{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T05:03:54Z","timestamp":1773378234820,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T00:00:00Z","timestamp":1767744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Humanities and Social Sciences Foundation of the Ministry of Education of China","award":["22YJCZH153"],"award-info":[{"award-number":["22YJCZH153"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>In urban road networks, queuing delays at signalized intersections often account for over half of the total travel time. The complexity of traffic signals and vehicle queuing makes traditional shortest path algorithms insufficient for real-time optimal path finding. This study proposes a Time-Dependent Dijkstra\u2019s algorithm to address these challenges. The network topology is redesigned to model vehicle turning behaviors accurately. A periodic queuing delay parameter matrix for signalized intersections is introduced, storing traffic flow and signal phase parameters. Additionally, a time-varying weight matrix tracks the vehicle\u2019s position in the signal cycle upon intersection arrival. Using cumulative curve theory, a periodic queuing-delay model is constructed to capture delays for vehicles arriving at different times. The algorithm updates the network weight matrix in real-time based on vehicle arrival times at intersections, enabling FIFO-consistent time-dependent shortest path computation for a given departure time. Numerical and SUMO simulations on a real-world road network in Suzhou Industrial Park (comprising 15 signalized intersections and 22 road segments) demonstrate the algorithm\u2019s effectiveness. Results show a 25.36% reduction in travel time compared to the traditional Dijkstra\u2019s Algorithm and a 10.46% reduction compared to an algorithm considering only signalized intersection waiting time when departure times vary. The results highlight the impact of periodic queuing delays, with the algorithm reducing travel time and improving path planning.<\/jats:p>","DOI":"10.3390\/systems14010061","type":"journal-article","created":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T11:46:43Z","timestamp":1767786403000},"page":"61","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Time-Dependent Dijkstra\u2019s Algorithm for the Shortest Path Considering Periodic Queuing Delays at Signalized Intersections"],"prefix":"10.3390","volume":"14","author":[{"given":"Binghao","family":"Ji","sequence":"first","affiliation":[{"name":"School of Automotive and Transportation Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automotive and Transportation Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1543-5790","authenticated-orcid":false,"given":"Chao","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Automotive and Transportation Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junhui","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automotive and Transportation Engineering, Jiangsu University, Zhenjiang 212013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenquan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1287\/trsc.34.2.198.12304","article-title":"Least expected time paths in stochastic, time-varying transportation networks","volume":"34","author":"Mahmassani","year":"2000","journal-title":"Transp. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3324","DOI":"10.1016\/j.cor.2005.03.027","article-title":"Heuristic shortest path algorithms for transportation applications: State of the art","volume":"33","author":"Fu","year":"2006","journal-title":"Comput. Oper. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s10589-008-9172-y","article-title":"Fast paths in large-scale dynamic road networks","volume":"45","author":"Nannicini","year":"2010","journal-title":"Comput. Optim. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.trc.2012.08.003","article-title":"State-based accelerations and bidirectional search for bi-objective multi-modal shortest paths","volume":"27","author":"Artigues","year":"2013","journal-title":"Transp. Res. Part C"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1002\/net.3230140206","article-title":"Shortest-path methods: Complexity, interrelations and new propositions","volume":"14","author":"Pallottino","year":"1984","journal-title":"Networks"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1002\/net.3230140208","article-title":"Shortest-path algorithms: Taxonomy and annotation","volume":"14","author":"Deo","year":"1984","journal-title":"Networks"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Huang, B., Zhang, F., and Lei, L. (2022). Dynamic path planning based on service level of road network. Electronics, 11.","DOI":"10.3390\/electronics11203267"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"55126","DOI":"10.1109\/ACCESS.2022.3174598","article-title":"An