Stochastic Queueing Model For Traffic Flows At Signalized Intersections

The variability and uncertainty of traffic demands are the most important characteristics of traffic phenomenon at urban intersections.Such phenomenon can be directly characterized by the randomness of queues of vehicles at the intersections.For the general traffic movements(e.g.,through movements),complex traffic movements(e.g.,left-turn movements),and innovative traffic movements under the designs of untraditional control schemes,focusing on the random characteristics of the queueing processes of different types of movements at signalized intersections,the stochastic queueing models are developed to quantitatively analyze and describe the queueing performance of traffic flow at signalized intersections under different signal control strategies.The key contribution of this thesis is that it overcomes the dependency on the average values of traffic indicators(such as the average queue length,average delay)when measuring the traffic performance of signalized intersections,and formulates the formation and dissipation process of queues along with the signal state at signal junctions.In particular,a more complete analytical framework for evaluating the control strategies of signal junctions is established.The stochastic queueing models can provide the theoretical basis and method for deep understanding of queueing phenomenon and provide an accurate quantitative description of the formation and dissipation of traffic congestion.Furthermore,in engineering practice,the analytical framework for traffic flows at signalized intersections can provide a theoretical basis for determining the signal timing,control strategy,and road designs,etc.The main works of the thesis are as follows:1.Aiming at the dynamic features of queues of vehicles at signalized intersections,a stochastic queueing model considering the service vacations for vehicles on the multilane is proposed.Specifically,the periodic vacation behavior of signalized intersection because of the red phase and the update of queue length within a signal cycle are definitely considered under the batch arrivals of vehicles.The stationary queue length distributions of vehicles along with the time are obtained,which can be used to fully capture the effects of batch arrival pattern on the queueing process of vehicles at signalized intersections.And some key performance indices are also obtained.Additionally,numerical simulations are employed to study how the queue length of vehicles is impacted by the arrival pattern of vehicles,traffic volumes,and traffic signal timing,etc.2.In general,three types of operational modes are employed to left-turn vehicles at signalized intersections: protected-only,permitted-only,and protected/permitted phasing.Aiming at the features of uncertain vacation of signalized intersections under different left-turn operational modes,a random queueing model is developed to analytically measure the queueing performance of left-turn movements,in which the key factors are considered,such as left-turn operational mode,signal timing,left-turn volume,opposing volume,types of lane,number of lanes,and sneakers,etc.For different operations of left-turn movements,the features of left-turn queueing processes are analytically formulated,and the stationary queue length distributions of left turns along with the time are obtained.Moreover,three types of left-turn traffic performance indices are given: primary queueing indices,fuel-consumption related indices,and left-turn safety related index.Using the above performance indices,an analytical framework for the using of left-turn phasing is established,it provides a more accurate tool for measuring the traffic performance of left turns for different left-turn phasing,and therefore can be used to improve the operational control of left-turn movements.Model validation shows that for different traffic conditions,the left-turn queueing model proposed in this thesis can provide an effective estimation of left-turn traffic performance under different left-turn phasing.Additionally,numerical simulations are also conducted to determine the factors that could impact the left-turn traffic movements at signalized intersection under different scenarios.3.Focusing on the queueing processes of vehicles at signalized intersections with different types of waiting areas,a random queueing model is presented to analytically evaluate the use of waiting areas,and the primary indices are derived,including the stationary queue length distribution,average queue length,average delay,average queue length at an arbitrary time,etc.The traffic performance of the intersection with waiting areas can be explicitly measured based on the obtained indices;moreover,the dynamic nature of queueing process at signalized intersections is directly captured under the design of waiting areas,and the maximum number of vehicles during the whole signal cycle is also measured.In addition,numerical experiments are designed to investigate the queues of vehicles at signalized intersections under different conditions when different sizes of waiting areas are employed.4.The approaches of signalized intersection are not fully utilized during the green time when the protected-only left-turn phasing is used.To improve the capacity of the intersection,the strategy of pre-signals was introduced.With the help of the pre-signals,different traffic movements are reorganized in the sorting area,so that vehicles on the all lanes of the approach with sorting area can leave the intersection when signal turns green.In order to analytically measure the traffic performance of the signalized intersections with pre-signal control strategy,a queueing model is developed,and the steady state distributions of queue length with signal state are derived,such an index can accurately capture the formation and dissipation process of queues of vehicles at the pre-signal intersections.In addition,two levels of traffic performance evaluation indicators are obtained: primary indicators and auxiliary indicators.The above two sets of indicators can establish a clear analysis and evaluation framework to realize a more comprehensive quantitative evaluation of the pre-signal control strategy,which will help further improve the application of the strategy.In particular,the results of numerical experiments confirm that the use of pre-signals is suitable for the saturated traffic conditions,whereas it will have negative effects when traffic volume is low.