{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T02:53:03Z","timestamp":1770519183173,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T00:00:00Z","timestamp":1609200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Reserve capacity is the core of reliability analysis based on road network capacity. This article optimizes its bi-level programming model: the upper-level model has added service level coefficient and travel time limit, which realizes the unification of capacity and travel time reliability analysis to a certain extent. Stochastic user equilibrium (SUE) model based on origin has been selected as the lower-level model, which added capacity constraints to optimize distribution results, and allows the evaluation of reliability to be continued. Through the SUE model, the iterative step size of the method of successive averages can be optimized to improve the efficiency of the algorithm. After that, the article designs the algorithm flow of reliability analysis based on road network capacity, and verifies the feasibility of the designed algorithm with an example. Finally, combined with the conclusion of reliability analysis, this article puts forward some effective methods to improve the reliability of the urban road network.<\/jats:p>","DOI":"10.3390\/a14010007","type":"journal-article","created":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T10:04:46Z","timestamp":1609236286000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Modified Network-Wide Road Capacity Reliability Analysis Model for Improving Transportation Sustainability"],"prefix":"10.3390","volume":"14","author":[{"given":"Kui","family":"Ji","sequence":"first","affiliation":[{"name":"College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China"},{"name":"Jiangsu Institute of Urban Planning and Design, Nanjing 210096, China"}]},{"given":"Jianxiao","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Automobile and Traffic Engineering, Nanjing Forestry University, Nanjing 210037, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,29]]},"reference":[{"key":"ref_1","unstructured":"Mine, H., and Kawai, H. (1982). Mathematics for Reliability Analysis, Asakura Shoten."},{"key":"ref_2","unstructured":"Iida, Y., and Wakabayashi, H. (1989, January 10\u201314). An Approximation Method of Terminal Reliability of Road Network Using Partial Minimal Path and Cut Sets. Proceedings of the Transport Policy, Management & Technology towards 2001: Selected Proceedings of the Fifth World Conference on Transport Research, Yokohama, Japan."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Nicholson, A., Schm\u00f6cker, J.-D., Bell, M.G.H., and Iida, Y. (2003). Assessing Transport Reliability: Malevolence and User Knowledge. The Network Reliability of Transport, Emerald Publishers.","DOI":"10.1108\/9781786359544-001"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Bell, M.G.H., and Lida, Y. (1997). Transportation Network Analysis, John Wiley & Sons, Inc.","DOI":"10.1002\/9781118903032"},{"key":"ref_5","first-page":"30","article-title":"Research on the Connectivity Reliability of Transport Networks","volume":"9","author":"Liao","year":"2011","journal-title":"J. Transp. Eng. Inf."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Li, B., Hu, X., and Xie, B. (2009, January 25\u201327). Transportation Network Reconstruction for Natural Disasters in Emergency Phase Based on Connectivity Reliability. Proceedings of the Second International Conference on Transportation Engineering, Chengdu, China.","DOI":"10.1061\/41039(345)488"},{"key":"ref_7","first-page":"273","article-title":"Reliability Measures of an Origin and Destination Pair in a Deteriorated Road Network with Variable Flows","volume":"1999","author":"Asakura","year":"1999","journal-title":"Transp. Netw. Recent Methodol. Adv."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1002\/atr.5670330203","article-title":"Basic concepts and future directions of road network reliability analysis","volume":"33","author":"Iida","year":"1999","journal-title":"J. Adv. Transp."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/15472450600793586","article-title":"New Methodology for Estimating Reliability in Transportation Networks with Degraded Link Capacities","volume":"10","author":"Emam","year":"2006","journal-title":"J. Intell. Transp. Syst."},{"key":"ref_10","first-page":"A66","article-title":"Combining Travel Time and Capacity Reliability for Performance Measure of a Road Network","volume":"109","author":"Lo","year":"1999","journal-title":"J. Am. Diet. Assoc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.trb.2003.10.006","article-title":"Modeling network travel time reliability under stochastic demand","volume":"39","author":"Clark","year":"2005","journal-title":"Transp. Res. Part B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"80","DOI":"10.3141\/2391-08","article-title":"Connecting Networkwide Travel Time Reliability and the Network Fundamental Diagram of Traffic Flow","volume":"2391","author":"Mahmassani","year":"2013","journal-title":"Transp. Res. Rec. J. Transp. Res. Board"},{"key":"ref_13","first-page":"667","article-title":"Study on Travel Time Reliability Based on Monte Carlo Method","volume":"36","author":"Zhang","year":"2012","journal-title":"J. Wuhan Univ. