Modeling vehicle delays at signalized junctions: Artificial neural networks approach

Transcription

1 Journal of Scientific & Industrial Research Vol. 65, July 2006, pp Modeling vehicle delays at signalized junctions: Artificial neural networks approach Y Sazi Murat* and Özgür Baskan Civil Engineering Department, Engineering Faculty, Pamukkale University, 20070, Kınıklı, Denizli, Turkey Received 24 June 2005; accepted 10 April 2006 Delay of vehicles at signalized junctions is one of the main criteria used for evaluation of control systems performances. The vehicle delay is uniform and non-uniform delay types. The uniform part consists of signal timings; the non-uniform part includes vehicle queuing, random arrivals and over-saturation cases of traffic flows. The uniform part of the vehicle delays is basically determined using conventional delay formulas. But for the non-uniform part, artificial neural network (ANN) approach is used and a vehicle delay estimation model [artificial neural network delay estimation of traffic flows (ANNDEsT)] is developed. ANNDEsT model compared with Webster, HCM and Akçelik delay calculation methods and field observations, shows encouraging results especially for the cases of over-saturation or non-uniform conditions. Keywords: Artificial neural networks, Intersections, Signalization, Traffic flows, Vehicle delay model Introduction Signalized intersections are designed considering the average delays of the intersection. The average delay is the key parameter that determines the level of service of an intersection. In addition, travel time, network reliability and analysis, evacuation management is related to delay estimation. In order to prevent congestion in road networks and to maintain accessibility, the value of vehicle delay should be known as accurate as possible. Vehicle delay is uniform and non-uniform delay types. Uniform delay is determined based on signal timings and traffic volumes. Non-uniform delay is determined considering the vehicle queue and random arrivals. The vehicle delay at signalized intersections has been defined with overall, stopping, acceleration and deceleration delays 1 (Fig. 1). The overall delay is the most common delay in evaluation of traffic signal control systems or signal design 2. The Webster 3, HCM 4 or the Akçelik 5 delay calculation methods are preferred by traffic engineers for many years. Although the methods have considered similar parameters in determination of vehicle delays, the results obtained are not comparable to each other. The Webster delay formula is not valid for this case. However, the HCM and Akcelik delay formulas give more reasonable results compared with Webster delay *Author for correspondence Tel: (ext-1539); Fax: ysmurat@pamukkale.edu.tr formula, but both methods do not represent delay for over-saturation case. This situation is due to the illdefined parameters in the problem; following headway, driver behavior, arrival type, age, education, weather condition etc. are some of these parameters. Measuring of these parameters is very difficult. Detectors that work based on magnetic induction or high sensitive cameras are used for measuring vehicle delays. Although usage of these equipment is the most convenient and accurate way for measuring vehicle delays, costs of installation and maintenance are very high. Some measurable parameters such as traffic flow, cycle time, red time, green time, saturation flow and queue length are used in delay calculation. On the other hand, the vehicle headways, weather condition Fig. 1 Definition of delays of vehicles

