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Literature Review on Ramp Metering. Zichuan Li, Xiaoli Sun 05/21/2010. Outline. Introduction Ramp-metering algorithms Local ramp-metering algorithms Coordinated ramp-metering algorithms Summary References. Note:

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literature review on ramp metering

Literature Review on Ramp Metering

Zichuan Li, Xiaoli Sun

05/21/2010

outline
Outline
  • Introduction
  • Ramp-metering algorithms
    • Local ramp-metering algorithms
    • Coordinated ramp-metering algorithms
  • Summary
  • References

Note:

This literature review aims to introduce the general concept of ramp metering and focuses on local ramp metering algorithms.

introduction
Introduction
  • Definitions
    • A ramp meter is a red-green (or red-green-yellow) traffic signal on a freeway on-ramp that is used to regulate the flow of vehicles onto the freeway.
    • A ramp metering strategy is an important part of Advanced Traffic Management System (ATMS) which is a component of the Intelligent Transport System (ITS).
  • Objectives of applying ramp metering
    • Break up on-ramp platoons to smooth out the merging of traffic onto the freeway mainline so as to reduce bottlenecks caused by merging traffic.
    • Ensure that total flow on the freeway does not exceed capacity at downstream bottlenecks.
    • Some metered ramps have bypass lanes for high occupancy vehicles, allowing carpoolers and vehicles like buses to skip the queue and get directly on the highway.
introduction1
Introduction
  • The first pre-timed ramp meter was installed in Chicago, IL in 1963. This first application involved a police officer who stopped traffic on an entrance ramp and release vehicles one at a time at a predetermined rate determined from a pilot detection program, so that the objectives of safer and smoother merging onto the freeway traffic were easier without disrupting the mainline flows. [2]
  • Since then ramp-meters have been systematically deployed in many urban areas including
    • Los Angeles, CA (1968);
    • Minneapolis-St. Paul, MN (1970);
    • Austin, TX (late 1970s, withdraw later);
    • Seattle, WS (1981);
    • Denver, CO (1981);
    • Portland, OR (1981);
    • Detroit, MI (1984);
    • Etc.
introduction2
Introduction

Downstream Detectors

  • Main components
    • Ramp-Metering Signal and Controller
    • Advance warning signal
    • Mainline detectors
      • Upstream detectors
      • Downstream detectors
    • On-ramp detectors
      • Check-in detectors
      • Check-out detectors
    • Queue detectors (optional)
    • HOV detectors (optional)
    • Other optional components

Upstream Detectors

Ramp metering signal

Check-out Detector

Check-in Detector

HOV Detector

HOV Bypass Lane

Queue Detector

Advance

warning signal

Source:

Pearson et al. (2001) [3]

Local Road

Freeway

ramp metering algorithms
Ramp-metering algorithms
  • Ramp metering rate [3]
    • Typically ranges 4 -15 sec/veh;
    • Lower than 4 sec/veh may confuse drivers since it takes 2 seconds for vehicle to start up;
    • Higher than 15 sec/veh may result in ramp violation because of impatient waiting.
ramp metering algorithms1
Ramp-metering algorithms
  • Classified by control philosophy
    • The pre-timed control allows vehicles to enter the freeway mainline at a pre-set rate based on time-of-day schedule. The control interval could range from 30 minutes to the entire period of peak hours. [3]
    • The traffic-responsive control uses real-time traffic data to determine the metering rate to better serve the current traffic characteristics. [55]
      • Actuated control operates based on traffic demands as registered by the actuation of vehicle detectors. The green time is a function of the traffic flow, and can be varied between minimum and maximum lengths depending on flows. Signals are traffic-responsive, but are not adaptive when the change of traffic condition is substantial.
      • Adaptive control uses real time data from detectors to perform constant optimizations on the signal timing plan for an arterial or a network. Signals can adapt to non-recurring congestion, incidents, events, or traffic demand growth over time, without needing to be reset.

