Study On The Minimum Traffic Delay At A Multi-phase Intersection Considering The Dynamical Evolution Process Of Queues

Traffic Flow Theory,like any other science research,seeks to understand and improve a physical phenomenon.The target suggested by Traffic Flow Theory is,for sure,roadway traffic,and the problems resulted from it,such as traffic congestion.But how does traffic congestion happen?Long ago,people go out on foot.Nowadays,with the invention of automobile,a person is willing to buy things in his car instead of walking.Traffic congestion is caused when many people and vehicles turns out at the intersection at the same time.In order to improve road safety and reduce traffic congestion,traffic administration department induces Traffic signals,which come from the railway management technology.Since Traffic signal control method is insufficient to understand the inner working pattern of automobile traffic,the effect of Traffic signal is not so obvious,then Traffic Flow Theory was born on the scene.In the middle of the 20th century,some remarkable researchers'work forms the foundation of Traffic Flow Theory.Based on those pioneering research contributions,much work is made,some of it is very creative and could solve some practical traffic problems.Many scientists enter this research territoryand aim to apply their knowledge to model traffic flow phenomenon.But some of their models fail to describe realistic human behavior,nor to capture real-time traffic characteristics.Mere good fit with traffic collection data is far from enough to justify a model.Traffic flow model should follow the rational consideration of physical properties of traffic flow,because traffic flow model is meant to concentrate on the description of the real traffic flow phenomenon.Traffic Flow Theory,is requested not only to describe traffic movement,but to model movement character of city intersection.By modeling city intersection,the capacity of intersection is improved through some devices such as traffic signals or other means of managing the traffic flow rate past a control point.The tremendous improvement of Traffic Flow Theory is once again on going,in the case of the development of traffic control theory for congested or uncongested system.Based on the researchresults of former physicians,this paper analyses the minimum delay of multi-phase signalized intersection,and develops the cellular automata model for two-phase signalizedcrossroad by considering the dynamicalevolution process of queues.The major contents of this paper are as flows:We have studied the minimum traffic delay at a two-phase intersection,takinginto account the dynamical evolution process of queues.The feature of delay functionhas been studied,which indicates that the minimum tra:ffic delay must be achievedwhen equality holds in at least one of the two constraints.We have derived theminimum delay as well as the corresponding traffic signal period,which shows thattwo situations are classified.Under certain circumstance,extra green time is neededfor one phase while otherwise no extra green time should be assigned in both phases.Our work indicates that although the clearing policies were shown in manyexperiments to be optimal at isolated intersections,it is sometimes not the case.Based on the analytical result of two-phase intersection,we study the minimumtraffic delay at a three-phase signalized T-type intersection,considering the dynamicalevolution process of queues.We firstly demonstrate that the minimum traffic delaymust be achieved on the surface of the 3D space constituted by the three constraints.Next we prove that the minimum traffic delay must be achieved on the threeborderlines of the surface.Finally,we show that the minimum delay is achieved eitheron one specific borderline or at the vertex of the surface.In the former case,extragreen time is needed for the stream with largest demand,while no extra green timeshould be assigned to any stream in the latter case.We have studied two-phase signalized intersection by using mathematicalanalytical method.Next,we model two-phase signalized crossroadwith two one-waystreams by using cellular automata,taking into account the need of real-time trafficapplication.Two signal control strategies adopted in the model,they are fixed-timestrategy and queue fully evacuation adaptive strategy.The simulation result of thefixed-time strategy shows that,when the inflows of two streams are equal,simulationresult fits analytical result pretty good,and the minimum delay is achieved when thegreen time appointed to both streams is identical.Otherwise,when the inflows of twostreams are unequal,the average delay of simulation result is always higher than thatof analytical result.In the case of adaptive strategy,traffic delay of simulation result islower than that of analytical result in any circumstances.The research result showsthat traffic delay is proportional to total inflow rate,and that adaptive strategy is betterthan fixed-time strategy in condition of two-phase signalized crossroad with twoone-way streams.Because of the relative simplicity and rare sighting in real life of the infrastructure of two-phase signalized crossroad with two one-way streams,we model two-phase signalized crossroad with two two-way streams by using traffic cellular automata.There are also two types of signal control strategies included in the model,which are fixed-time strategy and adaptive strategy.The simulation result indicates that,when the fixed-time strategy is used in the model,the difference between simulation result and analytical result depends on the total inflow rate of the system.When the total inflow rate is low,simulation result is better,while when the total inflow rate is relatively high,analytical result is better.When the adaptive strategy is used in the model,under the circumstance of equality of two inflows of west-east and east-west streams or south-north and north-south streams,the queue length in simulation model is longer than the calculation result of analytical model,that makes analytical result is better than simulation result.But in condition of inequality of two inflows of west-east and east-west streams,in addition,south-north and north-south streams,simulation result is better than analytical result.This paper studies the minimum traffic delay of two-phase and three-phase intersection,and derives the expressions of the minimum delay as well as the corresponding taffic signal period.We model signalized crossroad with two one-way and two two-way streams by using traffic cellular automata.We compare fixed-time strategy with adaptive strategy.Our research work could not only provide theoretical instructions to relieve traffic congestion phenomenon at city intersection,but promote the development of traffic signal control system.