IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v240y2015i1p109-126.html
   My bibliography  Save this article

A PH/PH(n)/C/C state-dependent queuing model for metro station corridor width design

Author

Listed:
  • Hu, Lu
  • Jiang, Yangsheng
  • Zhu, Juanxiu
  • Chen, Yanru

Abstract

Metro station corridor width design considering demand fluctuation as well as the randomness and state-dependence of service time is an urgent concern and a complicated random planning issue. This paper confirms the accuracy of phase-type distribution (PH) fitting for passenger arrival intervals and service times with randomness and state-dependence in metro station corridors. A PH/PH(n)/C/C state-dependent queuing model is thus established by a finite level-dependent quasi-birth–death (QBD) process. The existing M/G(n)/C/C, M/G/1/C, and D/D/1/C models are proved to be special cases of the PH/PH(n)/C/C model through theoretical derivation and the precision of the proposed model is analyzed through simulation tests. The quantitative relationship between the level of service (LOS) and the corridor width is established based on the proposed model. A total of 81 experiments are designed to compare the calculations between the proposed model and the M/G(n)/C/C, M/G/1/C, and D/D/1/C models. Comparison results demonstrate that (1) the value of effective width of the PH/PH(n)/C/C queuing model is higher than those of the M/G(n)/C/C, M/G/1/C, and D/D/1/C models; (2) the real area occupied per person in the corridor of the PH/PH(n)/C/C queuing model is mostly proximate to the designed LOS, whereas those of the M/G(n)/C/C, M/G/1/C, and D/D/1/C models fail to meet the designed LOS; and (3) the performance measures of the PH/PH(n)/C/C queuing model enjoy high performance-width elasticity and are significantly improved compared with those of the M/G(n)/C/C, M/G/1/C, and D/D/1/C models.

Suggested Citation

  • Hu, Lu & Jiang, Yangsheng & Zhu, Juanxiu & Chen, Yanru, 2015. "A PH/PH(n)/C/C state-dependent queuing model for metro station corridor width design," European Journal of Operational Research, Elsevier, vol. 240(1), pages 109-126.
    • Handle: RePEc:eee:ejores:v:240:y:2015:i:1:p:109-126
    DOI: 10.1016/j.ejor.2014.06.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714004937
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.06.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Lam, William H. K. & Lee, Jodie Y. S. & Chan, K. S. & Goh, P. K., 2003. "A generalised function for modeling bi-directional flow effects on indoor walkways in Hong Kong," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(9), pages 789-810, November.
    2. Krishnamoorthy, A. & Babu, S. & Narayanan, Viswanath C., 2009. "The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service," European Journal of Operational Research, Elsevier, vol. 195(1), pages 174-185, May.
    3. Liu, Jialu & Yang, Sheng & Wu, Aiguo & Hu, S. Jack, 2012. "Multi-state throughput analysis of a two-stage manufacturing system with parallel unreliable machines and a finite buffer," European Journal of Operational Research, Elsevier, vol. 219(2), pages 296-304.
    4. Blue, Victor J. & Adler, Jeffrey L., 2001. "Cellular automata microsimulation for modeling bi-directional pedestrian walkways," Transportation Research Part B: Methodological, Elsevier, vol. 35(3), pages 293-312, March.
    5. Miaomiao Yu & Yinghui Tang & Yonghong Fu, 2013. "A geometric process model for /(/)/1/ queue with new service machine procurement lead time," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(6), pages 1061-1075.
    6. Moonsoo Ko & Taewan Kim & Keemin Sohn, 2013. "Calibrating a social-force-based pedestrian walking model based on maximum likelihood estimation," Transportation, Springer, vol. 40(1), pages 91-107, January.
    7. MacGregor Smith, J., 1991. "State-dependent queueing models in emergency evacuation networks," Transportation Research Part B: Methodological, Elsevier, vol. 25(6), pages 373-389, December.
    8. Masuyama, Hiroyuki, 2011. "Subexponential asymptotics of the stationary distributions of M/G/1-type Markov chains," European Journal of Operational Research, Elsevier, vol. 213(3), pages 509-516, September.
    9. Mitchell, David H. & MacGregor Smith, J., 2001. "Topological network design of pedestrian networks," Transportation Research Part B: Methodological, Elsevier, vol. 35(2), pages 107-135, February.
    10. Ram Chakka, 1998. "Spectral expansion solution for some finite capacity queues," Annals of Operations Research, Springer, vol. 79(0), pages 27-44, January.
    11. Ramin Sadre & Boudewijn R. Haverkort, 2011. "Decomposition-Based Queueing Network Analysis with FiFiQueues," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. Dijk (ed.), Queueing Networks, chapter 15, pages 643-699, Springer.
    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. Sheng Dong & Afaq Khattak & Feng Chen & Feifei Xu, 2024. "Stay Two-Meters Apart: Assessing the Impact of COVID-19 Social Distancing Protocols on Subway Station Walkway Performance," Sustainability, MDPI, vol. 16(16), pages 1-18, August.
    2. Shi, Yihan & Xu, Jie & Zhang, Hui & Jia, Limin & Qin, Yong, 2022. "Empirical investigation on turning behavior of passengers in subway station," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    3. Afaq Khattak & Hamad Almujibah & Feng Chen & Hussain S. Alyami, 2022. "Modified State-Dependent Queuing Model for the Capacity Analysis of Metro Rail Transit Station Corridor during COVID-19," Sustainability, MDPI, vol. 14(21), pages 1-14, October.
    4. Chen, Yanru & Yi, Bing & Jiang, Yangsheng & Sun, Jidong & Wahab, M.I.M., 2018. "Inter-arrival time distribution of passengers at service facilities in underground subway stations: A case study of the metropolitan city of Chengdu in China," Transportation Research Part A: Policy and Practice, Elsevier, vol. 111(C), pages 227-251.
    5. Khattak, Afaq & Hussain, Arshad, 2021. "Hybrid DES-PSO framework for the design of commuters’ circulation space at multimodal transport interchange," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 205-229.
    6. Zhang, Hui & Xu, Jie & Jia, Limin & Shi, Yihan, 2021. "Research on walking efficiency of passengers around corner of subway station," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    7. Hu, Lu & Zhao, Bin & Zhu, Juanxiu & Jiang, Yangsheng, 2019. "Two time-varying and state-dependent fluid queuing models for traffic circulation systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 997-1019.
    8. Shi, Yihan & Xu, Jie & Zhang, Hui & Jia, Limin & Qin, Yong, 2022. "Walking model on passenger in merging passage of subway station considering overtaking behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    9. Hamad Almujibah & Afaq Khattak & Saleh Alotaibi & Raed Alahmadi & Adil Elhassan & Abdullah Alshahri & Caroline Mongina Matara, 2023. "Two-Level Full Factorial Design Approach for the Analysis of Multi-Lane Highway Section under Saturated and Unsaturated Traffic Flow Conditions," Sustainability, MDPI, vol. 15(12), pages 1-14, June.