Pre-timed control

Ramp Metering

Actuated Control

Traffic-responsive control

Adaptive Control

ramp metering algorithms2
Ramp-metering algorithms
  • Pre-timed ramp metering [3]
    • It is the simplest form of metering.
    • Detectors may be installed on the ramp to actuate and terminate the metering cycle, but the metering rate is fixed. The metering rate is determined on historical average traffic conditions.
    • No detector is needed on the freeway mainline.
    • Pre-timed ramp metering benefits on incident reduction from merging conflicts, but often leads to under-utilization of the freeway mainline capacity under time-varying traffic conditions and unnecessary ramp queuing and delays caused by over restrictive metering rates.
    • Example study: Linear programming method [17], etc .
ramp metering algorithms3
Ramp-metering algorithms
  • Control philosophy of Actuated Control [54]
    • There are two basic components to the phase green time: the initial interval, the extendable interval.
      • The initial interval is determined by the specified minimum green and the variable initial operation. The controller will hold the phase in green for the duration of the initial interval regardless of demand or conflicting calls.
      • During the extendable interval, the phase will be allowed to terminate (i.e., gap out) if the vehicle headways exceed the specified vehicle extension (passage) time.
      • However, the phase must terminate at the end of the extendable interval even when there is demand (i.e., max out). The duration of the extendable interval is either calculated from the specified maximum green or can be directly specified.
    • If the traffic demand is substantially high, the green phase terminates at the maximum green time (e.g., max out), in that case the actuated controller operates no different to the pre-timed controller and loses the flexibility to respond to fluctuating traffic flow.
ramp metering algorithms4
Ramp-metering algorithms
  • Adaptive control [55]
    • Adaptive control systems are currently the most advanced and complex control systems available.
    • They receive real-time data through detectors, then uses an online computer to create an optimal timing plan.
    • Adaptive control works well for areas with high rates of growth, where timing plans would need to be updated frequently.
  • Some adaptive control strategies have an explicit objective function linking to its control strategy.
    • Example objective functions
      • Minimizing total travel time
      • Maximizing system throughput
ramp metering algorithms5
Ramp-metering algorithms
  • Classified by geometric extent
    • In local ramp metering algorithms, the metering rate is determined based on local traffic conditions.
      • Volume-based metering uses the freeway main volume at the upstream and the downstream capacity to compute the metering rate.
      • Occupancy-based metering determines the ramp-metering rate based on the occupancy of the downstream freeway mainline, and uses feedback regulation to maintain a pre-specified occupancy.
    • The coordinated ramp metering measures and controls several ramps as a system to optimize traffic over an area.

Local ramp-metering

Ramp Metering

Coordinated ramp-metering

slide12

Demand-capacity strategy [3, 5, 6 , 16]

Volume-based

Congested pattern control [27]

Local

ALINEA [7]

Occupancy-based

Local fuzzy logic control [9, 10, 11]

Local neural network control [12, 13, 26]

Iterative-learning [28]

Cooperative

Ramp

Metering

algorithms

BOTTLENECK algorithm [29]

Competitive

Pre-timed

SWARM algorithm [34,35]

HELPER algorithm [32]

METALINE [36]

LINKED-ramp algorithm [33]

FUZZY LOGIC algorithm [37, 38, 39, 11]

Coordinated

NEURAL NETWORK algorithm [40]

Integrated

LP (linear programming) algorithm [41, 42, 43, 44]

DYNAMIC algorithm [45]

LQ (linear-quadratic) feedback control algorithm [18, 46, 47, 48, 49]

Zone control

[25, 26]

SUCCESIVE OPTIMIZATION algorithm [50, 51]

Coordinated ALINEA

ramp metering algorithms6
Ramp-metering algorithms
  • Both local and coordinated algorithms [53]
    • Bottleneck
    • Compass
    • Dynamic metering control
    • FLOW
    • Helper
    • Linked
    • Neural Control
    • RAMBO
    • SWARM (System Wide Adaptive Ramp Metering).
    • ZONE
local ramp metering algorithms demand capacity strategy
Local ramp-metering algorithms- Demand-capacity strategy
  • The ramp meter is triggered when the upstream flow exceeds a predetermined threshold or the downstream flow is below a predetermined threshold.
  • The metering rate is the difference between the upstream flow measured in the previous time interval and the downstream freeway capacity.
  • The metering rate is truncated if it drop below the Rmin.

