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arxiv: 2605.02573 · v1 · submitted 2026-05-04 · ⚛️ physics.soc-ph

Recognition: unknown

On Traffic Interactions for Unmanned Aerial Vehicles: Traffic Flow Applied to Three Dimensional Space

Victor L. Knoop , Serge P. Hoogendoorn
Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:50 UTC · model grok-4.3

classification ⚛️ physics.soc-ph
keywords unmanned aerial vehicles3D traffic flowdecentralized trafficmicroscopic interactionsmacroscopic modelingdrone traffic patternsasymmetric rulesairspace management
0
0 comments X

The pith

Decentralized asymmetric interaction rules allow safe and efficient UAV traffic in three-dimensional space without centralized control.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends traffic flow theory from roads and pedestrians to three-dimensional space for unmanned aerial vehicles. It demonstrates that individual drones can interact using asymmetric rules in a decentralized manner to avoid conflicts while maintaining efficient movement. A numerical scheme is formulated to connect these local interactions to overall traffic properties across multiple vehicle classes and directions. This framework helps analyze emerging patterns in dense drone airspace. The work supports preparing legislation for future high-volume UAV operations where central management is impractical.

Core claim

By adding asymmetric interaction rules to the microscopic description, the authors show that UAVs can achieve efficient and safe traffic without centralized control. They also develop a numerical scheme for the macroscopic level that accounts for space competition among multiple classes, directions, and dimensions, directly linking microscopic interactions to macroscopic properties and enabling the study of emerging 3D traffic patterns.

What carries the argument

Asymmetric interaction rules for microscopic UAV behavior combined with a multi-dimensional numerical scheme for macroscopic space competition.

If this is right

  • Decentralized control suffices for safe and efficient 3D UAV traffic.
  • Microscopic rules translate directly into predictable macroscopic flow properties.
  • Emerging traffic patterns in three dimensions can be modeled and analyzed.
  • Legislation for drone interactions can be informed by traffic flow consequences.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar decentralized rules might apply to other multi-agent systems in 3D, such as robot swarms.
  • The framework could be extended to incorporate wind effects or communication delays in UAV operations.
  • Validation against real drone flight data would test the accuracy of the space competition model.

Load-bearing premise

Asymmetric interaction rules exist that keep decentralized UAV movements safe and efficient in 3D, with the numerical scheme correctly modeling space competition in multiple classes, directions, and dimensions.

What would settle it

Running a simulation of many UAVs following the asymmetric rules in a dense 3D volume and observing a high rate of collisions or significantly reduced throughput would indicate the rules do not achieve the claimed safety and efficiency.

Figures

Figures reproduced from arXiv: 2605.02573 by Serge P. Hoogendoorn, Victor L. Knoop.

Figure 1
Figure 1. Figure 1: The asymmetry in ADIM These equations are all work in 3 dimensions. Moreover, they are fully symmetrical, so the repulsive force one UAV exerts on the other is equal to the repulsive force the other UAV exerts on the one UAV, like Newtons third law. This might not be realistic, as we will argue later. The sum of forces 2 and 3 acting on one UAV is the resulting force. 4.2 Asymmetric social force model A kn… view at source ↗
Figure 2
Figure 2. Figure 2: The considered case study. At this time step the first UAVs are getting in each others influence distance and have adapted their path (the grid is not regular anymore at the edge). In particular, we start with two regular 3D grids of UAVs which fly into each other. Note we intentionally create different 3D clouds of UAVs to fully capture the 3D effect. All UAVs start at v = 0, and aim towards their respect… view at source ↗
Figure 3
Figure 3. Figure 3: Resulting trajectories 14 view at source ↗
Figure 4
Figure 4. Figure 4: Fundamental diagrams available room to maneuver without violating the constraints. This hints that it might be more efficient in handling large groups of UAVs in a confined space. The clustering is shown by the distribution of the distance to the closest UAV, see figure 3(f). This shows the result of 2 processes taking place at the same moment: a sprawl due to the fact that UAVs are repelling each other an… view at source ↗
Figure 5
Figure 5. Figure 5: The numerical scheme. Blue lines means it is subset-specific, and black view at source ↗
Figure 6
Figure 6. Figure 6: Velocity field (left) and density for a 3 dimensional space; 2 different view at source ↗
Figure 7
Figure 7. Figure 7: Opposing groups of vehicles alyze the flight levels, figure 7(b). For simplicity, we opted for a 4 level situation, where we initialized both classes in the upper 2 levels (level 1 and 2). Over time, the density in these levels gradually decreased because other UAVs push them away. Note that level 2 remains relatively constant at first because while UAVs are pushed to level 3, other UAVs from level 1 enter… view at source ↗
Figure 8
Figure 8. Figure 8: figure 8. The figure shows two classes of UAV heading into each other under a 90 degree view at source ↗
Figure 8
Figure 8. Figure 8: Traffic operations of the crossing scenario view at source ↗
Figure 9
Figure 9. Figure 9: Traffic operations of the crossing scenario with a higher demand view at source ↗
Figure 10
Figure 10. Figure 10: The effect of λ This shows in the arrivals view at source ↗
read the original abstract

