Methods for Optimization of Signal Cycle Length

GRD Journals- Global Research and Development Journal for Engineering | Volume 3 | Issue 12 | November 2018 ISSN: 2455-5703

Methods for Optimization of Signal Cycle Length Vaidehi J. Patel UG Student Department of Civil Engineering Dr. S. & S.S. Ghandhy Government Engineering College, Surat Vipinkumar G. Yadav Assistant Professor Department of Civil Engineering Dr. S. & S.S. Ghandhy Government Engineering College, Surat

Pratik V. Parmar UG Student Department of Civil Engineering Dr. S. & S.S. Ghandhy Government Engineering College, Surat

Abstract Traffic on the existing road is increasing due to rapid urbanization and industrialization due to extreme growth of vehicles all over the world. Due to this, some problems like congestion, delay and pollution remain a big challenge. These problems can be solved by providing an effective traffic signal control at the intersection for achieve continuous movement of vehicles at the intersection.

The primary objective of this study is to review methods for develop an optimized traffic signal cycle length model for signalized intersections. Most traffic signal timing plans are designed to decrease delay time of vehicle. Signal timing is most important and it is used to decide green time of the traffic signal.

Keywords- Effective Traffic Control, Signal Cycle Length, Delay Time, Green Time, Optimization

I. INTRODUCTION Traffic engineering is a branch of engineering that deals with efficient and safe movement of people, goods and vehicles. It also deals with planning and geometric design of highways and measures to reduce accidents on highway.

Traffic signal is a commonly used traffic operation management device at roadway intersections in urban area. The capacity of urban road network generally depends on the capacity of the traffic signals. Traffic signal control is one of the most useful methods to reduce the effect of traffic congestion at intersections.

Traffic optimization is an emerging area in the recent few years, with the rapid development of data analysis studies and techniques. Intersection is the hub of road traffic and plays a vital role in alleviating the pressure on road traffic. With the rapid development of India’s economy, the urban population has expanded constantly, and the amount of traffic has significantly increased. As a result, serious road congestion, traffic chaos and other issues are occurring. Therefore, it is quite urgent to improve the road service capacity and achieve the scientific management of road conditions.

The intersection is a vital part of urban road networks which plays a key role in the speed of vehicle and for operating the entire road network effectively. However, with rapidly increase in motorization during past two decades, bottle-neck effects have been exposed more and more at intersection of urban areas.

The benefits for developing the signalized intersections are many. First one is the control afforded by the traffic lights separates the irrelevant traffic flows in time and improves safety of vehicle and operation efficiency; second one is the vehicles on the approach are suspended periodically, causing delays. Therefore, the traffic signal cycle plays a vital role in traffic control at intersection. A suitable cycle length can decrease or prevent traffic congestion and reduce noise pollution, emissions, energy consumption and travel delay time effectively.

II. LITERATURE REVIEW Cheng et al. (2003) modified old Webster’s minimum delay cycle length equation based on HCM 2000. For an isolated intersection, the delay will become infinity when the degree of saturation of a lane group approaches one based on Webster’s delay equation, which is unrealistic, while the delay based on HCM 2000 method can accommodate some random failures and short-term oversaturation situations. They used HCS software to conduct experiments for a typical four-phase intersection over a wide range of volume and lost time scenarios. And the results were used to modify the original Webster minimum delay cycle length equation.

The modified equation significantly improves the accuracy of predicting the optimal cycle length for isolated intersections at high traffic volume conditions.

To improve the Webster’s optimal cycle length equation, three regression models were implied. The form of recalibrated Webster model is, aL+b Co = (1) 1−Y

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Methods for Optimization of Signal Cycle Length (GRDJE/ Volume 3 / Issue 12 / 003)

By using SPSS software a=1 and b=7.6 were obtained.

For developing second model, the optimal cycle length from HCM2000 and Webster’s equation were plotted with 1/ (1Y) for the total lost time. For lower values of 1/ (1-Y) Webster’s and HCM2000 give nearer result but for higher values they do not give better result. For these following modified Webster’s model is suggested: aL+b Co = +c (2) 1−Y Where, a and b can be obtained by linear regression on slope versus the lost time and c is equal to the mean value of intercepts.