C

V(t-1)

R(t)

Source: [3, 5]

local ramp metering algorithms demand capacity strategy1
Local ramp-metering algorithms- Demand-capacity strategy
  • The demand-capacity strategy (1975) is the earliest traffic-responsive ramp metering control algorithm implemented in field sites.
  • It actually uses the short-term “historical” (i.e., the previous interval) data to determine the current metering rate. So it is not able to “predict” the traffic conditions and select metering rate before congestion occur.
  • It is an “open-loop” control strategy, hence it is sensitive to disturbance.
    • A “open-loop” controller is also called “non-feedback” controller which uses only the current state and its model to compute the output of the controller and does not use feedback to determine if the output achieves its desired goal.

output

input

Source: [3, 5, 6, 16]

controller

slide16

Local ramp-metering algorithms- ALINEA strategy

O(t-1)

  • The goal of the ALINEA strategy is to maintain the traffic density on the mainline equal to a pre-set value and optimize the traffic flow on the mainline.
  • The metering rate is based on the downstream mainline occupancy.
  • The metering rate is truncated if it exceeds a range [Rmin, Rmax].
  • In field experiments, it was found that ALINEA is not very sensitive to the choice of the KR. A value of KR = 70 vph was found to yield excellent results at many different sites.

Os

R(t)

Source: [7, 14, 15, 16]

slide17

Local ramp-metering algorithms- ALINEA strategy

  • ALINEA (1991) is a “closed-loop” algorithm using “feedback” to determine the ramp metering rate for the subsequent periods, and attempt to predict operational problems before they occur. [7, 14, 15, 16]
    • The “feedback” means that the algorithm takes the traffic condition in previous time interval into account in order to predict current traffic condition and select metering rate.
  • ALINEA works better than demand-capacity strategy but it does not consider queue spill-back directly, so ALINEA has difficulty to balance freeway congestion and ramp queues when traffic becomes heavily congested.
  • Some optimized algorithms
    • To enhance the efficiency to address specific issues which were not covered by ALINEA. [4, 16]
      • FL-ALINEA (flow-based), UP-ALINEA (upstream-occupancy-based), UF-ALINEA (upstream-flow-based), X-ALINEA/Q (combination of strategies with ramp-queue control), etc.

input

output

controller

feedback

local ramp metering algorithms local fuzzy logic control flc
Local ramp-metering algorithms- Local fuzzy logic control (FLC)
  • Objective
    • For example: maximize total distance traveled and minimize total travel time and vehicle delay, while maintaining acceptable ramp queues.
  • Calculation procedure
    • Step 1: fuzzification to convert the numerical input variables into descriptive variables.
      • Example input variables: upstream occupancy, downstream occupancy, mainline speed, ramp queue occupancy, etc.
    • Step 2: rule evaluation to implement the control logic.
      • “if … then…” rule base describes the control strategy.
    • Step 3: defuzzification to map the descriptive outcomes to a numerical output. The resulting control action is metering rate.

Source: [11]

local ramp metering algorithms local fuzzy logic control flc1
Local ramp-metering algorithms- Local fuzzy logic control (FLC)
  • Fuzzy logic control strategy
    • Advantages over traditional ramp-metering controllers [10, 11]
      • FLC does not require extensive system modeling.
      • FLC utilizes partial or imprecise information. Hence, reduce sensitivity to input measurement errors and missing data.
      • FLC can compromise between conflicting objectives and incorporate experts knowledge into control.
      • Easy to tune algorithm without recompiling the code.
      • Simulation results showed that FLC outperforms no metering, pre-timed metering, demand-capacity metering and speed metering under various conditions.
    • Disadvantages
      • Calibration of FLC parameters and fuzzy rules under various traffic conditions.
        • Some researchers proposed methods to adjust the parameters in FLC to improve the performance. For example, Zhu (2008 [9]) used Particle Swarm Optimization (PSO) to adjust some important parameters in FLC.
local ramp metering algorithms local neural network nn control