optimal path-finding algorithm in smart cities by considering traffic congestion and air pollution","volume":"10","author":"Ghaffari","year":"2022","journal-title":"IEEE Access"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, J., Tian, S., Zhang, N., Liu, G., Wu, Z., and Li, W. (2023). Optimization strategy for electric vehicle routing under traffic impedance guidance. Appl. Sci., 13.","DOI":"10.3390\/app132011474"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.trd.2019.10.020","article-title":"Development and evaluation of a vehicle platoon guidance strategy at signalized intersections considering fuel savings","volume":"77","author":"Ye","year":"2019","journal-title":"Transp. Res. Part D"},{"key":"ref_11","first-page":"104013","article-title":"Integrated optimization of traffic signal timings and vehicle trajectories considering mandatory lane-changing at isolated intersections","volume":"160","author":"Liu","year":"2024","journal-title":"Transp. Res. Part C"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/S0191-2615(03)00048-1","article-title":"Adaptive routing considering delays due to signal operations","volume":"38","author":"Yang","year":"2004","journal-title":"Transp. Res. Part B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"102159","DOI":"10.1016\/j.tre.2020.102159","article-title":"Finding the reliable shortest path with correlated link travel times in signalized traffic networks under uncertainty","volume":"144","author":"Shen","year":"2020","journal-title":"Transp. Res. Part E"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.ijtst.2024.01.003","article-title":"Does the minimization of the average vehicle delay and the minimization of the average number of stops mean the same at the signalized intersections?","volume":"13","author":"Cakici","year":"2024","journal-title":"Int. J. Transp. Sci. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"100877","DOI":"10.1016\/j.segan.2022.100877","article-title":"A reliable energy consumption path finding algorithm for electric vehicles considering the correlated link travel speeds and waiting times at signalized intersections","volume":"32","author":"Qin","year":"2022","journal-title":"Sustain. Energy Grids Netw."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Liu, J., Chen, L., Tian, Z., Zhao, N., and Roberts, C. (2025). A Novel Multi-Agent-Based Approach for Train Rescheduling in Large-Scale Railway Networks. Appl. Sci., 15.","DOI":"10.3390\/app15147996"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"18237","DOI":"10.1109\/TITS.2022.3165757","article-title":"Data-driven optimization for dynamic shortest path problem considering traffic safety","volume":"23","author":"Jiang","year":"2022","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","article-title":"A note on two problems in connexion with graphs","volume":"1","author":"Dijkstra","year":"1959","journal-title":"Numer. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1145\/367766.368168","article-title":"Algorithm 97: Shortest path","volume":"5","author":"Floyd","year":"1962","journal-title":"Commun. ACM"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1145\/1056777.1056779","article-title":"Correction to: A formal basis for the heuristic determination of minimum cost paths","volume":"37","author":"Hart","year":"1972","journal-title":"SIGART Bull."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.amc.2006.06.094","article-title":"An improved Dijkstra\u2019s shortest path algorithm for sparse network","volume":"185","author":"Xu","year":"2007","journal-title":"Appl. Math. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s40747-018-0083-y","article-title":"Dijkstra algorithm for shortest path problem under interval-valued Pythagorean fuzzy environment","volume":"5","author":"Enayattabar","year":"2019","journal-title":"Complex Intell. Syst."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Jin, S., Zhang, X., Hu, Y., Liu, R., Wang, Q., and He, H. (2025). Research on mobile agent path planning based on deep reinforcement learning. Systems, 13.","DOI":"10.3390\/systems13050385"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"8881684","DOI":"10.1155\/2021\/8881684","article-title":"Path planning for smart car based on Dijkstra algorithm and dynamic window approach","volume":"2021","author":"Liu","year":"2021","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/S0968-090X(97)00004-1","article-title":"Design and implementation of parallel time-dependent least time path algorithms for Intelligent Transportation Systems applications","volume":"5","author":"Ziliaskopoulos","year":"1997","journal-title":"Transp. Res. Part C"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"107407","DOI":"10.1016\/j.cie.2021.107407","article-title":"A new exact algorithm for the shortest path problem: An optimized shortest distance matrix","volume":"158","author":"Yuan","year":"2021","journal-title":"Comput. Ind. Eng."