A PROPOSAL OF A REAL-TIME DEMAND RESPONSIVE SIGNAL …

A PROPOSAL OF A REAL-TIME DEMAND

RESPONSIVE SIGNAL CONTROL ALGORITHM FOR DISPLACED LEFT-TURN INTERSECTIONS

CORRIDOR IN DEVELOPING COUNTRIES

Sherif SHOKRY1, Shinji TANAKA2, Fumihiko NAKAMURA3, Ryo ARIYOSHI4 and Shino MIURA5

1Member of JSCE, Doctoral student, Graduate School of Urban Innovation, Yokohama National University

(79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan) E-mail: [email protected]

2Member of JSCE, Associate Professor, Graduate School of Urban Innovation, Yokohama National University (79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan)

E-mail: [email protected] 3Member of JSCE, Executive Director, Vice President, Yokohama National University

(79-1 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan) E-mail: [email protected]

4Member of JSCE, Associate Professor, Graduate School of Urban Innovation, Yokohama National University (79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan)

E-mail: [email protected] 5Member of JSCE, Assistant Professor, Graduate School of Urban Innovation, Yokohama National University

(79-5 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan) E-mail: [email protected]

To alleviate congestions at signalized intersections, Displaced Left-turn Crossovers (DLTs), also known as Continuous Flow Intersections (CFIs) are becoming as prevalent treatments over the past dec-ade in some developed cities around the world. Through the novel solution provided by DLTs, left turn flows could cross the opposing traffic lanes upstream of the main intersection. As a result, DLTs lead to higher capacities, lower delays and fewer crashes. In spite of the extensive preliminary studies focused on the operational performance of DLTs, little research has been conducted considering the coordination of DLTs. In addition, although the considerable sparse works highlighted the DLT intersection, the hetero-geneous traffic condition as a dominant operation environment in lots of developing countries has never been estimated. Hence, in order to fulfill the heterogeneous condition needs and considering the coordi-nation of DLTs, the driving force of this study context is developing a real-time demand-responsive sig-nal control system on the solid foundation of the optimization principles. This entire algorithm was built based on developing a mathematical model and utilizing PTV-VISSIM as a micro-simulator based ap-proach. In order to test the proposed algorithm, an inter-process communication and dynamic object crea-tion were provided by employing VISSIM-COM interface and MATLAB a multi-paradigmnumerical computing environment. Although the academic in nature, the proposed algorithm presented in this con-text could be evolved through a real-world practical application. As a realistic study case, actually ob-tained data were made available of three signalized intersections located in an arterial corridor in central Cairo, Egypt. Key Words : displaced left-turn crossovers, heterogeneous traffic conditions, signal coordination

1. INTRODUCTION

Over the last decade, as an innovative at-grade signalized intersection treatment, DLTs intersections also known as Continuous Flow Intersections (CFIs), that is one of Unconventional Arterial Inter-

section Designs (UAIDs) have been presented to alleviate congestions at signalized intersections1),2),3). A unique solution is provided through DLTs by in-troducing a particular geometric layout as well as a special signalized control scheme. DLTs’ operation-al control scheme ensures a simultaneous flow of

J. JSCE, Ser. D3 (Infrastructure Planning and Management), Vol.75, No.5, Special Issue, I_1151-I_1165, 2019.

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both through traffic as well as left-turn movements during the same phase green time3). Through the geometric layout provided, left turn flows could cross opposing traffic lanes upstream of the main intersection. By eliminating the left-turn conflicts through displacing the left-turn lane to the opposing direction, the safety performance could be en-hanced4). Only a two-phase signal control is in-stalled instead of four phases for the conventional signals, the through and left-turn traffic flows could operate at the main intersection simultaneously5),6). Therefore, intersection capacity was significantly increased and delays were also decreased7).