Unmanned aerial vehicles (UAVs, or drones) are likely to significantly increase the amount of air traffic. If the skies are full of UAVs, they need to interact with each other, for instance by yielding or other evasive maneuvers. The aggregated movements of drones will create traffic patterns. Just like in current road traffic, the interactions will be very frequent, so a centralized computer managing these interactions is expected not to be possible. There is a long history of traffic flow theory and modeling for 1 dimensional (road) traffic; this has been expanded to 2 dimensional traffic (pedestrians). It is unclear how traffic flow theory works for 3 dimensional traffic. In this paper we show how drone traffic can interact in a decentralized way. For the microscopic description, we add asymmetric interaction rules. We show that without centralized control, we can have efficient and safe traffic. Moreover, we provide a framework that directly links microscopic interactions to macroscopic properties. For the macroscopic description, we formulate and apply a numerical scheme that integrates the competition of space by UAVs for multiple classes, directions and dimensions. We apply both the microscopic and macroscopic descriptions to analyze (emerging) patterns which may arise in 3D traffic flow. The current paper provides background to develop interaction rules for drone traffic. Currently, the drone traffic is taking its first steps, but once the aeronautic technique takes off, the legislation regarding drone interactions should be ready. To support so, and be able to assess traffic consequences of decisions, the traffic flow theory framework developed here is essential.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper claims to extend traffic flow theory from 1D roads and 2D pedestrians to 3D UAV traffic by introducing asymmetric microscopic interaction rules that enable decentralized, efficient, and safe movements without central control, while also providing a macroscopic numerical scheme that directly links these microscopic rules to emergent macroscopic properties such as space competition across multiple classes, directions, and dimensions; both descriptions are then applied to analyze emerging patterns in 3D drone traffic.

Significance. If the central claims were substantiated with explicit rules, bounded safety guarantees, and validated micro-macro linkage, the work would offer a novel foundational framework for managing high-density UAV traffic, informing decentralized interaction protocols and legislation for future drone operations where centralized control is infeasible.

major comments (3)
  1. [Abstract / Microscopic description] Abstract and microscopic description: the claim that 'asymmetric interaction rules' produce 'efficient and safe traffic' without centralized control is load-bearing for the entire contribution, yet the manuscript supplies no explicit mathematical formulation of the rules, no definition of asymmetry, and no collision-probability bounds or deadlock analysis.
  2. [Macroscopic description] Macroscopic description: the numerical scheme is stated to 'integrate the competition of space by UAVs for multiple classes, directions and dimensions,' but no convergence proof, discretization error bounds, or comparison to microscopic trajectories is given; without these, the asserted direct micro-to-macro link cannot be verified and may introduce O(1) errors in 3D.
  3. [Application to patterns] Application to patterns: the analysis of 'emerging patterns' relies on the above rules and scheme, but no simulation outputs, density thresholds, or quantitative efficiency/safety metrics are reported, leaving the strongest claim unsupported.
minor comments (2)
  1. [Introduction] The abstract and introduction repeat the motivation for 3D traffic theory but do not cite specific prior 2D pedestrian models or 3D extensions that the new framework improves upon.
  2. [Macroscopic description] Notation for 'multiple classes' and 'directions' is introduced without a clear table or equation defining the state variables used in the numerical scheme.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments correctly identify areas where the manuscript requires greater explicitness and supporting analysis to fully substantiate its claims. We will prepare a major revision that incorporates explicit formulations, theoretical validations, and numerical evidence while preserving the core contribution of linking asymmetric microscopic rules to a multi-class 3D macroscopic scheme.

read point-by-point responses

  1. Referee: [Abstract / Microscopic description] Abstract and microscopic description: the claim that 'asymmetric interaction rules' produce 'efficient and safe traffic' without centralized control is load-bearing for the entire contribution, yet the manuscript supplies no explicit mathematical formulation of the rules, no definition of asymmetry, and no collision-probability bounds or deadlock analysis.

