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FINAL REPORTOptimized Traffic SignalManagementSubmitted by:Ankit Sharma (200901099)Vishesh Narwaria (200901097)
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Problem StatementGiven a whole city network, the waiting time of the vehicles on the junctions is not optimized. Sothe vehicles have to wait longer which results into traffic congestion and negative effects related tocongestion. So here we have to discuss a method for computing optimized waiting time for the links ofevery junction using control units installed at every junction. Optimized waiting time will depend on thecurrent traffic (or the vehicular queue) of the junction and the incoming flow from the neighboringjunctions. The Queue size parameter requires a real-time estimation based on real observation which canbe accomplished by a simple prediction procedure using sensors before being used by the model. Controlunits will be communicating to their neighboring control units all the time to share their incoming andoutgoing vehicular flow with each other to obtain the optimized waiting time.The methods and strategies utilizing traffic-light controls may be classified into two categories.i) History based strategies, which determines the optimal waiting times and optimal cycle times, based onthe history.ii) Real Time Traffic Response strategies, which are based on constructing real-time control systems withoptimum signal settings.In the present work, a signalized intersection with its input and output flows is considered to be a hybridsystem, thereby including both real time and history based components.Assumptions1. Every link of a junction has sensors to determine the queue size of that particular link.2. Physical queue sizes of vehicles in real time are considered the main parameter for thisframework.3. Every junction has a control unit which is working 24x7.4. Every control unit is communicating to its neighboring junctions‟ control unit.5. Every citizen will obey this system.6. Here we have considered a city-like network where 2 to 3 KM is the maximum possible distancebetween two neighboring junctions.7. If at any point of time, control unit fails to work properly than it will traffic signal system willswitch to traditional fixed time system.
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ApproachTraffic Signal optimization is one of the most complex problems as it requires all the control strategiestogether. In this section, a description of the model formulation for the signal optimization problem basedon observed queue sizes in real time, and also on the distance and queue size of the adjoining junction‟slink which would be dependent on the output flow of the corresponding link is presented. First, a generalsignalized junction is defined, then, information and parameters of the considered signalized junction arestated, and finally a method for calculation of green time durations of each link for one cycle isdeveloped.1. Definition of a signalized junctionSignalized junction can be defined as nodes of an urban traffic network connecting adjacent roadsfrom which vehicle flows come and to which vehicle flows go. At each signalized junction, a multi-phasetraffic light rules the vehicle flows by means of the light signal, which can assume the three usual logicvalues: green, yellow, and red.In general, a generic signalized junction consists of a set IN = {INi/ i = 1 to n} of n incominglinks, a set OUT = {OUTj/ j = 1 to m} of m outgoing directions, and one crossing area. To each input linkINi, we have a unique, independent queue size Qi of vehicles waiting for the green signal with an inputvehicle flow Фin and an output vehicle flow Фout. Output vehicle flow represents the flow crossing theintersection, entering from the incoming link i when enabled by the traffic light. On the other hand, foreach outgoing direction OUTj we have an output vehicle flow φj.2. Parameters to be used for calculating green time durationBasically, a generic signalized junction may be described by the following information: Queue sizes on all incoming links: Qi[veh] = [Q1(t), Q2(t), . . . ,Qn(t)] Green times corresponding to the incoming links for cycle time t: Gi(t) [sec] =[G1(t),G2(t),…,Gn(t)] Input flow rates of different incoming links for cycle time t: Фini(t)[veh/sec] =[ Фin1(t), Фin2(t),…, Фinn(t)] Output flow rates of different incoming links for cycle time t: Фouti(t)[veh/sec] =[ Фout1(t),Фout2(t), …,Фoutn(t)] Current cycle time C(t) [sec] Next cycle time C(t+1) [sec] Output flow rates of different outgoing directions at time t: φnji(t) [veh/sec] Distance between the adjoining junction from each link Dnji= [D1, D2,…. Dn] Maximum velocity of a vehicle on the road between junctions x and y = V