Despite, the extensive preliminary studies focused on the operational performance of DLTs, little re-search has been conducted considering the coordina-tion of DLTs. Most of the previous considerable works on UAIDs dealt only with isolated UAIDs. Although, few articles have been turned to placing a series of UAIDs on a coordinated corridor, no study has found to investigate the integration of the DLTs intersections applicability8). On the other hand, even though the early deployment of DLTs, they are mainly installed in the developed world where the ideal traffic conditions assumed. Therefore, almost all previous sparse studies focused on studying the operational performance of DLTs under the ideal traffic flow. However, DLTs under the heterogene-ous traffic conditions as a dominant operation in the developing countries has never been examined.

This article is a part of an ongoing research pro-ject that proposes the UAIDs under the heterogene-ous traffic conditions. The operational performance of DLTs was evaluated as isolated intersections un-der such conditions by the authors9). Moreover, in another article the authors utilized the branch-and-bound algorithmto solve the mixed-integer linear programming optimization problems for a pre-timed (fixed-time) coordination based on the bandwidth maximization technique10).

The main objective of this research is directed to placing a series of DLTs on a coordinated corridor under dominant heterogeneous traffic conditions in order to accommodate the dynamic traffic demand. Thus the driving force of this study context is de-veloping a real-time demand-responsive signal con-trol system based on the online optimization funda-mentals. The designed system endeavors to mini-mize the total delay for consecutive DLTs traffic signals by considering the individual vehicle arrivals caused by platoon dispersion as natural stochastic variations of heterogeneous traffic conditions. Hence, in this study, the optimization is individually performed for each intersection, accordingly, the coordination of the DLTs is implicitly achieved.

In this article, the optimization problem is formu-

lated as a single objective optimization problem toobtain the optimal extension green time that min-imizes the total intersection control delay for both road users at an intersection. The objective function is formulated as a linear mixed-integer problem. The proposed algorithm spots the movement of each ve-hicle iteratively on each lane and automatically modifies the signal timing accordingly. 2. LITERATURE REVIEW

In order to comprehend and establish a theoretical

framework for this study context, this literature re-view is presented. It is divided into three parts to discusssome of the previous related research work to DLTs, adaptive traffic control schemes as well as other studies focused on heterogeneous traffic con-ditions.

(1) Previous studies on DLTs evaluation

Indeed, several valuable studies provided a con-siderable in-depth literature review of existing ana-lyzing DLTs operational performance methods rele-vant to this study. A valuable enhancement in the operational performance of three traditional inter-sections has been highlighted in a comparative study of three different DLT configurations to their similar conventional designs. Under low, moderate and high traffic volumes, prominent savings in average con-trol delays and average queue lengths. The DLTs outputs emphasized a reduction in the average con-trol delay by 48% to 85%, 58% to 71% and 19% to 90% for low, moderate and high traffic volumes respectively. Consequently, the average number of stops reduction pointed to 15% to 30% for under saturated traffic flows and 85% to 95% for saturated traffic conditions. Accordingly, the analysis record-ed a significant intersection capacity growth for the three studied DLTs over the conventional ones11).

As a powerful simulation-based assessment ap-proach, another researchemployed VISSIM to eval-uate and compare the operational performance of four unconventional intersections: upstream signal-ized intersection (USC), crossover displaced left-turn (DLT), median U-turn (MUT) and double crossover intersection (DXI) (i.e., half USC) under balanced and unbalanced volume scenarios. The DLT is always experienced superior to all other studied intersections in almost all volume condi-tions. The results showed while the USC and DXI capacities were about 50% higher than the conven-tional intersections, DLT exhibited a significant growth of capacity by 99% higher than the conven-tional counterpart, whereas. Also, DLT constantly

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recorded the lowest delay among the all compared counterparts8).