△x

ρ v

qu(k)

q(k)

R(k)

Local ramp-metering algorithms- Local neural network (NN) control
  • Basic control logic
    • Formulated the ramp metering control as a nonlinear feedback control problem which composes of one or a number of feed-forward neural networks.
  • Information collected on site
    • Upstream & downstream traffic flow rate per hour per lane (qu,q respectively)
    • Number of lanes of the freeway mainline (λ)
    • Section distance between upstream and downstream detectors (Δx)

Procedure to calculate traffic density:

Number of vehicles in the segment at time interval t+1 is:

Define vehicle concentration (section density) as:

Then the traffic density is:

Source: [12, 13]

local ramp metering algorithms local neural network nn control1
Local ramp-metering algorithms- Local neural network (NN) control
  • Input
    • Traffic density of the section
  • Output
    • Metering rate
  • Training procedure:
    • Initialize parameters of the NN, i.e., initial the weights w(*,*).
    • Train the NN, which means adjust weights w(*,*) using input and output data.
    • Finish training when the NN well maps the input with the output.

w (i,j)

w (j,k)

Input 1

Output 1

Input 2

Output 2

Input m

Output p

Source: [12, 13]

local ramp metering algorithms
Local ramp-metering algorithms
  • Both of ALINEA and neural network (NN) control algorithms are effective for moderate congestion but not for heavy congestion where queue spillback may occur.
    • When queue spill-back occurs, these ALINEA and NN algorithms simply apply an overriding metering rate and have difficulty to balance freeway congestion and on-ramp queues.
coordinated ramp metering algorithms
Coordinated ramp-metering algorithms
  • Cooperative ramp-metering
    • Metering rates are first computed with the local traffic information, then adjusted according to the conditions of the entire system.
  • Competitive ramp-metering
    • Two metering rates are computed for each ramp, one is based on local traffic conditions, and the other is based on system conditions, and the restrictive one is chosen
  • Integrated ramp-metering
    • Local traffic conditions and system-wide traffic conditions are both used to determine metering rates.
  • Zone control strategy [25, 26]
    • It is a volume-based algorithm. This control divides the freeway into several zones and each contains no more than one on-ramp and thus operate the mainline at capacity.
  • Coordinated ALINEA
summary
Summary
  • Ramp metering is a component of the Advanced Transportation Management System (ATMS) under the frame of ITS.
  • Ramp metering is one of the most direct, effective, and practical measures to manage freeway traffic if appropriately implemented.
  • In spite of positive impacts on freeway mainline flow, ramp metering potentially has significant negative impacts on traffic on ramps and local street network.
summary1
Summary
  • Benefits and dis-benefits of deploying ramp metering strategies

Source: Rebecca, et al., 2001 [3]; Arnold, 1998 [1]

