{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T15:19:04Z","timestamp":1762010344949,"version":"build-2065373602"},"reference-count":12,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1961,1,1]],"date-time":"1961-01-01T00:00:00Z","timestamp":-283996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1961,1,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title>\n               <jats:p>A theoretical formula is found for the average speed achieved over a long journey by a vehicle travelling along a road according to certain rules governing overtaking, when the other traffic on the road is postulated to be of a particularly simple kind.<\/jats:p>\n               <jats:p>Except for the vehicle whose behaviour is studied, vehicles in each direction travel at the same speed, and are spaced at random, but with a certain minimum distance between vehicles. The vehicle being studied wishes to travel faster than the other vehicles; when it overtakes, it must pass the whole of a bunch of vehicles at minimum spacing in a single manoeuvre. It overtakes without delay if there is a sufficient gap in the opposing traffic. If delay occurs, then a greater gap in the opposing traffic is required, to allow for time lost in accelerating. An alternative application of the theory is to one half of a dual carriageway, in which the two traffic lanes are occupied by vehicles travelling at two different speeds.<\/jats:p>\n               <jats:p>A curious feature of the results is that when the traffic flows increase beyond a certain level, appreciably below the theoretical capacity of the road, the fast vehicle cannot maintain a higher average speed than that of the other vehicles: the whole time is spent waiting for opportunities to overtake, and the average wait per overtaking becomes infinite.<\/jats:p>\n               <jats:p>Numerical values of the average speed have been tabulated using an electronic computer. Standard values of all the constants of the model were selected for two-way and one-way roads separately, and these constants were then varied two, three or four at a time. Two general conclusions are indicated by the numerical results. Firstly, more acceleration, obtained at the expense of reduced maximum speed (and perhaps greater fuel consumption) by lowering the top gear ratio, would probably provide increased mean journey speeds for most modern cars under typical traffic conditions. Secondly, the cutting of safety margins and clearances when overtaking would not normally provide any worthwhile increase in mean journey speed.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1961.tb00390.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T05:27:01Z","timestamp":1544160421000},"page":"38-63","source":"Crossref","is-referenced-by-count":13,"title":["Two Papers on Applications of Stochastic Processes to Road Traffic Problems: Delays on a Two-Lane Road"],"prefix":"10.1093","volume":"23","author":[{"given":"J. C.","family":"Tanner","sequence":"first","affiliation":[{"name":"Road Research Laboratory, Department of Scientific and Industrial Research"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"volume-title":"Studies in the Economics of Transportation","year":"1955","author":"Beckmann","key":"2024090922043051300_cit1"},{"key":"2024090922043051300_cit2","first-page":"452","article-title":"Sur l'emploi du th\u00e9or\u00e8me de Bernoulli pour faciliter le calcul d'un infinit\u00e9 de coefficients. Application au probl\u00e8me de l'attente \u00e0 un guichet","volume":"214","author":"Borel","year":"1942","journal-title":"C.R. Acad. Sci. Paris"},{"key":"2024090922043051300_cit3","article-title":"The basic requirements for the roads of Great Britain","volume-title":"Conference on the Highway Needs of Great Britain, 1957","author":"Glanville","year":"1958"},{"key":"2024090922043051300_cit4","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1287\/opre.6.6.813","article-title":"Towards a unified theory of road traffic","volume":"6","author":"Haight","year":"1958","journal-title":"Operations Research"},{"key":"2024090922043051300_cit5","first-page":"79","article-title":"On the theoretical solution of highway traffic capacity under mixed traffic","volume":"17","author":"Kometani","year":"1955","journal-title":"Mem. Fac. Engng Kyoto Univ."},{"issue":"I","key":"2024090922043051300_cit6","first-page":"281","article-title":"On kinematic waves. A theory of traffic flow on long crowded roads","volume":"229","author":"Lighthill","year":"1955","journal-title":"Proc. roy. Soc. A"},{"volume-title":"Highway Capacity Manual","year":"1950","author":"Normann","key":"2024090922043051300_cit7"},{"key":"2024090922043051300_cit8","first-page":"631","article-title":"Le calcul des probabilit\u00e9s et la circulation des v\u00e9hicules sur une chauss\u00e9e \u00e0 deux voies","volume":"125","author":"Schuhl","year":"1955","journal-title":"Ann. Fonts Chauss"},{"key":"2024090922043051300_cit9","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1093\/biomet\/40.1-2.58","article-title":"A problem of interference between two queues","volume":"40","author":"Tanner","year":"1953","journal-title":"Biometrika"},{"key":"2024090922043051300_cit10","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1111\/j.2517-6161.1958.tb00307.x","article-title":"A simplified model for delays in overtaking on a two-lane road","volume":"20","author":"Tanner","year":"1958","journal-title":"J. R. statist. Soc. B"},{"key":"2024090922043051300_cit11","article-title":"Traffic capacity of town streets","volume-title":"Roads and Road Construction","author":"Wardrop","year":"1952"},{"key":"2024090922043051300_cit12","article-title":"Factors affecting road capacity","volume-title":"International Study Week in Traffic Engineering, 1956","author":"Wardrop","year":"1956"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1961.tb00390.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/23\/1\/38\/49172854\/jrsssb_23_1_38.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/23\/1\/38\/49172854\/jrsssb_23_1_38.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T22:30:03Z","timestamp":1725921003000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/23\/1\/38\/7035674"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1961,1,1]]},"references-count":12,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1961,1,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1961.tb00390.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"type":"print","value":"1369-7412"},{"type":"electronic","value":"1467-9868"}],"subject":[],"published-other":{"date-parts":[[1961,1]]},"published":{"date-parts":[[1961,1,1]]}}}