Seeking a fair travel time comparison of the con-ventional intersection and seven unconventional designs: Quadrant Roadway (QR), Median U-Turn (MUT), Super Street Median (SSM), Bowtie, Jughandle, split intersection and Continuous Flow Intersection (CFI) another comparative study was conducted7). CORSIM simulation software was used in order to represent the different configurations. Authors concluded that at least one unconventional scheme would outperform its conventional counter-part in at least one volume scenario. The conven-tional designs never produced the lowest average total time. The continuous flow intersection always had the highest move-to-time ratio for all designs. Additionally, CFIs design was also keeping traffic moving as its name implies, even if QR and MUT designs vied for the lowest average total time7). (2) Previous studies on adaptive traffic control

schemes Regarding the signal control coordination, several

available and various pioneering studies have been presented since Webster developed the traffic signal control optimization principles. Depending on Web-ster efforts, other models have been provided con-sidering the stochastic conditions12),13). Three wide-ly-used optimization methods namely genetic algo-rithm simulated annealing and OptQuest engine were employed to present a stochastic traffic signal optimization method. Under the micro-simulation environment, the performance of the proposed method which consists of the stochastic simulation model and an external optimizer was compared with the existing optimization programs including TRANSTY-7F as well as SYNCHRO14). Although the comparison results emphasized the outperfor-mance of the provided method over the existing aforementioned programs, the six tested networks were selected in the ideal traffic environment. In other words, the non-lane based phenomena as well as aggressive driving behavior as a salient property of the heterogeneous traffic characteristics were not appropriately investigated.

On the other hand, based on queue discharge rates, a simple estimation procedure accounting for arri-vals and estimated departures was developed. The RHODES system that referred to a real-time traffic-adaptive signal control system showed promising results of several CORISM models of actual trans-portation networks15). Taking into consideration bal-ancing the interests of cyclists and motorized traffic, a traffic signal optimization system was developed. The presented multi-objective function aimed to

optimize the traffic signals of a coordinated corridor by taking into account the number of stops, delay and desired speed of cyclists in addition to the delay of motorized traffic. Both motorized vehicle and cyclist’s delay was calculated by summing up the delay caused by the traffic signal, the delay because of the formed queues and the overflow delay. The overall delay occurs when the arrival rate is greater than the service rate at the traffic signal. The pro-posed system was implemented and tested by em-ploying VISSIM-COM and Fmincon Multistart op-timizer in MATLAB. Four different software name-ly; VRIGen, TRAFCod, PTV-VISSIM and MATLAB were employed to accomplish this study objective. As a traffic control generator, VRIGen was used to find the optimum structure, minimum total cycle time and green times for all traffic streams. The output-generatedfiles with the traffic program of VRIGen are the input of TRAFCod as a full-scale traffic simulator program that allows for external traffic signal controllers. The proposed sys-tem could enhance the cyclists’ performance by giv-ing speed advice to cyclists based on optimal green times, either by synchronizing the traffic signals at cyclists’ speeds or by combining both strategies16). As an important step in dividing strategies for heter-ogeneous traffic conditions implementation, a vehi-cle-actuated signal controller was developed. The developed controller proposed several strategies such as changing the detector configuration and the loop size, logical grouping of signal phases and the use of dummy phases. Although the implementation strategy overcame the existing pre-timed signals, the sensitivity of the thresholds for cycle time, green time, gaps need more investigation17).

Relying on estimating the sampled travel times measured between upstream and downstream loca-tions of a signalized intersection, an estimated delay algorithm was proposed. The different signal phases could be estimated from the delay patterns, without the need to know signal timing or traffic flow in-formation. Regarding the delay characteristics, the proposed model was represented. Piecewise linear curves were plotted due to the characteristics of the queue forming and discharging. On the other hand, for a nontrivial increase in delay after the start of the red time, detection of the start of a cycle could be obtained. To accomplish the study objectives, least squares–based algorithm was developed to match measured delays in each cycle by using piecewise linear curves18).

To model the movement of the traffic along the streets between the intersections in a time-expanded network, the platoon dispersion constraints directly translated into the signal control model. The prob-

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lem was formulated as a linear multi-commodity network flow problem. The results revealed the fast solution for the proposed algorithm19).

El-Tantawyet al., (2014) utilized Reinforcement Learning (LR) as one of the efficient approaches to solve such stochastic closed loop optimal control problem, a seamless application of adaptive traffic signal control scheme was provided. The proposed LR controller could save 48% of average vehicle delay comparing to the optimized pre-timed control-ler and fully actuated controller20).