summary2
Summary
  • Local ramp metering algorithms
    • Demand-capacity algorithm is the first actuated ramp metering implemented on field site. But since it is an open-loop non-feedback algorithm, it is sensitive to disturbs and cannot predict traffic condition before congestion or occurs.
    • ALINEA and NN algorithms use feedback to maintain a desired level of occupancy, and both are effective on moderate traffic demand. But they have difficulty to balance freeway congestion and on-ramp queue under heavily congested traffic condition.
    • Fuzzy logic algorithm can handle missing or imprecise traffic data, and can compromise conflicting objectives. But parameters of the FL controller need calibration in order to reach the premium performance.
    • In summary, all the local ramp-metering strategies only responses to traffic around a single ramp and does not consider traffic conditions on other ramps or freeway mainline segments. They are suitable for localized problems.
summary3
Summary
  • Coordinated ramp metering algorithms
    • With more cost, the coordinated ramp-metering strategies looks at both of the local traffic conditions and the system-wide information, and is capable to prevent both freeway mainline congestion and ramp spillback.
    • In addition, some field experiments and many simulation studies have reported that coordinated metering strategies yield significant delay [31].
summary4
Summary
  • Recommendations for further research
    • Extend the control boundaries to cover both the freeway and its neighboring arterials, to better balance the freeway congestion, the ramp queue, and the local street congestion.
    • Coordinate ramp metering control with local road network traffic control system to improve the overall system. For example, reduce on-ramp traffic demand.
    • Integrate ramp metering system with the diversion routing system. For example, develop coordinated signal timing on local arterials in favor of diversion routes, etc.
    • Integrate ramp metering system with other control strategies. For example, speed control strategies.
references
References
  • [1] Arnold, E. D. Jr. (1998) Ramp Metering: A Review of the Literature (VTRC 99-TAR5), Virginia Transportation Research Council.
  • [2] Piotrowicz, Gary and Robinson, James. (1995) Ramp Metering Status in North America - 1995 Update, Federal Highway Administration, Washington, D.C.
  • [3] Pearson, Rebecca, Black, Justin, and Wanat Joe. (2001) Ramp Metering, http://www.calccit.org/itsdecision/serv_and_tech/Ramp_metering/ramp_metering_summary.html
  • [4] Scariza, Joseph R. (2003) Evaluation of Coordinated and Local Ramp Metering Algorithms using Microscopic Traffic Simulation, Master thesis, Massachusetts Institute of Technology.
  • [5] Masher, D. P., Ross, D. W., Wong, P. J., Tuan, P. L., and Zeidler, Peracek, S. (1975) Guidelines for Design and Operating of Ramp Control Systems, Stanford Research Institute Report, NCHRP 3-22, SRI Project 3340, SRI, Menid Park, CA.
  • [6] Koble, H. M., Adams, T. A., and Samant, V. S. (1980) Control Strategies in Response to Freeway Incidents, Report No. FHWA/RD-80/005, Federal Highway Administration, Washington, DC.
references1
References
  • [7] Papageorgiou, M, Salem, H. Hadj, and Blosseville J. (1991) ALINEA: A Local Feedback Control Law for On-Ramp Metering, Transportation Research Record 1320, pp. 58-64.
  • [8] Chu, Lianyu, Yang, Xu, and Recker, Will. (2005) ATMS Testbed Technical Report TTR3-15, Institute of Transportation Studies, University of California Irvine.
  • [9] Zhu, Peng. (2008) An automatic tuning strategy for local fuzzy logic ramp metering algorithm using Particle Swarm Optimization (PSO), Ph.D. Dissertation, Florida International University.
  • [10] Taylor, Cynthia and Meldrum, Deirdre. (2000) Algorithm Design, User Interface, and Optimization Procedure for a Fuzzy Logic Ramp Metering Algorithm - A Training Manual for Freeway Operations Engineers, Report No. WA-RD 481.1, Washington State Department of Transportation.