2 MURAT & BASKAN: MODELING VEHICLE DELAYS AT SIGNALIZED JUNCTIONS: ANN APPROACH 559 and age of driver are not taken into account in the existing delay formulas. The existing delay formulas give exaggerated results for over-saturated conditions. Therefore, an efficient and comprehensive model is required. In this study, Artificial Neural Network (ANN) approach is employed for modeling delays of vehicles. The present model [Artificial Neural Networks Delay Estimation Model (ANNDEsT)] is improved based on real data collected from field studies. Delay Phenomenon The delay has been calculated by the following equation in Webster Method 3 : 2 2 C(1 λ) x d = + 0,65( C/ q ) x 2(1 λx) 2 q(1 x) 2 1/3 2+ 5λ (1) where, d=average delay for vehicles on arm of the intersection, sec/veh; C= cycle time, sec; q= traffic volume, vph; λ= ratio of effective green to the cycle time; s= saturation flow, vph; g= green signal time, sec; x= degree of saturation. This formula is not valid if the degree of saturation is more than 1. Akçelik 5 assumed that the total delay includes both acceleration and deceleration delays and stated that effect of the queue length must be considered in delay calculation. Queue length is determined as: ( + ) QT f 2 12 x x N0 = z+ z + 4 QT f 0 (2) where, N o = average overflow queue (the number of vehicles); Q= capacity, vph; T f = flow period; QT f = maximum number of vehicles which can be discharged during interval T f ; x= q/q degree of saturation; z= x-l; x o = degree of saturation below which the average overflow queue is approx zero, is given by x 0 = sg / 600 (3) ( 1 u) qc = + N x (4) 2(1 y) D 0 2 where, D= total delay (in vehicle-hours per hour); q= flow in vehicles per sec; c= cycle time in sec; u= green time ratio, g/c; y= flow ratio, q/s; N o = average overflow queue in vehicles. The average delay per vehicle can be expressed as: d=d/q (5) where, D= total delay; q= flow in vehicles per sec. The updated formula for the HCM method 6 is as follows: d = d ( + d + d (6) 1 PF) 2 3 where, d= control delay per vehicle, sec/veh; d 1 = uniform control delay assuming uniform arrivals, sec/veh; PF= progression adjustment factor, which accounts for effects of signal progression; d 2 = incremental delay to account for effect of random arrivals and over-saturation queues, adjusted for duration of analysis period and type queue for lane at start of analysis period, sec/veh; and d 3 = initial queue delay, which accounts for delay to all vehicles in analysis period due to initial queue at start of analysis period, sec/veh. PF applies to all coordinated lane groups, including both pre-timed control and non-actuated lane groups in semi-actuated control systems 6. Good signal progression gives a high proportion of vehicles arriving on the green; while poor signal progression gives a low proportion of vehicles arriving on the green. PF is determined as: (1 P) f PF = PA g 1 c (7) where, P= proportion of vehicles arriving on green; g/c= proportion of green time available; f PA = supplemental adjustment factor for platoon arriving during green. The following equation gives the uniform control delay in HCM s approach 6 : where, s= saturation flow in vehicles/sec; g= effective green time, sec. The total delay for isolated fixed-time signalized intersection is calculated as: g 2 0,5 c(1 ) d1 = c g 1 [min(1, x) ] c (8)

3 560 J SCI IND RES VOL 65 JULY 2006 where, d 1 = uniform control delay assuming uniform arrivals, sec/veh; c= cycle length, sec; g= effective green time for lane group, sec; x= v/c ratio or degree of saturation for lane group. Non-uniform arrivals, cycle failures and oversaturation conditions cause an incremental delay of traffic flows, which is calculated as: 2 8klx d2 = 900 T[( x 1) + ( x 1) + ] (9) ct where, d 2 = incremental delay to account for effect of random and over-saturation queues; T= duration of analysis period; k= incremental delay factor; l= upstream filtering/metering adjustment factor; c= lane group capacity, vph; x= lane group degree of saturation. In addition to these fundamental formulas, many studies have been carried out to fit the best model for vehicle delays. Kimber & Daly 7 studied measurements of queue lengths and vehicle delays in testing the predictions of time-dependent queuing models. Akçelik 8 studied on the 1985 HCM delay formula and suggested a calibration process. Burrow 9 recommended additional factors for the formula improved by Akçelik 8. Prevedouros & Koga 10 compared the 1985 HCM delay formula with that of the Powell 11 proposed some correction factors representing the deceleration and acceleration delays of vehicles based on queuing to improve the 1997 HCM delay formula 12. Quiroga et al 13 conducted a study related to the measuring vehicle delays using Geographic Information and Global Positioning Systems. To simulate the 1997 HCM delay formula, Qiao et al 14 developed a fuzzy logic model. Dion et al 1 compared various analytic models with microscopic simulation software (INTEGRATION). Washburn et al 15 carried out performance comparison of three software packages (TRANSYT-7F, SYNCHRO and HCS). There is still vagueness in the determination of delay especially for over-saturated conditions. Therefore, this study concentrates on delay estimation at signalized intersections for both under-saturated and over-saturated conditions. Artificial Neural Networks Delay Estimation (ANNDEsT) Model Data Collection The required data for the model was collected in 2002 and from 10 different signalized Fig. 2 Locations of the reference points used in delay observations intersections located in two cities (Denizli and İzmir). The geometric conditions, number of lanes, on road parking, lane usage, bus stops, pedestrians etc. were determined. Numbers of observers, observation locations, reference points were ascertained based on the inspections made in before. The overall delay data including deceleration, stopping and acceleration delays were collected for considering lane group basis at peak and off-peak periods during the weekdays. The arriving headways, departing headways, signal timings, phase sequences, roadside parking, bus stops and pedestrians were also observed and noted during field studies. Two reference points, one located at 100 m away from stop-line (RP 1) and the other located at middle of the junction (RP 2), were determined in field studies (Fig. 2). In order to measure the acceleration delay, location of (RP 1) was especially selected at the middle of intersections. Similarly, to measure the deceleration delays, RP 2 (100 m away from the stopline) was ascertained based on the maximum observed queue lengths. Two people were employed for each lane type during this survey. One of them counted the number of passing vehicles and arriving times considering crossing RP 2 by using a stopwatch and the other one saved the data on the survey form. After the light turns to green, departing time of each vehicle was also noted considering RP 1. The difference of arriving and departing times were determined as overall delays of vehicles. Each lane type was observed separately and the data were collected carefully during 1 h period considering cycle by cycle. Delay of each vehicle is summed for each hourly observation period and average delay is computed dividing by traffic volume obtained for the same period. By this way, 100 hourly data sets collected from different signalized intersections at different observation periods.