Girianna and Benekohal in (2003) formulated a discrete-time signal coordination model as a dynam-ic optimization problem and to solve a signal coor-dination problem on two-way arterial networks with oversaturated intersections by using Genetic Algo-rithm (GA). Their proposed algorithm intelligently generates optimal signal timing depending on the scheme of queue dissipation process. Based on the notion of ideal offsets that dissipate queue such as the signal cycle rolls, the ideal offsets must be at-tained earlier relative to the opposite direction in order to promote the traffic progression in both di-rections. For the one-way directional traffic progres-sion with balanced flows, the presented algorithm confirmed that the notion of the traffic progression should start from the critical intersection and move in the direction of coordinated movements. Howev-er, for the two-way directional traffic progression with unbalanced flows, the algorithm showed a ca-pability of dissipating queue in both directions with ideal offsets. These optimal offsets are attained ear-lier in the primary direction and later in the oppos-ing one21).

In spite of the many attempts that have been made as adaptive control systems to set the timing of the signals for traffic flow satisfactory, most of these trials relayed on predicting the traffic flow upstream the signals. Although such adaptive control systems are appropriate when the flow ismoving as platoons, they do not always lead to the best possible solution where the heterogeneous traffic conditions are exist-ing. Also, these control systems typically require an extensive input of system parameters and different weighting factors to favor individualmovements in addition to a large number of detectors to collect movement-specific traffic data22).

(3) Previous studies on heterogeneous traffic im-

pact The heterogeneous traffic conditions involve the

complexities of mixed traffic compositions such as diverse dynamic and static properties of vehicles, aggressive drivers’ behavior and the lack of lane discipline. Likewise, complex operating systems

existed due to the diversity in the operating perfor-mance characteristics pertain to the heterogeneous traffic system compared to homogeneous one23). As a result, the operational performances of such condi-tions as speed limits, queue discharge rates and satu-ration flow rates have been obviously influenced. Although, the average nation saturation flow rate was revealed to be between 1700 and 2080 PCU/h/ln24), it was reported to be 1617 PCU/h/ln according to the previous findings in Egypt25). For these reasons, the speed limits also have been influ-enced dramatically. For instance, the published re-port of the World Bank emphasized the average speeds were reduced by at least half (15 to 40km/h) of the normally expected speeds (60 to 80 km/h) in central Cairo26).

The heterogeneous traffic properties such as traffic violation caused by the aggressive driving behavior and various dynamic characteristics of the mixed traffic composition results in platoon dispersion. Moreover, the traditional optimization programs which do not consider stochastic variability in driv-ers’ behavior, vehicular inter-arrival times as well as mixed traffic composition and so far, are not appro-priate to satisfy the heterogeneous traffic needs27).

Summarizing the highlighted literature, it could be summarized that most of the previous studies built up their architecture algorithms and analysis upon platoon arrivals fundamentals to develop arterial traffic-adaptive control systems. However, the im-pacts of the heterogeneous traffic conditions on the optimizing the intersections’ delays along corridors were not considered. Therefore, the novelty of this study is developing a real-time demand-responsive signal control system by taking into consideration the heterogeneous traffic complexities’ impacts. Hence, the intersection delay is estimated depending on each individual vehicle characteristics. 3. METHODOLOGY

In order to achieve this research objective, a math-ematical model was driven and micro-simulation platform was employed to implement the control strategy. The methodology followed in this context is illustrated within the next six subsections. As an increasingly important approach to solve real-world problems, the micro-simulation approach followed in this study is explained firstly. Second, the realis-tic traffic environment of the case study is illustrat-ed. Third, the representation of different vehicle types are represented and discussed. Fourth, the simulated DLT intersections are illustrated. Finally, in order to minimize a discrepancy of the credible

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results, it is essential to calibrate and validate the simulated models to sufficiently represent the real world conditions, particularly, when the heteroge-neous conditions are considered. Hence, in the fifth and sixth subsections the model calibration and val-idation procedures are described in details. (1) The micro-simulation platform