  • [11] Taylor, C. E., Meldrum, D. R., and Jacobson, L. (1998) Fuzzy Ramp Metering: Design Overview and Simulation Results, Transportation Research Record 1634, Transportation Research Board, pp. 10-18.
  • [12] Zhang, Hongjun, and Ritchie, Stephen G. (1995) An Integrated Traffic Responsive Ramp Control Strategy via Nonlinear State Feedback, Report No. UCI-ITS-WP-95-1, Institute of Transportation Studies, University of California at Irvine.
references2
References
  • [13] Zhang, H. Michael, and Ritchie, Stephen G. (1997) Freeway ramp metering using artificial neural networks, Transportation Research Part C, Vol. 5, No. 5, Elsevier, pp. 273-286.
  • [14] Papageorgiou M., Salem, H. Hadj, and Middelham F. (1997) ALINEA Local Ramp Metering Summary of Field Results. Transportation Research Record 1603, pp. 90-98.
  • [15] Salem, H. Hadj, Poirier, Philippe, Heylliard, Jean-Franqois, and Peynaud, Jean-Paul, (2001) ALINEA: a local Traffic Responsive Strategy for Ramp Metering: Field Results on A6 Motorway in Paris, In IEEE Intelligent Transportation Systems Conference Proceedings - Oakland (CA), USA, August 25-29.
  • [16] Smaragdis, Emmanouil and Papageorgiou, Markos. (2003) Series of New Local Ramp Metering Strategies, Transportation Research Record 1856, pp. 74-86.
  • [17] Wattleworth, J. (1963). "Peak-period control of a freeway system–some theoretical considerations." Chicago area expressway surveillance project.
  • [18] Yuan, L. S. and J. B. Kreer (1971). "Adjustment Of Freeway Ramp Metering Rates To Balance Entrance Ramp Queues." Transportation Research 5(2): 127-&.
  • [19] Tabac, D. (1972). A linear programming model of highway traffic control.
  • [20] Wang, C. F. (1972). "On a ramp-flow assignment problem." TRANSPORTATION SCIENCE 6(2): 114-130.
references3
References
  • [21] Wang, J. and A. May (1973). Computer model for optimal freeway on-ramp control, Highway Research Board.
  • [22] Chen, C., J. B. Cruz, et al. (1974). "Entrance ramp control for travel rate maximization in expressways." Transportation Research 8: 503-508.
  • [23] Schwartz, S. and H. Tan (1977). Integrated control of freeway entrance ramps by threshold regulation.
  • [24] Papageorgiou, M. (1980). "A new approach to time-of-day control based on a dynamic freeway traffic model." Transportation Research Part B: Methodological 14(4): 349-360.
  • [25] Stephanedes, Y. (1994). Implementation of on-line zone control strategies for optimal ramp metering in the minneapolis ring road, Institution of Electrical Engineers.
  • [26] Xin, W., P. Michalopoulos, et al. (2004). "Minnesota's New Ramp Control Strategy: Design Overview and Preliminary Assessment." Transportation Research Record: Journal of the Transportation Research Board 1867(-1): 69-79.
  • [27] Kerner, B. (2005). "Control of spatiotemporal congested traffic patterns at highway bottlenecks." Physica A: Statistical Mechanics and its Applications 355(2-4): 565-601.
references4
References
  • [28] Hou, Z., J.-X. Xu, et al. (2008). "An iterative learning approach for density control of freeway traffic flow via ramp metering." Transportation Research Part C: Emerging Technologies 16(1): 71-97.
  • [29] Jacobson, L., K. Henry, et al. (1989). "Real-time metering algorithm for centralized control." Transportation Research Board 1232: 17-26.
  • [30] Nihan, N. and D. Berg (1991). "Predictive Algorithm Improvements for a Real-Time Ramp Control System." Final Report GC8286 (16), WA-RD 213.
  • [31] Bogenberger, K. and A. May (1999). "Advanced coordinated traffic responsive ramp metering strategies." California PATH Paper UCB-ITS-PWP-99-19.
  • [32] Lipp, L., L. Corcoran, et al. (1991). "Benefits of central computer control for Denver ramp-metering system." Transportation Research Record 1320: 3-6.
  • [33] Banks, J. (1993). "Effect of response limitations on traffic-responsive ramp metering." Transportation Research Record 1394: 17-25.