4 MURAT & BASKAN: MODELING VEHICLE DELAYS AT SIGNALIZED JUNCTIONS: ANN APPROACH 561 Model Structure and Selection Procedure ANNDEsT model is developed considering traffic volume, cycle and green times. These parameters are selected considering relations to the vehicle delay. There is a linear relation between traffic volume and delay. The vehicle delay increases by increasing traffic volume. Non-dissipating queues occur and cause an increase in vehicle delay if traffic volumes are very high and over the capacity. In addition to traffic volume, cycle time has an importance on vehicle delay. It has been known that, the vehicle delay can be higher for very short and very long cycle times. The relation between the cycle time and delay is non-linear. Vehicle delay is also affected by red signal timing. Stopping delay occurs during red signal time. The red signal time is also part of cycle time. But effects of these two timings on vehicle delay can be different. This difference comes from signal phasing. In order to represent signal phasing, these two timings are used in the model. On the other hand, all of these parameters can easily be obtained without detailed field studies and also have been used in the conventional delay formulas. Therefore it was considered in ANNDEsT model. Fig. 3 Structure of the ANNDEsT Model The feed-forward neural network type and error back propagation algorithms are used in developing ANNDEsT model (Fig. 3). The number of hidden layer, neurons in hidden layer, learning rate, momentum coefficient and the number of iterations are determined by trial and error approach. The verification of the model is done using the three-way data split method 17 and data are considered using 12 partitions The data are divided into three fold for the partitions I to VI and the training and validation data are subdivided into two equal parts for the partitions VII to XII. Data used for the network is as follows: training, 70; validation, 15; and testing, 15. For each of the partition, the network architecture is trained and its performance is tested with validation data set that was not used in training. For each run, the best network architecture is selected with the minimum network error. One and two hidden layers with maximum number of neurons are 20 for each layer tried. The final network architecture for delay estimation model is determined based on Mean Absolute Error (MAE) values for train, test and validation data (Fig. 4), Akaike (Fig. 5) Information Criteria (AIC) and coefficient of correlation values (Fig. 6). The train, test and validation error values are multiplied by the ratio of the data used in each set and the weighted error values (Fig. 4) are calculated. The average error rates for different network architecture are calculated using the train, test and validation error values. The network architectures that have the lowest weighted and average error rates are considered. The network architectures that have error values between the ranges of 4 and 5 (Fig. 4) are firstly selected as the best fit architecture candidates for vehicle delay modeling. Fig. 4 The weighted and average error values for different network architectures

5 562 J SCI IND RES VOL 65 JULY 2006 Fig. 5 Akaike information criteria values for different network architectures Fig. 6 Coefficient of determination values for different network architectures (Fig. 6). The ultimate network architecture is determined as (3 16 1) based on the entire criterion regarded. Fig. 7 Comparisons of delay models with field observations AIC values of the considered network architectures are calculated and evaluated using the lowest is the better approach. Two architectures [(3 16 1) and (3 3 1)] are regarded as the significant based on this criterion. The coefficient of determination values of network architectures are calculated and assessed Evaluation and Testing the ANNDEsT Model The results from ANNDEsT model were compared with that of HCM 2000, Akçelik and Webster conventional delay formulas and with the field studies (Table 1, Fig. 7). The ANNDEsT model gives better results than the conventional delay approaches. The conventional approaches are successful in general for under-saturated conditions. But it does not show the same performance for over-saturated conditions. Average Relative Error (ARE) rates of validation data calculated for under-saturated conditions are as: Akcelik, 0.20; Webster, 0.35; HCM 2000, 0.21; and ANNDEsT, It can be seen that the ANNDEsT model has the lowest ARE rate. On the other hand, priority of ANNDEsT model is apparent for oversaturated conditions. The conventional methods gave exaggerated results for over-saturated conditions. This