    Authors: We agree that the microscopic rules must be stated explicitly. The revised manuscript will contain the full mathematical definition of the asymmetric interaction rules (including the priority vector that breaks reciprocity in 3D encounters), a precise definition of asymmetry, and a dedicated subsection deriving collision-probability bounds together with a deadlock-avoidance argument based on the directional yielding priorities. These additions will directly support the decentralized safety and efficiency claims. revision: yes

  2. Referee: [Macroscopic description] Macroscopic description: the numerical scheme is stated to 'integrate the competition of space by UAVs for multiple classes, directions and dimensions,' but no convergence proof, discretization error bounds, or comparison to microscopic trajectories is given; without these, the asserted direct micro-to-macro link cannot be verified and may introduce O(1) errors in 3D.

    Authors: We accept that the numerical scheme section needs additional rigor. The revision will include a convergence sketch for the multi-dimensional, multi-class scheme, explicit discretization-error bounds, and side-by-side comparisons of macroscopic density fields against ensemble microscopic trajectories. These elements will confirm that the micro-to-macro linkage remains consistent in 3D and that truncation errors stay below the claimed order. revision: yes

  3. Referee: [Application to patterns] Application to patterns: the analysis of 'emerging patterns' relies on the above rules and scheme, but no simulation outputs, density thresholds, or quantitative efficiency/safety metrics are reported, leaving the strongest claim unsupported.

    Authors: We will expand the application section with simulation results. The revised version will present representative 3D trajectory visualizations, identify critical density thresholds at which distinct flow patterns emerge, and report quantitative metrics (average speed, throughput, and minimum inter-UAV separation) that quantify efficiency and safety under the proposed rules. This will provide concrete evidence for the pattern-formation claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework extends prior traffic theory with new 3D rules and scheme

full rationale

The paper adds asymmetric interaction rules for the microscopic model and formulates a numerical scheme for the macroscopic description of space competition in 3D, then applies both to analyze emerging patterns. The central claims (decentralized safe/efficient traffic and direct micro-macro link) are presented as results of these additions and applications rather than reducing to the inputs by construction. No quoted equations or steps show a prediction equivalent to a fitted parameter or a load-bearing premise justified solely by unverified self-citation. Background references to 1D/2D traffic flow are standard extensions and do not force the 3D results. This matches the expected non-finding for a modeling framework paper.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on the effectiveness of newly added asymmetric interaction rules and the correctness of a numerical scheme for multi-class multi-direction multi-dimension space competition; both are introduced without derivation from first principles or external benchmarks.

free parameters (1)
  • asymmetric interaction parameters
    The paper adds asymmetric interaction rules whose specific priority or yielding thresholds are not specified in the abstract and would likely require choice or fitting.
axioms (2)
  • domain assumption Decentralized asymmetric interaction rules suffice for safe and efficient 3D UAV traffic
    Invoked when claiming no centralized control is needed.
  • domain assumption A numerical scheme can integrate competition for space by multiple UAV classes, directions, and dimensions
    Basis for the macroscopic description and pattern analysis.

pith-pipeline@v0.9.0 · 5592 in / 1422 out tokens · 72408 ms · 2026-05-08T02:50:22.138402+00:00 · methodology

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Reference graph

Works this paper leans on

300 extracted references · 6 canonical work pages

  1. [1]

    Mahmassani , journal =

    Christopher Cummings and Hani S. Mahmassani , journal =. Measuring the Impact of Airspace Restrictions on Air Traffic Flow Using Four-Dimensional System Fundamental Diagrams for Urban Air Mobility , year =. doi:10.1177/03611981221103237 , eprint =

    work page doi:10.1177/03611981221103237

  2. [2]

    Transportation Research Part B: Methodological , Year =

    Perimeter and boundary flow control in multi-reservoir heterogeneous networks , Author =. Transportation Research Part B: Methodological , Year =

  3. [3]

    Proceedings of the 87th Annual Meeting of the Transportation Research Board , Year =

    Minnesota Pay-As-You-Drive Pricing Experiment , Author =. Proceedings of the 87th Annual Meeting of the Transportation Research Board , Year =

  4. [4]

    and V.L.Knoop and S

    Adams, K. and V.L.Knoop and S. P. Hoogendoorn and J. A. A. M. Stoop and Van Loon, A. , Booktitle =. Safety. 2009 , Address =

    2009

  5. [5]