Considering the novel nature of UAIDs, particular-ly DLTs, micro-simulation approach has been broadly employed in several research works. As a cost and time effective and crucial analytical ap-proach, PTV-VISSIM is utilized in this study28). Employing the given flexible PTV-VISSIM capabil-ity, especially, the psychophysical car-following model, construction of DLTs could be represented exactly as they would appear in the real life1). How-ever, for accurate simulation of heterogeneous traf-fic conditions, model-specific parameters’ adjust-ments were carried out. These adjustments include vehicles’ static and dynamic properties as well as driving behavior representation29),30),31),32). VISSIM-COM interface and MATLAB was provided as an inter-process communication and dynamic object creation to put capabilities to their potential. VIS-SIM-COM interface is used to manipulate the at-tributes of most of the internal objects dynamical-ly27),33). Vehicle trajectory generated data obtained via installed detectors in the simulated corridor is as a feeding data to MATLAB as a pro-actively re-sponding to the variations in explicit prediction. De-pending on a real-time algorithm provided a pro-prietary program developed to optimize the coordi-nated DLTs signals based on PTV-VISSIM sent data. Promoting the real-time data obtained from the field, the optimization is performed for each inter-section individually. As a result, the coordination of the intersections would implicitly achieve without a fixed offset.

Taking into account the heterogeneous traffic complexities, the provided algorithm is calculated by summing up the delay for each vehicle individu-ally. In other words, to fulfill the traffic heterogenei-ty needs such as the individual behavior of the vehi-cles as well as the various dynamic characteristics, the proposed system is not dealing with the traffic as a platoon, it calculates the delay of each vehicle up-on its speed and its distance from the stop lines. (2) Traffic environment

To make this system viable and applicable, a sin-gle arterial with three cross-minor approaches that carry considerable flow was selected as a realistic case study. The three intersections studied in this work are consecutive conventional signalized inter-

sections in Mostafa El-Nahas Street; a major urban corridor in central Cairo, Egypt as shown in Fig.1. The studied corridor is one of the main arterial cor-ridors located in the central business district (CBD). Therefore, based on the actual real data that made available by the Department of Civil Engineering, Ain Shams University, Egypt, the studied intersec-tions; MakramEbid (ME), Abbass Al-Akkad (AA) and Al Tayran (AT) intersections, receive daily heavy traffic volumes as shown in Fig.2. The typical geometric design and traffic operation to regulate directional flow around each existing conventional intersection is shown in Fig.3. The previous works emphasized the poor operational performance of these conventional intersections because of the het-erogeneous condition25), particularly, at the U-turns located in the up/downstream.

The relevant data needed for the heterogeneous traffic flow were collected by utilizing the video observation technique. The data collected include the intersections’ traffic volumes, the directional flow ratios as well as the traffic composition of each turning movement from the different approaches. Considering the adapting ability of the proposed control algorithm highlighted in this context for the daily variation of traffic volume, the conducted sur-

Fig.1 A Google map showing the central Cairo, Egypt as the case study.

Fig.2 The studied intersections’ traffic volumes.

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vey was carried out in the morning, afternoon, peak and off-peak periods as fifteen-minute recorded vid-eo shots. The morning observation period was con-ducted between (8:00 to 9:00) and (10:00 to 11:00), whereas the evening period was from (16:00 to 17:00). The relevant directional flow ratio data em-phasized that the arterial corridor experience high through traffic volumes. The through traffic move-ment for the intersections studied recorded 38% to 79% of the whole movements, while the left-turn movement ratios fluctuated from 6.5% to 65% and the right-turn free flow traffic has oscillated between 2.5% to 23%. Also, the video observation showed that the existing traffic composition consisted of 75% of normal vehicles, 10% heavy vehicles (in-cluding buses, minibuses, and small trucks) and 15% of motorcycles. Although the normal vehicles dominate the traffic composition, the traffic opera-tional functionality was influenced by such heterog-amous traffic. The videos recorded indicated the drivers’ aggressiveness, lane changing behavior as well as the maneuverability of small vehicles and stop line violation. The given traffic demand for thesimulation is as shown in Table 1.