},{"key":"ref_27","first-page":"2352492","article-title":"Finding the optimal reliable energy consumption path for electric vehicles under rainfall conditions","volume":"12","author":"Li","year":"2024","journal-title":"Transp. B"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1287\/opre.35.2.266","article-title":"Vehicle routing with time windows","volume":"35","author":"Kolen","year":"1987","journal-title":"Oper. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1057\/jors.1993.53","article-title":"Simple heuristics for the vehicle routing problem with soft time windows","volume":"44","author":"Balakrishnan","year":"1993","journal-title":"J. Oper. Res. Soc."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1287\/opre.44.3.501","article-title":"Probabilistic analyses and practical algorithms for the vehicle routing problem with time windows","volume":"44","author":"Bramel","year":"1996","journal-title":"Oper. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0191-2615(96)00001-X","article-title":"A note on least time path computation considering delays and prohibitions for intersection movements","volume":"30","author":"Ziliaskopoulos","year":"1996","journal-title":"Transp. Res. Part B"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.trc.2017.08.017","article-title":"Dynamic traffic routing in a network with adaptive signal control","volume":"85","author":"Chai","year":"2017","journal-title":"Transp. Res. Part C"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"121130","DOI":"10.1016\/j.jclepro.2020.121130","article-title":"The constrained reliable shortest path problem for electric vehicles in the urban transportation network","volume":"261","author":"Tu","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2304097","DOI":"10.1155\/2022\/2304097","article-title":"Hyperpath searching algorithm considering delay at intersection and its application in CVIS for vehicle navigation","volume":"2022","author":"Ju","year":"2022","journal-title":"J. Adv. Transp."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/S0191-2615(99)00023-5","article-title":"Shortest paths in traffic-light networks","volume":"34","author":"Chen","year":"2000","journal-title":"Transp. Res. Part B"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1287\/trsc.36.3.326.7827","article-title":"Minimum time and minimum cost-path problems in street networks with periodic traffic lights","volume":"36","author":"Ahuja","year":"2002","journal-title":"Transp. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Khanjary, M., Faez, K., Meybodi, M.R., and Sabaei, M. (2011, January 8\u201311). Shortest paths in synchronized traffic-light networks. Proceedings of the 24th Canadian Conference on Electrical and Computer Engineering (CCECE), Niagara Falls, ON, Canada.","DOI":"10.1109\/CCECE.2011.6030584"},{"key":"ref_38","first-page":"2403","article-title":"The real-time shortest path algorithm with a consideration of traffic-light","volume":"31","author":"Hu","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_39","first-page":"177","article-title":"Study on the shortest reliable path of stochastic time-dependent transportation networks considering waiting time at signalized intersections","volume":"18","author":"Sun","year":"2023","journal-title":"J. Adv. Transp."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1016\/j.trc.2019.03.020","article-title":"An energy-efficient reliable path finding algorithm for stochastic road networks with electric vehicles","volume":"102","author":"Shen","year":"2019","journal-title":"Transp. Res. Part C"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/0191-2615(95)00024-0","article-title":"Dual graph representation of transport networks","volume":"30","year":"1996","journal-title":"Transp. Res. Part B"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1061\/(ASCE)0733-947X(1991)117:6(602)","article-title":"Traffic assignment in practice: Overview and guidelines for users","volume":"117","author":"Easa","year":"1991","journal-title":"J. Transp. Eng. ASCE"},{"key":"ref_43","first-page":"27","article-title":"Using cumulative curves to measure saturation flow and lost time","volume":"58","author":"Shanteau","year":"1988","journal-title":"ITE J."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/1\/61\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T05:12:34Z","timestamp":1768021954000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/1\/61"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,7]]},"references-count":43,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["systems14010061"],"URL":"https:\/\/doi.org\/10.3390\/systems14010061","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,7]]}}}