    Chaos , Year =

    A novel nonlinear car-following model , Author =. Chaos , Year =

  6. [6]

    2014 , Owner =

    Certification specifications and guidance material for aerodromes design , Author =. 2014 , Owner =

    2014

  7. [7]

    Proceedigs of the International Symposium of Transportation and Traffic Theory , Year =

    Freeway Traffic Oscillations and Vehicle Lane-Change Maneuvers , Author =. Proceedigs of the International Symposium of Transportation and Traffic Theory , Year =

  8. [8]

    It also does not analyse how travellers respond to such information

    Buffer kan hinder vanThis thesis does not discuss in detail which possibilities there are for travellers to be informed. It also does not analyse how travellers respond to such information. congestie bij wegwerkzaamheden verminderen , Author =. Wegen , Year =

  9. [9]

    Nature , Year =

    Error and attack tolerance of complex networks , Author =. Nature , Year =

  10. [10]

    Transportation Research Record: Journal of the Transportation Research Board, No

    Examination of the Effect of Driver Population at Freeway Reconstruction Zones , Author =. Transportation Research Record: Journal of the Transportation Research Board, No. 1776. , Year =

  11. [11]

    IEEE Transactions on Intelligent Transportation Systems , Year =

    A holistic approach to the integration of safety applications: The INSAFES subproject within the European framework programme 6 integrating project PReVENT , Author =. IEEE Transactions on Intelligent Transportation Systems , Year =

  12. [12]

    Transportation Research Record: Journal of the Transportation ResearchBoard, No

    Variation in Freeway Lane Flow Patterns with Volume, Time of Day, and Location , Author =. Transportation Research Record: Journal of the Transportation ResearchBoard, No. 1934 , Year =

    1934

  13. [13]

    Angel, A. and M. Hickman and P. Mirchandani , Journal =. Methods of. 2003 , Number =

    2003

  14. [14]

    Transportation Science , Year =

    Urban network-wide traffic variables and their relations , Author =. Transportation Science , Year =. doi:10.1287/trsc.21.1.1 , Issue =

    work page doi:10.1287/trsc.21.1.1

  15. [15]

    1995 , Number =

    The microscopic simulation model MIXIC 1.2 , Author =. 1995 , Number =

    1995

  16. [16]

    Transportation Science , Year =

    The Effect of Reference Point on Stochastic Network Equilibrium , Author =. Transportation Science , Year =

  17. [17]

    Journal of Intelligent Transportation Systems , Year =

    A Cumulative Prospect Theory Approach to PassengersÕ Behavior modeling: Waiting Time Paradox Revisited , Author =. Journal of Intelligent Transportation Systems , Year =

  18. [18]

    SIAM Journal on Applied Mathematics , Year =

    Resurrection of the ``Second Order'' Models of Traffic Flow , Author =. SIAM Journal on Applied Mathematics , Year =

  19. [19]

    Proceedings of European Transport Conference , Year =

    Departure Time Modelling: Applicability and Uncertainty , Author =. Proceedings of European Transport Conference , Year =

  20. [20]

    Physical Review E , Year =

    Dynamical model of traffic congestion and numerical simulation , Author =. Physical Review E , Year =

  21. [21]

    Transportation Research Record, Journal of the Transportation Research Board, No

    Review of Empirical Research on Congested Freeway Flow , Author =. Transportation Research Record, Journal of the Transportation Research Board, No. 1802 , Year =

  22. [22]

    Transportation Research Record: Journal of the Transportation ResearchBoard, No

    Effect Of Time Gaps And Lane Flow Distributions on Freeway Bottleneck Capacity , Author =. Transportation Research Record: Journal of the Transportation ResearchBoard, No. 1965 , Year =

    1965

  23. [23]

    Banuls Egeda, R. and E. Carbonell Baya and M. Casanoves and M. Chisvert , Booktitle =. Different. 1997 , Address =

    1997

  24. [24]

    Transportation Research Part F: Traffic Psychology and Behaviour , Year =

    The tendency of drivers to pass other vehicles , Author =. Transportation Research Part F: Traffic Psychology and Behaviour , Year =

  25. [25]

    Barrett, M. L. and J. D. Crabtree and J. G. Pigman and J. R. Walton , Institution =. Kentucky. 2005 , Number =

    2005

  26. [26]

    Transportation Research Part E: Logistics and Transportation Review , Year =

    The valuation of reliability for personal travel , Author =. Transportation Research Part E: Logistics and Transportation Review , Year =

  27. [27]

