Urban transportation network reliability calculation considering correlation among the links comprising a route

Document Type : Article


1 Department of Engineering, University of Kurdistan, Sanandaj, Iran

2 Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran


Recently, the researchers in the field of urban transportation network planning have become increasingly interested in network reliability, publishing research works focused on the calculation of various types of network reliability. Accurate calculation of network reliability has led the transportation network optimizers toward new approaches . Travel time reliability is among the most important reliabilities investigated when analyzing urban transportation networks, with various approaches based on different assumptions proposed for calculating it. In the present research, the uncertainty associated with the demand for travel and the flows passing across links and also the correlations among the links comprising a route were considered to calculate the travel time for each of the network links. Moreover, it was shown that this process follows shifted log-normal distribution. These calculations are expected to serve as a basis for the employment of travel time reliability of a network within the modeling of an urban transportation system, so as to increase the accuracy and reliability of the simulations. Finally, in order to validate the model, an urban network with 12 nodes, 21 links, and 4 origin-destination pairs was subjected to the travel time reliability assessment by calculating the travel time over all forming links.


1.    Chen A, Zhou Z, Chootinan P, Ryu S, Yang C, Wong SC: Transport network design problem under uncertainty: a review and new developments. Transport Reviews 2011, 31:743-768.
2.    Srinivasan KK, Prakash AA, Seshadri R: Finding most reliable paths on networks with correlated and shifted log–normal travel times. Transportation Research Part B: Methodological 2014, 66:110-128.
3.    Al-Deek H, Emam EB: New methodology for estimating reliability in transportation networks with degraded link capacities. Journal of intelligent transportation systems 2006, 10:117-129.
4.    Herman R, Lam T: Trip time characteristics of journeys to and from work. Transportation and traffic theory 1974, 6:57-86.
5.    Polus A: A study of travel time and reliability on arterial routes. Transportation 1979, 8:141-151.
6.    Richardson AJ, Taylor MAP: Travel time variability on commuter journeys. High Speed Ground Transportation Journal 1978, 12.
7.    Taylor MAP: Modelling travel time reliability with the Burr distribution. Procedia-Social and Behavioral Sciences 2012, 54:75-83.
8.    Taylor MAP: Fosgerau's travel time reliability ratio and the Burr distribution. Transportation Research Part B: Methodological 2017, 97:50-63.
9.    Wardrop J: Some Theoretical Aspects of Road Traffic Research, reprinted in H. Mohring eds. The Economics of Transoport I 1952:299-352.
10.    Wu N, Geistefeldt J: Modeling Travel Time for Reliability Analysis in a Freeway Network. 2016.
11.    Chen P, Tong R, Lu G, Wang Y: Exploring travel time distribution and variability patterns using probe vehicle data: case study in Beijing. Journal of Advanced Transportation 2018, 2018.
12.    Eliasson J: The relationship between travel time variability and road congestion. In; 2007. 2007.
13.    Emam EB, Al-Deek H: Using real-life dual-loop detector data to develop new methodology for estimating freeway travel time reliability. Transportation research record 2006, 1959:140-150.
14.    Guessous Y, Aron M, Bhouri N, Cohen S: Estimating travel time distribution under different traffic conditions. Transportation Research Procedia 2014, 3:339-348.
15.    Kieu L-M, Bhaskar A, Chung E: Public transport travel-time variability definitions and monitoring. Journal of Transportation Engineering 2015, 141:04014068.
16.    Lu C, Dong J: Estimating freeway travel time and its reliability using radar sensor data. Transportmetrica B: Transport Dynamics 2018, 6:97-114.
17.    Park S, Rakha H, Guo F: Calibration issues for multistate model of travel time reliability. Transportation research record 2010, 2188:74-84.
18.    Rakha H, El-Shawarby I, Arafeh M: Trip travel-time reliability: issues and proposed solutions. Journal of Intelligent Transportation Systems 2010, 14:232-250.
19.    Cao P, Miwa T, Morikawa T: Modeling distribution of travel time in signalized road section using truncated distribution. Procedia-Social and Behavioral Sciences 2014, 138:137-147.
20.    Chen P, Yin K, Sun J: Application of finite mixture of regression model with varying mixing probabilities to estimation of urban arterial travel times. Transportation Research Record 2014, 2442:96-105.
21.    Guo F, Rakha H, Park S: Multistate model for travel time reliability. Transportation Research Record 2010, 2188:46-54.
22.    Chen Z, Fan WD: Analyzing travel time distribution based on different travel time reliability patterns using probe vehicle data. International Journal of Transportation Science and Technology 2020, 9:64-75.
23.    Ma Z, Koutsopoulos HN, Ferreira L, Mesbah M: Estimation of trip travel time distribution using a generalized Markov chain approach. Transportation Research Part C: Emerging Technologies 2017, 74:1-21.
24.    Van Lint JWC, Van Zuylen HJ, Tu H: Travel time unreliability on freeways: Why measures based on variance tell only half the story. Transportation Research Part A: Policy and Practice 2008, 42:258-277.
25.    Pu W: Analytic relationships between travel time reliability measures. Transportation Research Record 2011, 2254:122-130.
26.    Susilawati S, Taylor MAP, Somenahalli SVC: Distributions of travel time variability on urban roads. Journal of Advanced Transportation 2013, 47:720-736.
27.    Asakura Y, Kashiwadani M: Road network reliability caused by daily fluctuation of traffic flow. In; 1991. 1991.