The analyzed intersections had the following geo-metric criteria: 1- All intersections were four-leg intersections; 2- Each Intersection had the same number of lanes per approach three lanes of 3.5m per direction for-both the major and minor approaches. However, as a result of the lane lines absence, non-lane based phe-nomena as a salient property of the heterogeneous traffic has been observed. Therefore, under aggres-sive driving behavior, during the peak hour, vehicles could perform as four lanes per approach flow on the main studied corridor; 3- In addition, an exclusive bus lane of a 3.5 m width per direction was installed in the main corri-dor for the public buses. However, shuttle buses, private and school buses were not allowed to use those exclusive lanes; 4- For both major and minor free right-turning flows, a channelized right-turn lane was provided on

all studied intersections; (3) Vehicles’ representation

In this context, different vehicle types are consid-ered to represent the heterogeneous traffic composi-tion as mentioned in the previous section. These types include two-wheeled vehicles (motorcycles), normal cars, microbuses (15 passengers), minibuses (30 passengers) and buses. The various standard static and dynamic variables of the different vehicle types were altered based on the field observed data as a realistic study. The static properties include the vehicles’ length and width, and the dynamic ones refer to speeds, acceleration and deceleration rates as illustrated in Table 2. However, the driving be-havior as a unique characteristic of such conditions such as non-lane based driving behavior and vehi-cles maneuverability was represented. Accordingly, the simulation parameters of car following behavior, lane change and lateral behavior were modified based on field observation obtained data.

Seeking accurate results, VISSIM relevant pa-rameters were tuned and carefully calibrated to fulfil the real field conditions. In order to simulate the two-wheeled vehicles’ stimulus sneaking maneuver-ability, two measures were considered. First, two signal heads were installed for each lane to repre-sent. The first signal head was assigned to control two-wheeled vehicles, with 2.0 m ahead of the sec-ond, which was designated to the other vehicles types. Second, the diamond shaped queuing option was activated to allow staggered queues shaping as a representation of the two-wheeled vehicles behav-ior at the stop lines.

On the other hand, for free-lane change driving behavior representation of such conditions where no restrictions to change lanes exist; some required measures are essential to be checked. First, the min.

Fig.3 A typical traffic flow inside the studied intersections.

Table 1 The given traffic demand.

Intersection Movement Observed volumes (veh/h)

AT

W-E 2270

E-W 3040

S-N 1640

N-S 1434

AA

W-E 1905

E-W 3578

S-N 1596

N-S 1716

ME

W-E 2245

E-W 2574

S-N 1385

N-S 1244

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lateral distances were maintained for each corre-sponding speed of each vehicle category based on the similar previous studies29),30),31),32) as shown in Table 2. Second, the left and right sides overtaking were permitted by selecting the uncooperative lane change option. Finally, other simulation parameters such as the average standstill distance, the number of observed preceding vehicles, min. back and headway distances were also calibrated to fulfill the aggressive driving behavior as a common and unique characteristic of such heterogeneous condi-tions as shown in Table 3.

(4) DLTs representation

Following DLTs design principles and considering the earlier works, guide manuals as well as the pre- deployments of the scheme proposed, DLTs config-uration could be simulated. This study context con-siders DLTs implementation of in both major and minor approaches. Different DLT geometric designs were configured depending on the traffic volumes assigned for each intersection. A typical geometric configuration was assigned for the minor approach for all studied intersections. For the minor approach two exclusive lanes of 3.5m for through and other two lanes as crossover lanes with a channelized free right-turning lane. However, the geometric layout was different for the major approach in the studied intersections. For ME intersection, two exclusive lanes of 3.5m for each direction for through traffic flows weresettled, while the other two lanes of 3.5m were installed as crossover lanes as shown in Fig.4.