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1109\/TR.1985.5221990","article-title":"Integration of Reliability and Capacity in Performance Measure of a Telecommunication Network","volume":"R-34","author":"Aggarwal","year":"2009","journal-title":"IEEE Trans. Reliab."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1109\/24.693780","article-title":"Exact and approximate improvement to the throughput of a stochastic network","volume":"46","author":"Chan","year":"1997","journal-title":"IEEE Trans. Reliab."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/978-1-4899-1346-3_2","article-title":"Reliability Assessment of Electric Power Systems Using Monte Carlo Methods","volume":"1994","author":"Billinton","year":"1994","journal-title":"Reliab. Assess. Electr. Power Syst. Using Monte Carlo Methods"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0951-8320(93)90052-Z","article-title":"Capacity reliability of water distribution networks","volume":"42","author":"Li","year":"1993","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0191-2615(00)00048-5","article-title":"Capacity reliability of a road network: An assessment methodology and numerical results","volume":"36","author":"Chen","year":"2002","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1002\/atr.5670330207","article-title":"A capacity related reliability for transportation networks","volume":"33","author":"Chen","year":"1999","journal-title":"J. Adv. Transp."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bell, M.G.H., and Schm\u00f6cker, J.D. (2002, January 23\u201325). Network Reliability: Topological Effects and the Importance of Information. Proceedings of the International Conference on Traffic and Transportation Studies, Guilin, China.","DOI":"10.1061\/40630(255)63"},{"key":"ref_21","unstructured":"Wong, K.I., and Bell, M.G.H. (2004, January 20\u201324). An evaluation of reliability of taxi service quality. Proceedings of the 2nd International Symposium on Transportation Network Reliability, Queenstown, New Zeland."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1109\/TITS.2006.874680","article-title":"A reliability framework for traffic signal control","volume":"7","author":"Lo","year":"2006","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_23","first-page":"5","article-title":"Accessibility of Rural Credit in Northern Nicaragua: The Importance of Networks of Information and Recommen-Dation","volume":"25","author":"Vaessen","year":"2007","journal-title":"Work. Pap."},{"key":"ref_24","first-page":"10","article-title":"Traffic congestion and road service level","volume":"4","author":"Bingxun","year":"2004","journal-title":"Road Traffic Saf."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/0191-2615(80)90004-1","article-title":"Some developments in equilibrium traffic assignment methodology","volume":"14","author":"Fisk","year":"1980","journal-title":"Transp. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1287\/trsc.31.4.349","article-title":"Decomposition of Path Choice Entropy in General Transport Networks","volume":"31","author":"Akamatsu","year":"1997","journal-title":"Transp. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Ji, K., Cheng, L., and Tang, W. (2012, January 3\u20136). Model and Algorithm for Link-Based Stochastic User Equilibrium Traffic Assignment. Proceedings of the Twelfth COTA International Conference of Transportation Professionals, Beijing, China.","DOI":"10.1061\/9780784412442.060"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1061\/(ASCE)0733-947X(2010)136:1(52)","article-title":"Origin-Based partial linearization method for stochastic user equilibrium traffic assignment problem","volume":"136","author":"Lee","year":"2010","journal-title":"J. Transp. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ji, K., Ma, J., and Tang, W. (2017). Sensitivity analysis for stochastic user equilibrium traffic assignment with constraints. Adv. Mech. Eng., 9.","DOI":"10.1177\/1687814017704354"},{"key":"ref_30","first-page":"221","article-title":"Sensitivity analysis for link-based stochastic user Chen equilibrium network flows","volume":"43","author":"Chen","year":"2013","journal-title":"J. Southeast Univ."},{"key":"ref_31","unstructured":"Gao, A. (2010). A Study on the Urban Road Network Reliability and Its Safeguards Technology. [Ph.D. Thesis, Beijing University of Technology]."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/1\/7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:47:25Z","timestamp":1760179645000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/14\/1\/7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,29]]},"references-count":31,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["a14010007"],"URL":"https:\/\/doi.org\/10.3390\/a14010007","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,29]]}}}