IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v195y2009i1p127-138.html
   My bibliography  Save this article

Modeling traffic flow interrupted by incidents

Author

Listed:
  • Baykal-Gürsoy, M.
  • Xiao, W.
  • Ozbay, K.

Abstract

A steady-state M/M/c queueing system under batch service interruptions is introduced to model the traffic flow on a roadway link subject to incidents. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as complete service disruptions where none of the servers work or partial failures where servers work at a reduced service rate. We analyze this system in steady-state and present a scheme to obtain the stationary number of vehicles on a link. For those links with large c values, the closed-form solution of M/M/[infinity] queues under batch service interruptions can be used as an approximation. We present simulation results that show the validity of the queueing models in the computation of average travel times.

Suggested Citation

  • Baykal-Gürsoy, M. & Xiao, W. & Ozbay, K., 2009. "Modeling traffic flow interrupted by incidents," European Journal of Operational Research, Elsevier, vol. 195(1), pages 127-138, May.
    • Handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:127-138
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00154-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Harrison White & Lee S. Christie, 1958. "Queuing with Preemptive Priorities or with Breakdown," Operations Research, INFORMS, vol. 6(1), pages 79-95, February.
    2. Dirk Heidemann, 2001. "A Queueing Theory Model of Nonstationary Traffic Flow," Transportation Science, INFORMS, vol. 35(4), pages 405-412, November.
    3. Rajat Jain & J. Macgregor Smith, 1997. "Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models," Transportation Science, INFORMS, vol. 31(4), pages 324-336, November.
    4. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    5. Skabardonis, Alexander & Petty, Karl & Varaiya, Pravin & Bertini, Robert, 1998. "Evaluation Of The Freeway Service Patrol ( F S P ) In Los Angeles," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt3920p806, Institute of Transportation Studies, UC Berkeley.
    6. Sheu, Jiuh-Biing, 2007. "Microscopic modeling and control logic for incident-responsive automatic vehicle movements in single-automated-lane highway systems," European Journal of Operational Research, Elsevier, vol. 182(2), pages 640-662, October.
    7. O. J. Boxma & I. A. Kurkova, 2000. "The M/M\1 queue in a heavy‐tailed random environment," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(2), pages 221-236, July.
    8. Michael C. Dunne, 1967. "Traffic Delay at a Signalized Intersection with Binomial Arrivals," Transportation Science, INFORMS, vol. 1(1), pages 24-31, February.
    9. I. L. Mitrany & B. Avi-Itzhak, 1968. "A Many-Server Queue with Service Interruptions," Operations Research, INFORMS, vol. 16(3), pages 628-638, June.
    10. Lin, Wei-Hua & Daganzo, Carlos F., 1997. "A simple detection scheme for delay-inducing freeway incidents," Transportation Research Part A: Policy and Practice, Elsevier, vol. 31(2), pages 141-155, March.
    11. Sheu, Jiuh-Biing, 2004. "A sequential detection approach to real-time freeway incident detection and characterization," European Journal of Operational Research, Elsevier, vol. 157(2), pages 471-485, September.
    12. J. N. Darroch & G. F. Newell & R. W. J. Morris, 1964. "Queues for a Vehicle-Actuated Traffic Light," Operations Research, INFORMS, vol. 12(6), pages 882-895, December.
    13. B. Avi-Itzhak & P. Naor, 1963. "Some Queuing Problems with the Service Station Subject to Breakdown," Operations Research, INFORMS, vol. 11(3), pages 303-320, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ng, ManWo & Khattak, Asad & Talley, Wayne K., 2013. "Modeling the time to the next primary and secondary incident: A semi-Markov stochastic process approach," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 44-57.
    2. Karimi-Mamaghan, Maryam & Mohammadi, Mehrdad & Jula, Payman & Pirayesh, Amir & Ahmadi, Hadi, 2020. "A learning-based metaheuristic for a multi-objective agile inspection planning model under uncertainty," European Journal of Operational Research, Elsevier, vol. 285(2), pages 513-537.
    3. Yona Elbaum & Alexander Novoselsky & Evgeny Kagan, 2022. "A Queueing Model for Traffic Flow Control in the Road Intersection," Mathematics, MDPI, vol. 10(21), pages 1-15, October.
    4. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    5. L. G. Afanasyeva, 2020. "Asymptotic Analysis of Queueing Models Based on Synchronization Method," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1417-1438, December.