On the other hand, three lanes of 3.5m width wereemployed for the through westbound flows of AT DLT because of the high traffic demand. There-fore, only one lane of 3.5m width was left for left-turn crossover as shown in Fig.4. The high traffic demandof major approach through flows resulted in assigningthree lanes for both AA major approach

throughflows. Consequently, the rightchannelled lane of the westbound as well as the southbound was demolished and one lane was allocated for left-turn west and eastbound as shown in Fig.4. Fur-thermore, the two existing bus exclusive lanes were kept on the main street for all DLTs. The signal time plans for the conventional intersections and their DLTs are illustrated in Fig.4. (5) Model calibration

In the past, due to the data limitation, the difficul-ties related to the field data collection or/and the lack knowledge of the appropriate, readily and available procedures to calibrate and traffic simula-tion models, most of the previously conducted anal-ysis was done relying on values of default parame-ters21). Accordingly, skeptics always consider simu-lation platforms as inexact, unrealistic at best and unreliable black-box technology at worst. Hence, in order to avoid unrealistic expectations of the capa-bilities of consolidate models and aiming to mini-mize a discrepancy of the credible results, it is es-sential to calibrate and validate the simulated mod-els to sufficiently representthe real world conditions, particularly, when theheterogeneous conditions are considered. The effectiveness and practicability of the simulated models can be represented as close as possible to the reality by bridging a conditional match of the simulated parameter values with ob-served traffic field data.

In this study context, the driving behavior parame-ters are considered for the calibration process. The candidate driving behavior parameters in this re-search are the minimum lateral distances for differ-ent vehicle types, the number of observed preceding vehicles, the average standstill distance and look ahead and back distances. Accordingly, a sensitivity analysis is used to find the optimal values of the most significant driving behavior candidate parame-

Table 2 Operational performance indices of the studied corridor.

Vehicle type Static properties (m)

Dynamic properties

Desired Speed (km/h)

Acceleration (m/s2)

Deceleration (m/s2)

Min. lateral distance (m) in corresponding to different

speeds

Length Width Max. Desired Max. Desired 0 km/h 50 km/h

Motorcycle 1.8 0.6 40 2.5 1.7 1.7 1.2 0.3 0.7

Normal car 4.0 1.6 50 1.5 1.2 1.2 1.0 0.5 0.9

Microbus 5.0 1.9 50 1.5 1.2 1.2 1.0 0.5 0.9

Minibus 8.0 2.0 30 0.8 0.7 1.2 0.6 0.6 0.9

Bus 10.3 2.5 30 1.3 0.8 1.4 0.6 0.6 1.0

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ters that influence the models’ efficiency. First, the network elements are defined by representing the geometric configuration, vehicles properties, traffic control system and driving behavior initially in the default setting (pre-calibrated) values to ascertain the need for calibration. Next, the default parameters are changed until the absolute error between the field and simulated Measure of Effectiveness (MOE) is less than the threshold values. For this purpose, the travel time between the consecutive intersections of both west and eastbound direction along the studied corridor is selected as MOE. In this study, the acceptable variation threshold is 17.0 % or less. By incrementing the values of the candidate parameters by small units, the sensitivity analysis is assessed. Consequently, to confirm the significant consistency of the candidate sensitive parameter(s) on the MOEs indices, a statistical test is needed. Finally, the model is represented on the new values given to the parameters until the abso-lute error is insignificant. In this study, the estima-tion of the maximum and minimum of parameter values were based on the relevant previous research, as well as the engineering judgment of the authors. As a recommended statistical test, ANOVA single factor test is utilized for measuring the closeness of the observed and simulated travel time. The out-comes of the ANOVA test indicated the significant consistency between the simulation models efficien-cy and the different simulation parameters. The travel time between the consecutive studied inter-sections as MOE for the different calibration trials is

shown in Table 4. The ANOVA results are reported in Table 5, as (SS) is the sum of squares, (df) is the degree of freedom, (MS) is the mean square devia-tion, (F) is the test statistics, (P-value) is the proba-bility value under the appropriate F, (F-crit) is the critical value of F (5,30) distribution under 5% sig-nificance level. The variance analysis shows the F-value is bigger than F-crit with a small P-value, which emphasizes that the null hypothesis is reject-ed, and the readjusted simulation parameters have a significant impact on the efficiency of models. The calibration results referred to the significant impact of the different vehicles’ dynamic characteristics, as well as the driving behaviorparameters on the model efficiency. (6) Model validation

