{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:30:49Z","timestamp":1760239849913,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,6]],"date-time":"2019-01-06T00:00:00Z","timestamp":1546732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Technological Development of Serbia","award":["TR 36012"],"award-info":[{"award-number":["TR 36012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Designing the crossroads capacity is a prerequisite for achieving a high level of service with the same sustainability in stochastic traffic flow. Also, modeling of crossroad capacity can influence on balancing (symmetry) of traffic flow. Loss of priority in a left turn and optimal dimensioning of shared-short line is one of the permanent problems at intersections. A shared\u2013short lane for taking a left turn from a priority direction at unsignalized intersections with a homogenous traffic flow and heterogeneous demands is a two-phase queueing system requiring a first in\u2013first out (FIFO) service discipline and single-server service facility. The first phase (short lane) of the system is the queueing system M(p\u03bb)\/M(\u03bc)\/1\/\u221e, whereas the second phase (shared lane) is a system with a binomial distribution service. In this research, we explicitly derive the probability of the state of a queueing system with a short lane of a finite capacity for taking a left turn and shared lane of infinite capacity. The presented formulas are under the presumption that the system is Markovian, i.e., the vehicle arrivals in both the minor and major streams are distributed according to the Poisson law, and that the service of the vehicles is exponentially distributed. Complex recursive operations in the two-phase queueing system are explained and solved in manuscript.<\/jats:p>","DOI":"10.3390\/sym11010055","type":"journal-article","created":{"date-parts":[[2019,1,9]],"date-time":"2019-01-09T03:06:06Z","timestamp":1547003166000},"page":"55","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["New Analytic Solutions of Queueing System for Shared\u2013Short Lanes at Unsignalized Intersections"],"prefix":"10.3390","volume":"11","author":[{"given":"Ilija","family":"Tanackov","sequence":"first","affiliation":[{"name":"Faculty of technical sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Darko","family":"Dragi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of technical sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3641-5107","authenticated-orcid":false,"given":"Sini\u0161a","family":"Sremac","sequence":"additional","affiliation":[{"name":"Faculty of technical sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vuk","family":"Bogdanovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of technical sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bojan","family":"Mati\u0107","sequence":"additional","affiliation":[{"name":"Faculty of technical sciences, University of Novi Sad, Trg Dositeja Obradovi\u0107a 6, 21 000 Novi Sad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1313-5460","authenticated-orcid":false,"given":"Milica","family":"Milojevi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Architecture, University of Belgrade, Bulevar kralja Aleksandra 73, 11 000 Belgrade, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,6]]},"reference":[{"key":"ref_1","unstructured":"Harders, J. (1968). Die Leistungsf\u00e4higkeit Nicht Signalgeregelter St\u00e4dtischer Verkehrsknoten, Schriftenreihe \u201cStra\u00dfenbau und Stra\u00dfenverkehrstechnik\u201d."},{"key":"ref_2","unstructured":"Wu, N. (1994). An approximation for the distribution of queue lengths at unsignalized intersections. Proceedings of the Second International Symposium on Highway Capacity, Australian Road Research Board Ltd."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4685","DOI":"10.3390\/su6074685","article-title":"Comprehensive assessment on sustainable development of highway transportation capacity based on entropy weight and TOPSIS","volume":"6","author":"Li","year":"2014","journal-title":"Sustainability"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1016\/j.trpro.2017.05.216","article-title":"Development of Saturation Flow Model at Signalized Intersection for Heterogeneous Traffic","volume":"25","author":"Chand","year":"2017","journal-title":"Transp. Res. Procedia"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.physa.2016.11.025","article-title":"Effects of signal light on the fuel consumption and emissions under car-following model","volume":"469","author":"Tang","year":"2017","journal-title":"Physica A"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.buildenv.2018.04.042","article-title":"Fine-scale variations in PM2.5 and black carbon concentrations and corresponding influential factors at an urban road intersection","volume":"141","author":"Wang","year":"2018","journal-title":"Build. Environ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1093\/biomet\/46.3-4.420","article-title":"Overflow at a traffic light","volume":"46","author":"Haight","year":"1959","journal-title":"Biometrika"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1214\/aoms\/1177703761","article-title":"On the traffic-light queue","volume":"35","author":"Darroch","year":"1964","journal-title":"Ann. Math. Stat."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.physa.2018.05.140","article-title":"Effects of the design of waiting areas on the dynamic behavior of queues at signalized intersections","volume":"509","author":"Yang","year":"2018","journal-title":"Physica A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1016\/S0360-8352(97)00240-4","article-title":"A M\/Dx\/1 vacation queue model for a signalized intersection","volume":"33","author":"Hu","year":"1997","journal-title":"Comput. Ind. Eng."},{"key":"ref_11","first-page":"181","article-title":"Increasing the capacity of signalized intersections with left-turn waiting areas","volume":"105","author":"Ma","year":"2017","journal-title":"Transp. Res. Part A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1016\/j.trb.2018.03.013","article-title":"Analytical evaluation of the use of left-turn phasing for single left-turn lane only","volume":"111","author":"Yang","year":"2018","journal-title":"Transp. Res. Part B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0191-2615(96)00021-5","article-title":"Queueing at unsignalized intersections","volume":"31","author":"Heidemann","year":"1997","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_14","first-page":"555","article-title":"Stochastic user equilibrium traffic assignment with turn-delays in intersections","volume":"5","author":"Nielsen","year":"1998","journal-title":"Int. Trans. Oper. Res."