    6. Vishal Mandal & Abdul Rashid Mussah & Peng Jin & Yaw Adu-Gyamfi, 2020. "Artificial Intelligence-Enabled Traffic Monitoring System," Sustainability, MDPI, vol. 12(21), pages 1-21, November.
    7. Gao, Jingqin & Zuo, Fan & Ozbay, Kaan & Hammami, Omar & Barlas, Murat Ledin, 2022. "A new curb lane monitoring and illegal parking impact estimation approach based on queueing theory and computer vision for cameras with low resolution and low frame rate," Transportation Research Part A: Policy and Practice, Elsevier, vol. 162(C), pages 137-154.
    8. Niek Baer & Richard J. Boucherie & Jan-Kees C. W. van Ommeren, 2019. "Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic," Transportation Science, INFORMS, vol. 53(2), pages 585-596, March.
    9. Larisa Afanasyeva & Ekaterina Bulinskaya, 2013. "Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 935-950, December.
    10. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    11. Mohammadi, Mehrdad & Jula, Payman & Tavakkoli-Moghaddam, Reza, 2019. "Reliable single-allocation hub location problem with disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 123(C), pages 90-120.
    12. Shah, Nirav & Kumar, Subodha & Bastani, Farokh & Yen, I-Ling, 2012. "Optimization models for assessing the peak capacity utilization of intelligent transportation systems," European Journal of Operational Research, Elsevier, vol. 216(1), pages 239-251.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pedro Cesar Lopes Gerum & Andrew Reed Benton & Melike Baykal-Gürsoy, 2019. "Traffic density on corridors subject to incidents: models for long-term congestion management," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 795-831, December.
    2. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    3. Pedram Sahba & Bariş Balciog̃lu & Dragan Banjevic, 2013. "Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 331-342, June.
    4. Neda Mirzaeian & Soo-Haeng Cho & Alan Scheller-Wolf, 2021. "A Queueing Model and Analysis for Autonomous Vehicles on Highways," Management Science, INFORMS, vol. 67(5), pages 2904-2923, May.
    5. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    6. Osorio, Carolina & Flötteröd, Gunnar & Bierlaire, Michel, 2011. "Dynamic network loading: A stochastic differentiable model that derives link state distributions," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1410-1423.
    7. Pedram Sahba & Barış Balcıog̃lu & Dragan Banjevic, 2022. "The impact of disruption characteristics on the performance of a server," Annals of Operations Research, Springer, vol. 317(1), pages 239-252, October.
    8. Sheng Zhu & Jinting Wang & Bin Liu, 2020. "Equilibrium joining strategies in the Mn/G/1 queue with server breakdowns and repairs," Operational Research, Springer, vol. 20(4), pages 2163-2187, December.
    9. Sauer Cornelia & Daduna Hans, 2003. "Availability Formulas and Performance Measures for Separable Degradable Networks," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 165-194, January.
    10. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    11. Fiems, Dieter & Maertens, Tom & Bruneel, Herwig, 2008. "Queueing systems with different types of server interruptions," European Journal of Operational Research, Elsevier, vol. 188(3), pages 838-845, August.
    12. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    13. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    14. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    15. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    16. Niek Baer & Richard J. Boucherie & Jan-Kees C. W. van Ommeren, 2019. "Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic," Transportation Science, INFORMS, vol. 53(2), pages 585-596, March.
    17. Herwig Bruneel & Dieter Fiems & Joris Walraevens & Sabine Wittevrongel, 2014. "Queueing models for the analysis of communication systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 421-448, July.
    18. Lan Lu & Zheng Zhu & Pengfei Guo & Qiao‐Chu He, 2022. "Service Operations for Mixed Autonomous Paradigm: Lane Design and Subsidy," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1595-1612, April.
    19. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    20. Chen, Shih-Pin, 2016. "Time value of delays in unreliable production systems with mixed uncertainties of fuzziness and randomness," European Journal of Operational Research, Elsevier, vol. 255(3), pages 834-844.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:127-138. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.