 Thank you for your attention. Acknowledgements BMW Group Oregon Engineering Technology Industry Council Portland State University Steven Boice