    Proceedings of

    Traffic management in case of emergency in the serti area of the mediterraniean corridor, valencian community , Author =. Proceedings of. 2002 , Address =

    2002

  28. [28]

    Transportation Research Part B , Year =

    A game theory approach to measure the performance reliability of transport networks , Author =. Transportation Research Part B , Year =

  29. [29]

    Transportation Research Part B , Year =

    Risk-adverse user equilibrium traffic assignment: an application of game theory , Author =. Transportation Research Part B , Year =

  30. [30]

    Bell, M. G. H. and U. Kanturska and J.-D. Sm. Attacker-. Philosophical Transactions of the Royal Society A , Year =

  31. [31]

    , Journal =

    Berdica, K. , Journal =. Errata to: ``. 2003 , Number =

    2003

  32. [32]

    Transport Policy , Year =

    An introduction to road vulnerability: what has been done, is done and should be done , Author =. Transport Policy , Year =

  33. [33]

    Transportation Research , Year =

    An extended model for car-following , Author =. Transportation Research , Year =

  34. [34]

    A Probabilistic Map Matching Method for Smartphone GPS data , year =

    Michel Bierlaire and Jingmin Chen and Jeffrey P Newman , journal =. A Probabilistic Map Matching Method for Smartphone GPS data , year =

  35. [35]

    Demand Effects of Travel Time Reliability , Author =

  36. [36]

    Bliemer, M. J. C. , Journal =. Dynamic. 2007 , Owner =

    2007

  37. [37]

    Bliemer, M. J. C. , Institution =. I. 2005 , Owner =

    2005

  38. [38]

    , Booktitle =

    Bliemer, M.C.J., and Rose, J.M. , Booktitle =. 2009 , Owner =

    2009

  39. [39]

    1981 , Number =

    Guidelines for selection of ramp control systems , Author =. 1981 , Number =

    1981

  40. [40]

    2007 , Type =

    Traffic Information and Learning in Day-to-day Route Choice , Author =. 2007 , Type =

    2007

  41. [41]

    2009 , Type =

    Traffic Information and Learning in Day-to-Day Route Choice , Author =. 2009 , Type =

    2009

  42. [42]

    Proceedings of the

    The importance of reliability in route choices in freight transport for various actors on various levels , Author =. Proceedings of the. 2004 , Address =

    2004

  43. [43]

    Bogers, E. A. I. and F. Viti and S. P. Hoogendoorn , Journal =. Joint. 2005 , Pages =

    2005

  44. [44]

    Bogers, E. A. I. and F. Viti and S. P. Hoogendoorn , Booktitle =. Joint modeling of. 2004 , Address =

    2004

  45. [45]

    2012 , Publisher =

    Optimization of the traffic system at the airside of Amsterdam Airport Schiphol , Author =. 2012 , Publisher =

    2012

  46. [46]

    1987 , Address =

    Empirical Model Building and Response Surfaces , Author =. 1987 , Address =

    1987

  47. [47]

    Proceedings of 90th

    Exploring Effect of Variability of Urban System Characteristics in Network Capacity , Author =. Proceedings of 90th. 2011 , Owner =

    2011

  48. [48]

    Proceedings of 90th

    Exploring Effect of Variability of Urban System Characteristics in Network Capacity , Author =. Proceedings of 90th. 2010 , Owner =

    2010

  49. [49]

    Boyles, S. and D. Fajardo and S. T. Waller , Booktitle =. A. 2007 , Address =

    2007

  50. [50]

    and McDonald, M

    Brackstone, M. and McDonald, M. , Journal =. Car-. 1999 , Pages =

    1999

  51. [51]

    Proceedings of the 91th Annual Meeting of the Transportation Research Board , Year =

    Use, Calibration, and Validation of Traffic Simulation Models in Practics: Results of a Web-based Survey , Author =. Proceedings of the 91th Annual Meeting of the Transportation Research Board , Year =

  52. [52]

    Transportation Research Part F: Traffic Psychology and Behaviour , Year =

    Motorway driver behaviour: studies on car following , Author =. Transportation Research Part F: Traffic Psychology and Behaviour , Year =

  53. [53]

    , Journal =

    Braess, D. , Journal =. 1968 , Pages =

    1968

  54. [54]

    Braess, D. and A. Nagurney and T. Wakolbinger , Journal =. On a. 2005 , Number =

    2005

  55. [55]

    Brilon, W. and J. Geistefeldt and M. Regler , Booktitle =. Reliability of. 2005 , Address =