The third model, the exponential type of nonlinear regression model is given as: Co = ιLeβY (3) Where ι and β are two regression parameters. ι= 1.5 and β= 1.8.

For comparing these three models, the R-squared values for the above models are calculated using; SS SS R2 = R = 1 − E (4) SST

SST

Where SSR= regression sum of squares; SSE= the error sum of squares; SST= total corrected sum of squares.

SST SSE R2

Table 1: R-squared Values for the Minimum Delay Cycle Length Models Webster Equation Recalibrated Webster Model Modified Webster Model Exponential Cycle Length Model 19196 19196 19196 19196 18938 7620 824 2011 0.013 0.603 0.957 0.895

From the Table 1 it is concluded that recalibrated Webster model is better than Webster equation and the modified Webster model is the best.

Zakariya and Rabia (2016) proposed two regression formulas for estimating the minimum delay optimal cycle length based on a time-dependent delay formula. This formula overestimates the cycle length for high degrees of saturation. These time dependent models are widely used in capacity guides as in the Canadian Capacity Guide and the Highway Capacity Manual (HCM) to improve the estimate of the overall vehicle delay. They provide good estimate of the optimal cycle length for high degrees of saturation and have same performance as Webster’s method for lower degree of saturation.

The basic equation for estimating the average overall delay is, d = k f d1 + d2 (5) Where, d= average overall delay kf = progression adjustment factor d1= average overall uniform delay =

g C(1− e )2 c

g 2(1−min(X,1) e ) C

d2= average overflow delay = 15t e [(X − 1) + √(X − 1)2 +

240X cte

]

C= cycle length (sec) ge= effective green time (sec) X= degree of saturation c= capacity (PCU/h) te= evaluation time (min) The new minimum delay cycle length formula improves the accuracy of predicting the optimal cycle length for isolated intersection at higher traffic flow. Two regression models are proposed to modify Webster’s optimal cycle length formula. First one recalibrates the Webster’s minimum delay cycle length formula as follows: đ?‘Žđ??ż+đ?‘?

Co = (6) 1−đ?‘?đ?‘Œ Where; a, b and c is regression parameters. With help of MATLAB software a= 1.978, b= 5.109 and c= 0.9013.

Second one is the exponential type of non-linear regression model: d Copt = aLebY + c (7) Where a, b, c and d is regression parameters. They are estimated by MATLAB software.

1.712 Copt = 0.6256Le3.694 Y + 14.87 (8)

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Methods for Optimization of Signal Cycle Length (GRDJE/ Volume 3 / Issue 12 / 003)

Fig. 1: Comparison between Webster’s model, search algorithm, regression formulas, and simulation results

From Figure 1 it is clear that the regression formulas and the search algorithm give approximately the same performance as the simulation results.

Wu, et al. (2015), collected traffic data from 50 signalized intersections in Xi’an city. The primary objective of this study was to develop an optimization traffic signal cycle length model for signalized intersections. In this study they used many models like Webster’s delay model, optimization cycle length model, TRRL model and ARRB model. Using comprehensive delay data, the optimization cycle length model is re-recalibrated to the Chinese traffic conditions based on the Webster delay model. In the optimization cycle length model, they took vehicle delay time, pedestrian crossing time, and drivers’ anxiety into consideration.

To evaluate the effects of the optimization cycle length model, three intersections were selected for a simulation. They compared optimization cycle length model and Webster delay model on the basis of delay time and queue length.

Table 2: Comparison of Signal Cycle Length TRRL model NEW model Cycle length (sec) Co = (1.5L + 5) / (1- Y) C = (1.45L + 3) / (1-Y) Intersection 1 30 40 Intersection 2 140 120 Intersection 3 230 180

In Table 2, intersection 1 has low traffic flow; intersection 2 has medium traffic flow; intersection 3 has very busy traffic flow. From these observations, it was concluded that, for the medium and high traffic flow the NEW model gives small cycle length as compared to TRRL model considering pedestrian and anxiety of driver.