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1061\/(ASCE)0733-947X(1983)109:4(499)","article-title":"Additional through lanes at signalized intersections","volume":"109","author":"Guell","year":"1983","journal-title":"J. Transp. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wu, N. (2007). Total approach capacity at signalized intersections with shared-short lanes\u2014A generalized model based on simulation study. Transp. Res. Rec., 19\u201326.","DOI":"10.3141\/2027-03"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1061\/(ASCE)0733-947X(2006)132:3(205)","article-title":"Probabilistic model for signalized intersection capacity with a short right-turn lane","volume":"132","author":"Tian","year":"2006","journal-title":"J. Transp. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.trpro.2016.06.008","article-title":"Variability of Capacity and Traffic Performance at Urban and Rural Signalised Intersections","volume":"15","author":"Chodur","year":"2016","journal-title":"Transp. Res. Procedia"},{"key":"ref_19","first-page":"291","article-title":"Limited priority merge at unsignalized intersections","volume":"33","author":"Troutbeck","year":"1999","journal-title":"Transp. Res. Part A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s11134-017-9533-2","article-title":"Batch arrival single-server queue with variable service speed and setup time","volume":"86","author":"Yajima","year":"2017","journal-title":"Queueing Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.trf.2018.10.002","article-title":"Binomial and multinomial regression models for predicting the tactical choices of bicyclists at signalised intersections","volume":"60","author":"Twaddle","year":"2019","journal-title":"Transp. Res. Part F"},{"key":"ref_22","first-page":"101","article-title":"Sur le probl\u00e8me d\u2019attente","volume":"38","author":"Kolmogorov","year":"1931","journal-title":"Matematicheskii Sbornik"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1007\/BF01194620","article-title":"Ueber eine Aufgabe der Wahrscheinlichkeits theory","volume":"32","author":"Pollaczek","year":"1930","journal-title":"Mathematische Zeitschrift"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1017\/S0305004100036094","article-title":"The single server queue in heavy traffic","volume":"Volume 57","author":"Kingman","year":"1961","journal-title":"Mathematical Proceedings of the Cambridge Philosophical Society"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0305-0483(91)90017-N","article-title":"Is queuing theory dead?","volume":"19","author":"Koenigsberg","year":"1991","journal-title":"Omega"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.omega.2015.10.013","article-title":"Performance analysis of time-dependent queuing systems: Survey and classification","volume":"63","author":"Schwarz","year":"2016","journal-title":"Omega"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s11134-018-9580-3","article-title":"A broad view of queuing theory through one issue","volume":"89","author":"Whitt","year":"2018","journal-title":"Queueing Syst."},{"key":"ref_28","unstructured":"Kinzer, J.P. (1933). Application of the Theory of Probability to Problems of Highway Traffic. [Doctoral Thesis, Polytechnic Press of the Polytechnic Institute of Brooklyn]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1680\/ijoti.1936.14802","article-title":"Road Traffic Considered as A Random Series","volume":"4","author":"Adams","year":"1936","journal-title":"J. Inst. Civ. Eng."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0191-2615(81)90042-4","article-title":"Estimation of gap acceptance parameters within and across the population from direct roadside observation","volume":"15","author":"Daganzo","year":"1981","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_31","unstructured":"Troutbeck, R.J. (1992). Estimating the Critical Acceptance Gap from Traffic Movements, Queensland University of Technology. Physical Infrastructure Centre, Research Report."},{"key":"ref_32","first-page":"623","article-title":"Delays at fixed-time traffic signals under time-dependent traffic conditions","volume":"31","author":"Brilon","year":"1999","journal-title":"Traffic Eng. Control"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1287\/trsc.29.2.109","article-title":"Modelling vehicular traffic using the discrete time Markovian arrival process","volume":"29","author":"Alfa","year":"1995","journal-title":"Transp. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1016\/j.physa.2018.04.043","article-title":"Safety time in critical gap of left turn manoeuvre from priority approach at TWSC unsignalized intersections","volume":"505","author":"Tanackov","year":"2018","journal-title":"Physica A"},{"key":"ref_35","unstructured":"Lakkundi, V.R., Park, B., Garber, N.J., and Fontaine, M.D. (2004). Development of Left-Turn Lane Guidelines for Signalized and Unsignalized Intersections Final Report, Mid-Atlantic Universities Transportation Center."},{"key":"ref_36","first-page":"255","article-title":"Capacity of shared-short lanes at unsignalized intersections","volume":"33","author":"Wu","year":"1999","journal-title":"Transp. Res. Part A"},{"key":"ref_37","first-page":"543","article-title":"Capacity analysis procedure for Four-Leg Non-Standard Unsignalised intersections","volume":"29","author":"Tanackov","year":"2017","journal-title":"Traffic Transp."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"121","DOI":"10.31181\/dmame1802128l","article-title":"A multicriteria model for the selection of the transport service provider: A single valued neutrosophic DEMATEL multicriteria model","volume":"1","author":"Liu","year":"2018","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_39","first-page":"108","article-title":"Multi-criteria FUCOM-MAIRCA model for the evaluation of level crossings: Case study in the Republic of Serbia","volume":"1","author":"Lukovac","year":"2018","journal-title":"Oper. Res. Eng. Sci."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/1\/55\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:23:49Z","timestamp":1760185429000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/1\/55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,6]]},"references-count":39,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1]]}},"alternative-id":["sym11010055"],"URL":"https:\/\/doi.org\/10.3390\/sym11010055","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,1,6]]}}}