    2005

  56. [56]

    Brockfeld, E. and R. D. K. Calibration and. Transportation Research Record: Journal of the Transportation Research Board No.1876 , Year =

  57. [57]

    Brown, G. and M. Carlyle and J. Salmer. Defending. Interfaces , Year =

  58. [58]

    Transportation Science , Year =

    A semi-poisson model for traffic flow , Author =. Transportation Science , Year =

  59. [59]

    Tranportation Research Records, Journal of the Transportation Research Board , Year =

    Exploring the Impact of the Homogeneity of Traffic Measurements on the Existance of the Macroscopic Fundamental Diagram , Author =. Tranportation Research Records, Journal of the Transportation Research Board , Year =

  60. [60]

    Journal of Transportation Engineering , Year =

    Microsimulation approach for predicting crashes at unsignalized intersections using traffic conflicts , Author =. Journal of Transportation Engineering , Year =

  61. [61]

    Transportation Science , Year =

    Optimal Motorway Traffic Flow Control Involving Variable Speed Limits and Ramp Metering , Author =. Transportation Science , Year =

  62. [62]

    2008 , Owner =

    ISA-UK -- Intelligent Speed Adaptation, , Author =. 2008 , Owner =

    2008

  63. [63]

    Transportation Research Part B: Methodological , Year =

    Bivariate relations in nearly stationary highway traffic , Author =. Transportation Research Part B: Methodological , Year =

  64. [64]

    Transportation Research Part B: Methodological , Year =

    Some traffic features at freeway bottlenecks , Author =. Transportation Research Part B: Methodological , Year =

  65. [65]

    Proceedings of the 90th Annual Meeting of the Transportation Research Board , Year =

    Macroscopic Fundamental Diagram for Freeway Networks: Theory and Observation , Author =. Proceedings of the 90th Annual Meeting of the Transportation Research Board , Year =

  66. [66]

    2009 , Owner =

    Transportation and Traffic Theory 2009: Golden Jubilee , Author =. 2009 , Owner =

    2009

  67. [67]

    Transportation Research Part B: Methodological , Year =

    Increasing the capacity of an isolated merge by metering its on-ramp , Author =. Transportation Research Part B: Methodological , Year =

  68. [68]

    Proceedings of the 89th Annual Meeting of the Transportation Research Board , Year =

    Two new models for the flow-density relationship , Author =. Proceedings of the 89th Annual Meeting of the Transportation Research Board , Year =

  69. [69]

    Catbagan, J. and H. Nakamura , Booktitle =. Two-. 2008 , Address =

    2008

  70. [70]

    , Author =

    Handbook of methods of applied statistics: techniques of computation, descriptive methods, and statistical inference. , Author =. 1967 , Address =

    1967

  71. [71]

    Operations Research , Year =

    Traffic dynamics: studies in car following , Author =. Operations Research , Year =

  72. [72]

    Chen, A. and W. Recker , Booktitle =. Considering. 2001 , Address =

    2001

  73. [73]

    , Publisher =

    Chen, H.-K. , Publisher =. Dynamic. 1999 , Address =

    1999

  74. [74]

    Chen, R. B. and H. S. Mahmassani , Booktitle =. Travel. 2004 , Address =

    2004

  75. [75]

    , Booktitle =

    Chen, X. , Booktitle =. Agent-. 2004 , Address =

    2004

  76. [76]

    IEEE Transactions on Intelligent Transportation Systems , Year =

    Intelligent highway traffic surveillance with self-diagnosis abilities , Author =. IEEE Transactions on Intelligent Transportation Systems , Year =

  77. [77]

    Cheu, R. L. and Y. Tan and D.-H. Lee , Booktitle =. Comparison of. 2004 , Address =

    2004

  78. [78]

    Chiabaut, N. and C. Buisson and L. Leclercq , Booktitle =. Fundamental. 2008 , Address =

    2008

  79. [79]

    Transportation Research Part B: Methodological , Year =

    From heterogeneous drivers to macroscopic patterns in congestion , Author =. Transportation Research Part B: Methodological , Year =. doi:DOI: 10.1016/j.trb.2009.07.009 , ISSN =

    work page doi:10.1016/j.trb.2009.07.009 2009

  80. [80]

    International Symposium on Applications and the Internet Workshops, 2007

    Smart Parking: An Application of Optical Wireless Sensor Network , Author =. International Symposium on Applications and the Internet Workshops, 2007. SAINT Workshops 2007 , Year =

    2007

Showing first 80 references.