    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. Zhu, Juanxiu & Hu, Lu & Jiang, Yangsheng & Khattak, Afaq, 2017. "Circulation network design for urban rail transit station using a PH(n)/PH(n)/C/C queuing network model," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1043-1068.
    2. Lili Lu, A. & Gang Ren, B. & Wei Wang, C. & Ching-Yao Chan, D., 2015. "Application of SFCA pedestrian simulation model to the signalized crosswalk width design," Transportation Research Part A: Policy and Practice, Elsevier, vol. 80(C), pages 76-89.
    3. Hänseler, Flurin S. & Bierlaire, Michel & Farooq, Bilal & Mühlematter, Thomas, 2014. "A macroscopic loading model for time-varying pedestrian flows in public walking areas," Transportation Research Part B: Methodological, Elsevier, vol. 69(C), pages 60-80.
    4. MacGregor Smith, J. & Cruz, F.R.B., 2014. "M/G/c/c state dependent travel time models and properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 560-579.
    5. Yue, Hao & Guan, Hongzhi & Zhang, Juan & Shao, Chunfu, 2010. "Study on bi-direction pedestrian flow using cellular automata simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 527-539.
    6. Flötteröd, Gunnar & Lämmel, Gregor, 2015. "Bidirectional pedestrian fundamental diagram," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 194-212.
    7. Lee, Jodie Y.S. & Lam, William H.K., 2008. "Simulating pedestrian movements at signalized crosswalks in Hong Kong," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(10), pages 1314-1325, December.
    8. Tipakornkiat, Chalat & Limanond, Thirayoot & Kim, Hyunmyung, 2012. "Determining an influencing area affecting walking speed on footpath: A case study of a footpath in CBD Bangkok, Thailand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5453-5464.
    9. Zhang, Qi, 2015. "Simulation model of bi-directional pedestrian considering potential effect ahead and behind," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 335-348.
    10. Hänseler, Flurin S. & Bierlaire, Michel & Scarinci, Riccardo, 2016. "Assessing the usage and level-of-service of pedestrian facilities in train stations: A Swiss case study," Transportation Research Part A: Policy and Practice, Elsevier, vol. 89(C), pages 106-123.
    11. P. Daniel Wright & Matthew J. Liberatore & Robert L. Nydick, 2006. "A Survey of Operations Research Models and Applications in Homeland Security," Interfaces, INFORMS, vol. 36(6), pages 514-529, December.
    12. Konstantinos S. Boulas & Georgios D. Dounias & Chrissoleon T. Papadopoulos, 2023. "A hybrid evolutionary algorithm approach for estimating the throughput of short reliable approximately balanced production lines," Journal of Intelligent Manufacturing, Springer, vol. 34(2), pages 823-852, February.
    13. Mehrdad Moshtagh & Jafar Fathali & James MacGregor Smith & Nezam Mahdavi-Amiri, 2019. "Finding an optimal core on a tree network with M/G/c/c state-dependent queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 115-142, February.
    14. Fu, Zhijian & Li, Tao & Deng, Qiangqiang & Schadschneider, Andreas & Luo, Lin & Ma, Jian, 2021. "Effect of turning curvature on the single-file dynamics of pedestrian flow: An experimental study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    15. Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2017. "Characterisation of the output process of a discrete-time GI / D / 1 queue, and its application to network performance," Annals of Operations Research, Springer, vol. 252(1), pages 175-190, May.
    16. Kim, Bara & Kim, Jeongsim, 2012. "A note on the subexponential asymptotics of the stationary distribution of M/G/1 type Markov chains," European Journal of Operational Research, Elsevier, vol. 220(1), pages 132-134.
    17. Qingyan Ning & Maosheng Li, 2022. "Modeling Pedestrian Detour Behavior By-Passing Conflict Areas," Sustainability, MDPI, vol. 14(24), pages 1-17, December.
    18. Banerjee, Arunabha & Das, Sanhita & Maurya, Akhilesh Kumar, 2024. "Behavioural characteristics influencing walking speed of pedestrians over elevated facilities: A case study of India," Transport Policy, Elsevier, vol. 147(C), pages 169-182.
    19. Zhang, Qi & Han, Baoming, 2011. "Simulation model of pedestrian interactive behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 636-646.
    20. Guo, Ren-Yong, 2014. "Simulation of spatial and temporal separation of pedestrian counter flow through a bottleneck," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 428-439.

    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:240:y:2015:i:1:p:109-126. 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.