Surisetty and Sekhar (2017) used Highway Capacity Manual (HCM) intersection saturation for identifying periods of time when cycle length could be substantially short. These data are used to identify normal flow of the roadway and determine the influence of heavy vehicles or pedestrians on vehicular traffic volume. They compared HCM 2000 and Webster’s delay equation.

As a result, they concluded that Webster’s minimum delay cycle length equation overestimates the optimal cycle length compared to the results based on the HCM 2000 method.

Kesur (2017) found that mixed cycle length operation can substantially improve performance in traffic networks where there is a large difference in the volume of traffic processed by individual signals, Whereas Webster’s cycle length formula is generally used as a heuristic to determine which signals to operate at lower and higher cycle lengths. This study demonstrates that the use of mixed cycle lengths as given by the heuristic is inferior to operation under a common cycle length. Mixed cycle length operation is found to be of a more limited application.

In this method, he discusses the study of Kreer.

Table 3: Cycle Times Examined in Test Networks Kreer’s network Real world network Cycling scenario Cmin Cmax Cmin Cmax Common cycle 30 120 36 144

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Methods for Optimization of Signal Cycle Length (GRDJE/ Volume 3 / Issue 12 / 003)

Single/double cycling Double/ triple cycling

60 90

120 240

72 108

144 288

In Table 3, the domains of cycle times examined for each network and cycling scenario are given. In Table 3, the values of Cmin and Cmin for the mixed cycle length were chosen to ensure that the minimum and maximum implemented cycle lengths correspond to the minimum and maximum cycle lengths under the common cycle length scenario. From the table, Kreer’s network gives less and uniform value of Cmin and Cmax as compared to Real world network. So signal can operate with common cycle length ignoring longer cycle length.

Zhou et al. (2017) discussed traffic signal timing of individual interactions. In this method, a signal timing algorithm based on multi-objective optimization was developed after an analysis and comparison of various road indexes. The idea of multiobjective optimization is intended to achieve an optimized state of balance in problems involving more than one objective. In this paper, the algorithm obtains multi-objective optimization through the simultaneous improvement of road capacity, average delay time and the number of vehicle stops.

Table 4: Table of Indexes of Timing Design Algorithm Green time/ Green time ratio Timing method Period 1st phase 2nd phase 3rd phase Research status 114 57/0.5 23/0.2 25/0.22 Webster timing 72 37/0.47 14/0.19 15/0.21 Multi-objective optimization 152 80/0.53 29/0.19 34/0.22 Table 5: Table of Indexes of Timing Design Algorithm Timing method Average delay time Average number of stops Total traffic capacity Research status 29 85 4901 Webster timing 20 57 4448 Multi-objective optimization 36 109 5096

From the data in the tables 4 and 5 it is seen that, for low traffic flow Webster method gives smaller period than the multiobjective optimization. In the case of large traffic flow Webster method’s effect is not good.

Terzi et al. (2017) used Elimination Pairing System (EPS) for optimization of traffic signal timing at oversaturated intersections. The EPS system is used for calculating green times for oversaturated intersection. In this method, a performance index is calculated and optimized by the two input parameters as thedelay occurring at intersection and stop – start numbers for the cars approaching the intersection. Then the results are compared with Transyt 14 software and Webster method.

First of all, total cost value is calculated as: C(d, ∆) = ∑ d + ∑ ∆ (9) Where (d, Δ) is the total cost value according to the delay and stop-start arguments ($); ∑d is the total delay (pcu-hour/hour) and ∑∆ is the total stop-start number per hour. φ + Q clean τ ≤ g ∆= { (10) 3600 3600 2 ((τ − g)θ (( ) − 1) + φ) + (φ + (g ∗ θ)) ∗ ( )τ > g c

c

Where, φ is the number of vehicles at the beginning of green time; Qclean is the number of vehicles approaching the intersection during green time; τ is the time needed for cleaning up the queue; g is the green time; θ is the incoming flow rate; c is the cycle length.

Input parameters are selected as green time from phase one and the cycle time. The min and max values for the input parameters are as follow; c ∈ R, 20 ≤ c ≤ 150; g ∈ R, 1 ≤ g ≤ (c − t allred ).