28.    Bates J, Polak J, Jones P, Cook A: The valuation of reliability for personal travel. Transportation Research Part E: Logistics and Transportation Review 2001, 37:191-229.
29.    Booz A, Hamilton I: California Transportation Plan: Transportation System Performance Measures. California Department of Transportation 1998.
30.    Fosgerau M, Karlström A: The value of reliability. Transportation Research Part B: Methodological 2010, 44:38-49.
31.    Lomax T, Margiotta R: Selecting travel reliability measures. Citeseer; 2003.
32.    Tu H: Monitoring travel time reliability on freeways. Netherlands TRAIL Research School; 2008.
33.    Kim J, Mahmassani HS: A finite mixture model of vehicle-to-vehicle and day-to-day variability of traffic network travel times. Transportation Research Part C: Emerging Technologies 2014, 46:83-97.
34.    Kim J, Mahmassani HS, Vovsha P, Stogios Y, Dong J: Scenario-based approach to analysis of travel time reliability with traffic simulation models. Transportation research record 2013, 2391:56-68.
35.    Stogios YC, Mahmassani HS, Vovsha P, Kim J, Chen Y, Brijmohan A: Incorporating Reliability Performance Measures in Operations and Planning Modeling Tools. SHRP 2 Reliability Project L04 2013.
36.    Xing T, Zhou X: Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach. Transportation Research Part B: Methodological 2011, 45:1660-1679.
37.    Kim J, Mahmassani HS: Compound Gamma representation for modeling travel time variability in a traffic network. Transportation Research Part B: Methodological 2015, 80:40-63.
38.    Wu N, Geistefeldt J: Standard Deviation of Travel Time in a Freeway Network--A Mathematical Quantifying Tool for Reliability Analysis. In CICTP 2014: Safe, Smart, and Sustainable Multimodal Transportation Systems. 2014: 3292-3303.
39.    Arroyo S, Kornhauser AL: Modeling travel time distributions on a road network. In; 2005. Citeseer; 2005.
40.    Li R: Examining travel time variability using AVI data. In; 2004. 2004.
41.    Franklin JP: Modeling reliability as expected lateness: A schedule-based approach for user benefit analysis. Association for European Transport and contributors 2009.
42.    Mahmassani HS, Zhou X: Transportation system intelligence: Performance measurement and real-time traffic estimation and prediction in a day-to-day learning framework. In Advances in Control, Communication Networks, and Transportation Systems. Springer; 2005: 305-328.
43.    Peer S, Koopmans CC, Verhoef ET: Prediction of travel time variability for cost-benefit analysis. Transportation Research Part A: Policy and Practice 2012, 46:79-90.
44.    Richardson AJ: Travel time variability on an urban freeway. In; 2003. 2003.
45.    Van Lint JWC, van Zuylen HJ: Monitoring and predicting freeway travel time reliability: Using width and skew of day-to-day travel time distribution. Transportation Research Record 2005, 1917:54-62.
46.    Jia A, Zhou X, Li M, Rouphail NM, Williams BM: Incorporating stochastic road capacity into day-to-day traffic simulation and traveler learning framework: Model development and case study. Transportation research record 2011, 2254:112-121.
47.    Li M, Faghri A: Applying problem-oriented and project-based learning in a transportation engineering course. Journal of professional issues in engineering education and practice 2016, 142:04016002.
48.    Li M, Rouphail NM, Mahmoudi M, Liu J, Zhou X: Multi-scenario optimization approach for assessing the impacts of advanced traffic information under realistic stochastic capacity distributions. Transportation Research Part C: Emerging Technologies 2017, 77:113-133.
49.    Li M, Zhou X, Rouphail N: Planning-level methodology for evaluating traveler information provision strategies under stochastic capacity conditions. In; 2011. 2011.
50.    Li M, Zhou X, Rouphail NM: Quantifying benefits of traffic information provision under stochastic demand and capacity conditions: a multi-day traffic equilibrium approach. In; 2011. IEEE; 2011: 2118-2123.
51.    Li M, Zhou X, Rouphail NM: Quantifying travel time variability at a single bottleneck based on stochastic capacity and demand distributions. Journal of Intelligent Transportation Systems 2017, 21:79-93.
52.    United States. Bureau of Public R: Traffic assignment manual for application with a large, high speed computer. US Department of Commerce, Bureau of Public Roads, Office of Planning, Urban …; 1964.
53.    Fenton L: The sum of log-normal probability distributions in scatter transmission systems. IRE Transactions on communications systems 1960, 8:57-67.
54.    Kaboli A, Hr S, Al Hinai A, Al-Badi AH, Charabi Y, Al Saifi A: Prediction of Metallic Conductor Voltage Owing to Electromagnetic Coupling Via a Hybrid ANFIS and Backtracking Search Algorithm. Energies 2019, 12:3651.
55.    Mohamad Izdin Hlal A, Ramachandaramurthya VK, Sanjeevikumar Padmanaban B, Hamid Reza Kaboli C, Aref Pouryekta A, Abdullah TARBT: NSGA-II and MOPSO based optimization for sizing of hybrid PV/wind/battery energy storage system. 2019.
56.    Pourdaryaei A, Mokhlis H, Illias HA, Kaboli SHA, Ahmad S: Short-term electricity price forecasting via hybrid backtracking search algorithm and ANFIS approach. IEEE Access 2019, 7:77674-77691.
57.    Asadi H, Kaboli S, Oladazimi M, Safari M: A review on Li-ion battery charger techniques and optimize battery charger performance by fuzzy logic. ICICA 2011, 18:89-96.
58.    Kaboli SHA, Mohammadi A, Fallahpour A, Selvaraj J, Rahim NA: Fuzzy logic based encoder-less speed control of PMSM for hub motor drive. Fuzzy Control Systems: Design, Analysis and Performance Evaluation 2016.
59.    Saghafinia A, Kaboli S: Online adaptive continuous wavelet transform and fuzzy logic based high precision fault detection of broken rotor bars for IM. Sci Res 2016, 4:157-168.