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3. Control UnitsAll the necessary computations stated above are computed by control units. Every control is unit isconnected to its adjacent control unit sharing the queue size and the output flow after every cycle with thecorresponding neighboring control unit.4. Calculation of green time durationThe green light times for the traffic flow should depend on the queue sizes of vehicles for differentinput links, and also on the distance and outflow from the neighboring junction‟s link.CalculationsPredicted green light time for the traffic flow should depend on the current queue sizes of the vehicles fordifferent input links, average of the flow coming from the neighboring junctions(Avg φnji(t)) and waitingtime of the last cycle(C(t)).This work considers predication of queue size of next cycles(Qi(t+1)) by taking into account the realnumber of vehicles measured at the end of actual cycle time, i.e. Qi(t), plus the probable number ofarriving new vehicles per second for the next cycle (Фini(t+1))[veh/sec]. Фini(t+1) is predicted becausefor the calculation of each Qi(t+1) we need to first calculate the Фini(t+1).Fig. : A Real Traffic Interaction
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Gi(t) is the Green time corresponding to the link i for cycle time t.Now, we define the waiting time for a link i for a cycle by:(t)= ∑We have,φnji(t): Output flow of neighboring junction(nj) connected to link i at time t which will be communicatedby the control units.Vnji: Maximum speed between link i and the connected link of its neighboring junction.Dnji: Distance between link i and the connected link of its neighboring junction.Фini(t+1) [veh/sec] is the predicted average flow (Avg φnji(t)) coming from the neighboring junctionsand traffic flow rate (t)[veh/sec] during the waiting time of the last cycle(C(t)).Now, we define Avg φnji(t) which is the total no. of vehicles passed through the neighbouring junctionwithin the waiting time during the cycle time t.Avg φnji(t) is the average of all samples of φnji(t) calculated per second from the starting time (ts)of thewaiting period to the end of waiting period. Therefore total no. of samples (N) will be equal to total no.of seconds in the waiting time because output flow is calculated per second.N=no. of samples∑Now, (t) is the Average input traffic flow of the link „i‟ during the waiting time of the lastcycle(C(t)).Now we can‟t depend upon just one of these individual average flow rates. So we calculate Фini(t+1) bytaking the average of both, which is given byФini(t+1) =There is a possibility that control unit might not get the output flow of the neighboring junction due tosome technical difficulties. At that time, Фini(t+1) will only depend on (t) i.eФini(t+1) = (t)
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Therefore, The prediction model that calculates the probable queue size of arrival vehicles for an inputlink ILi during the next cycle time C (t+1) is as follows:Qi(t+1) = Qi(t) + Фini(t+1) . (t)Where Qi(t) is the current queue size and Фini(t+1) (t) will give us the predicted no. of incomingvehicles during the waiting period.Now, cycle time will be the summation of the green time of all the links.∑Now, we have got all the parameters required to calculate the Optimal green light time for one incomingdirection. It will depend upon the Queue size of that link and the previous cycle time C(t). But we have toconsider the queue sizes of all the direction in order to allocate the green time such that summation of allthe green light time equals to the cycle time.i.e. Optimal Green light time will depend upon the ratio of queue size of a particular direction link to thesummation of the queue size of all the links, which when further multiplied by the cycle time will give uspredicted Optimal Green light time.Finally, the predicted optimal green light time required for one incoming direction for next cycle timeC(t+1) is calculated using the following expression:(∑)Work ExtensionProblem of congestion avoidance is still an issue. Let there be a link(L1) of a junction(J1) which is alreadycongested and it is connected to a junction(J2). Now suppose that the cycle time of J2 is low. So the outputflow of J2 towards L1 will increase its congestion. Therefore, output flow towards L1 should be reduced.This can be done be decreasing the green time of J2 towards L1 by the congestion factor of L1.
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ConclusionA hybrid model of signalized intersections has been discussed in this paper. Traffic control system is avery huge and complicated system which brings great difficulty in modeling it. Special regard is given toqueue sizes of vehicles in input links and is considered a principal parameter for optimization. This is sobecause such optimization concerns the calculation of optimal green durations proportionally to the realtime queues sizes in input links, which is, basically based on the output flow of the neighboring junctions.A solution is proposed here to obtain an effective and real time implementation of the given problem.References[1] Diakaki, C., Papageorgiou, M., and Aboudolas, K., “A multivariable regulator approach to traffic-responsive network-wide signal control,” Control Engineering Practice, 10(2), 2002, pp.183-195.[2] Lee, J., and Song, S., “Modelling urban transportation systems with hybrid systems: An overview,”IEEE proceedings of Intelligent Transportation Systems, Vol.2, October, 2003, pp.1269-1272.
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