Table 6: Comparison of Signal Planning Methods Webster method Transyt 14 Elimination pairing system Calculated optimal cycle length 422 103 119 Green time for phase one 188 44 50 Green time for phase two 226 51 61

From the above table concluded that green time and cycle length calculated with Transyt 14 and EPS are more realistic than Webster method.

Krishna et al. (2018) used Webster method for signal design for four legged intersection. The design is totally based on Webster method, in this method, total cycle of the signal is determined which gives total least delay.

For the length of change of interval: v85 Y=t+ (11) 2a+19.6g

Where, y = length of yellow interval in seconds, t = reaction time of the driver, v85 = 85th percentile speed of approaching vehicles in m/s, a = deceleration rate of vehicles in m/s2, All rights reserved by www.grdjournals.com

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Methods for Optimization of Signal Cycle Length (GRDJE/ Volume 3 / Issue 12 / 003)

g = grade of approach expressed as a decimal.

SSD = stopping sight distance and v = speed of the vehicle The lost time can be given as: l = ∑ni=1 ei Where, ei = the difference between the actual headway and h for the ith vehicle The green time required to clear N vehicles can be found out as, T = l + hN Where, T = time required to clear N vehicles through signal, l = start-up lost time, and h = saturation headway in seconds.

(12)

(13)

III. CONCLUSION – – – – – – – –

Each intersection signal design method has its own characteristics. Optimization of signal cycle length is based on situation at location.

At low traffic volume condition, Webster’s optimal equation is good.

For an isolated intersection, HCM 2000 method is better than Webster’s delay formula.

Modified Webster’s delay cycle length equation significantly improves the accuracy for isolated intersections at high traffic volume condition.

Minimum delay optimal cycle length based on time dependent formula gives better estimation for the optimal cycle length at high intersection flow ratio compared to Webster’s formula.

Multi-objective optimization is used to achieve an optimized state of balance in problems involving more than one objective.

Mixed cycle length operation has been recommended for networks where individual intersection process considerably different traffic volumes.

EPS method optimizes cycle length and green time together whereas most of software or methods calculate them separately.

REFERENCES [1] [2] [3]

[4] [5] [6] [7] [8]

Ahmed Y. Zakariya and Sherif I. Rabia, “Estimating the minimum delay optimal cycle length based on a time-dependent delay formula” Alexandria Engineering Journal (2016) 55,pp. 2509–2514.

DingXin Cheng, Carroll J. Messer, Zong Z. Tian and Juanyu Liu, “Modification of Webster’s Minimum Delay Cycle Length Equation Based on HCM 2000” TRB 2003 Annual Meeting CD-ROM. Ekinhan Eriskin, Sebnem Karahancer, Serdal Terzi, Mehmet Saltan, “Optimization of Traffic Signal Timing at Oversaturated Intersections Using Elimination Pairing System” 10th International Scientific Conference Transbaltica 2017: Transportation Science and Technology, Procedia Engineering 187 ( 2017 ) 295 – 300.

K.Hari Krishna, K. Vinay Kumar, Dr. Ch. Hanumantha Rao, “Signal design using Webster’s method (4 legged intersections)” IndianJ.Sci.Res. 17(2): 113119, 2018.

Khewal Bhupendra Kesur, “Optimization of mixed cycle length traffic signals” journal of advanced transportation J. Adv. Transp. 2014; 48:431–442.

Pengzhe Zhou, Zhiyi Fang, Hongliang Dong, Jiayue Liu and Shuaining Pan, “Data Analysis with Multi-objective Optimization Algorithm: a Study in Smart Traffic Signal System” IEEESERA 2017, June 7-9, 2017, London, UK. Ramesh Surisetty and Soma N Sekhar, “Designing of a Traffic Signaling System at T-Intersection” Ramesh Surisetty. Int. Journal of Engineering Research and Application ISSN: 2248-9622, Vol. 7, Issue 4, (Part -3) April 2017, pp.82-86.

YaoWu, Jian Lu, Hong Chen and Haifei Yang, “Development of an Optimization Traffic Signal Cycle Length Model for Signalized Intersections in China”Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2015, Article ID 954295, 9 pages.

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