6 MURAT & BASKAN: MODELING VEHICLE DELAYS AT SIGNALIZED JUNCTIONS: ANN APPROACH 563 Table 1 The validation data set and compared results Validation Data No Cycle time sec Red time sec Traffic Volumes vph Degree of Saturation x Average Delay sec/veh. Akçelik Webster HCM ANNDEsT 2000 Observed value is due to the over-saturated parts of the formulas. But the ANNDEsT model results are promising and close to the observations. Success of the ANNDEsT model is based on the ANN methodology. Results of the ANNDEsT model are produced using a trained network structure that is not a static formula and based on the real observation data. Conclusions A vehicle delay estimation model based on ANN was developed as ANNDEsT model, which is more accurate than the conventional approaches. ANNDEsT model provides encouraging results for the over-saturation cases. But it is developed considering the data obtained from 10 signalized intersections and restricted for the observed data. In order to generalize the model, more data and conditions should be taken into account. In addition, the comparisons for the case of under-saturation show that the ARE rate of the ANNDEsT model is the lowest. Therefore, the ANN approach can be used as a reliable approach for delay estimation. In order to prevent the over-fitting problem, the three-way data split method was used. The MAE, AIC and coefficient of determination values are appraised together while selecting the ultimate network architecture, which is determined as (3x16x1). In training, 5000 iterative calculations are made and the learning rate is used as 0.1, momentum coefficient is used as 0.6 in calculations. In this model, traffic volume, cycle time and the red signal time are taken into account as significant parameters. ANNDEsT model can be used by traffic engineers or decision makers who may use it as a software tool for signalized intersection to be designed in the future and more accurate results may be obtained. In addition, the external costs that are aroused from improper design of intersections may also be prevented using ANNDEsT and the indirect benefits can also be increased. The isolated signalized junctions are taken into account in this study. Coordinated or vehicle-actuated controlled junctions may be analyzed for future studies. ANNDEsT model can also be joined to Intelligent Transportation Systems (ITS) considering travel time estimation, route choice etc. References 1 Dion F, Rakha H & Kang Y S, Comparison of delay estimates at under-saturated and over-saturated pre-timed signalized intersections, Transportation Res Part B, 37 (2003) Roess R P, McShane W R & Prassas E S, Traffic Engineering (Prentice-Hall, New Jersey) 1998, Webster F V, Traffic Signal Settings (Her Majesty Stationary Office, London) 1958, TRB, Special Report 209: Highway Capacity Manual (TRB Press, Washington D C) 1965, Akçelik R, Traffic Signals: Capacity and Timing Analysis (ARRB Press, Melbourne) 1981, TRB, Special Report 209: Hıghway Capacity Manual (TRB Press, Washington D C) 2000, Kimber R M & Daly P N, Time-dependent queuing at road junctions: observation and prediction, Transportation Res Part B, 20 (1986) Akçelik R, The highway capacity manual delay formula for signalized intersections, ITE J, 58 (1988)

7 564 J SCI IND RES VOL 65 JULY Burrow I, A note on traffic delay formulas, ITE J, 59 (1989) Prevedeorus P D & Koga C A, Comparison of 1985 and 1994 HCM: signalized intersection delay estimates, ITE J, 66 (1996) Powell J L, Field measurement of signalized intersection delay for 1997 update of the highway capacity manual, Transportation Res Rec, 1416 (1998) TRB Special Report 209: Hıghway Capacity Manual (TRB Press, Washington D.C.) 1997, Quiroga C A & Bullock D, Measuring control delay at signalized intersections, J Transporatation Engg, 125 (1999) Qiao F, Yi P, Yang H & Devarakonda S, Fuzzy logic based intersection delay estimation, Matl and Compu Modelling, 36 (2002) Washburn S S & Larson N, Signalized intersection delay estimation: case study comparison of TRANSYT-7F, Synchro and HCS, ITE J, 72 (2002) Başkan Ö, Modelling average vehicle delays at isolated signalized intersections using artificial neural networks, MSc. Dissertation, Institute of Natural and Applied Sciences, Pamukkale University, Denizli, Turkey, Osuna R G, CS790: Selected topics in computer science, Lecture Notes, Texas A&M University, 2002.