  • [34] Paesani, G., J. Kerr, et al. (1997). System wide adaptive ramp metering in southern California. ITS America 7th Annual Meeting.
  • [35] Ahn, S., R. Bertini, et al. (2007). "Evaluating Benefits of Systemwide Adaptive Ramp-Metering Strategy in Portland, Oregon." Transportation Research Record: Journal of the Transportation Research Board 2012(-1): 47-56.
references5
References
  • [36] Papageorgiou, M. (1990). "Modelling and real-time control of traffic flow on the southern park of Boulevard Peripherique in Paris: Part II: Coordinated on-ramp metering." TRANSP. RES. 24A(5): 361-370.
  • [37] Sasaki, T. and T. Akiyama (1986). Development of fuzzy traffic control system on urban expressway. Control in Transportation Systems, Vienna, Austria, Pergamon Press, Engl & New.
  • [38] Chen, L., A. May, et al. (1990). "Freeway ramp control using fuzzy set theory for inexact reasoning." Transportation research. Part A: general 24(1): 15-25.
  • [39] Meldrum, D. and C. Taylor (1995). "Freeway traffic data prediction using artificial neural networks and development of a fuzzy logic ramp metering algorithm." Report No. WA-RD 365.
  • [40] Wei, C.-H. and K.-Y. Wu (1996). "Applying an artificial neural network model to freeway ramp metering control." Transportation Planning Journal 25(3): 335-356.
  • [41] Yoshino, T., T. Sasaki, et al. (1995). "The Traffic-Control System on the Hanshin Expressway." Interfaces 25(1): 94-108.
  • [42] Lovell, D. and C. Daganzo (2000). "Access control on networks with unique origin–destination paths." Transportation Research Part B 34(3): 185-202.
references6
References
  • [43] Levinson, D. and L. Zhang (2006). "Ramp meters on trial: Evidence from the Twin Cities metering holiday." TRANSPORTATION RESEARCH PART A-POLICY AND PRACTICE 40(10): 810-828.
  • [44] Gomes, G. and R. Horowitz (2006). "Optimal freeway ramp metering using the asymmetric cell transmission model." Transportation research. Part C, Emerging technologies 14(4): 244-262.
  • [45] Chen, O., A. Hotz, et al. (1997). Development and evaluation of a dynamic ramp metering control model. 8th IFAC(International Federation of Automatic Control)/IFIP/IFORS Symposium on Transportation Systems Chania, Greece.
  • [46] Kaya, A. (1972). Computer and optimization techniques for efficient utilization or urban freeway systems.
  • [47] Papageorgiou, M. (1983). "A hierarchical control system for freeway traffic." Transportation Research Part B: Methodological 17(3): 251-261.
  • [48] Payne, H., D. Brown, et al. (1985). Demand-responsive strategies for interconnected freeway ramp control systems. Volume 1: metering strategies, FHWA/RD-85/109, VERSAC Incorporated, San Diego, California.
  • [49] Papageorgiou, M., J. M. Blosseville, et al. (1990). "Modelling and real-time control of traffic flow on the southern part of Boulevard Peripherique in Paris: Part I: Modelling." TRANSP. RES. 24A(5): 345-359.
references7
References
  • [50] Chang, G.-L., W. Jifeng, et al. (1994). "Integrated real-time ramp metering modeling for non-recurrent congestion: framework and preliminary results." Transportation Research Record 1446: 56-65.
  • [51] Wu, J. and Chang, G. (1999). "An integrated optimal control and algorithm for commuting corridors." International Transactions in Operational Research 6(1): 39-55.
  • [52] Zhang, M., T. Kim, et al. (2001). "Evaluation of on-ramp control algorithms." UC Berkeley: California Partners for Advanced Transit and Highways (PATH). Retrieved from: http://www. escholarship. org/uc/item/83n4g2rq.
  • [53] Rafferty, P. C., Treazise, M. (2007), Wisconsin Ramp Metering Operations and Implementation, Proceedings of the 2007 Mid-Continent Transportation Research Symposium
  • [54] Holm, P., Tomich, D., Sloboden, J., Lowrance, C. (2007). Traffic Analysis Toolbox Volume IV: Guidelines for Applying CORSIM Microsimulation Modeling Software, FHWA-HOP-07-079, Federal Highway Administration.
  • [55] Pearson, Rebecca, Traffic Signal Control, http://www.calccit.org/itsdecision/serv_and_tech/Traffic_signal_control/traffsigrep_print.htm