To ensure that the studied intersections were pre-sented as indisputable as reality, the model valida-tion has to be carried out. By comparing the simu-lated model outputs with the observed data, the val-idation could be executed. For this task, traffic vol-umes as well as the average travel time comparison was carried out. As a recommended effective meth-od, GEH empirical static formula was used to com-pare the observed and simulated traffic volumes in order to validate the simulated models. The GEH static model is a modified Chi-square static test that was designed for the purpose of comparing simulat-ed and observedhourly traffic volumes as shown in Eqn. (1).

Fig.4 The proposed DLT intersection geometric layouts and signal timing plans.

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2

0.5

M OGEH

M O

(1)

where: M: the observed flow on a link in (veh/h); O: the modeled flow for the same link in (veh/h). Regarding the GEH method, the simulated model is accepted when 85% of the volumes in a traffic mod-el with a GEH less than 5.034),35). The estimated re-sults of the executed test emphasized the acceptance criterion of the simulated models as shown in Table 6. The GEH values recorded less than 2 mostly, while west and eastbound of the major corridor rec-orded values fluctuated from 3.0 to 4.0.

4. DEVELOPMENT OF THE CONTROL

ALGORITHM The proposed system in this study context endeav-

ors to minimize the total delay for consecutive DLTs traffic signals by considering the platoon dis-persion as natural stochastic variations of heteroge-neous traffic conditions. Therefore, in order to fulfill the needs of the dominant heterogeneous traffic conditions, the vehicles’ movement at an intersec-tion is not considered as a platoon, and the delay is estimated for each vehicle individually. Hence, the optimization is individually performed for each in-tersection based on the real-time traffic demand. Accordingly, the coordination of the DLTs is im-plicitly achieved by considering the detected up-stream traffic demand of each intersection along the coordinated corridor. The designed system takes into consideration the main characteristics of DLTs, such as the storage length of the displaced left-turn lanes of each approach as well as the coordination among the signal phase groups to ensure the contin-uous operation and keep traffic moving as CFI im-plies.

(1) Delay calculation

The problem investigated in this article is to esti-mate the delay in the intersection by summing up the delay of each individual vehicle based on the individual vehicle arrival. The delay of a single ve-hicle in theupstream of an approach is calculatedat the subjected intersection as illustrated from Eqn. (2) to Eqn. (5). Consequently, the total delay for each approach could be estimated by summing up the delay of all arriving vehicles at the subjected intersection as illustrated in Eqn. (6) and Eqn. (7). The delay of each vehicle is calculated as the sum of two components: 1- The stopped delay;

Table 3 The optimal values of the calibrated parameters.

Simulation parameters Optimal values

Avg. standstill distance 0.5 m

No. of observed Vehicles 2 veh

Look back distance Min. 30.0 m Max. 150.0 m

Look ahead distance Min. 5.0 m Max. 100.0 m

Table 4 The travel time variations between the consecutive

intersections for the different calibration trials.

Trials ME-AA AA-AT YA-AT

AT-AA

AA-ME

AT-YA

1st 2.0% 32.2% 31.4% 28.5% 46.7% 32.8%

2nd 2.4% 4.9% 10.6% 16.4% 58.3% 31.7%

3rd 21.4% 10.9% 11.4% 30.7% 69.0% 19.0%

4th 2.1% 1.9% 44.1% 46.7% 36.3% 18.7%

5th 19.8% 61.9% 57.2% 26.5% 12.1% 39.9%

6th 21.9% 62.1% 11.7% 7.4% 10.7% 63.8%

7th 22.2% 61.9% 18.6% 38.8% 7.8% 66.6%

8th 22.2% 61.8% 17.2% 10.7% 13.7% 66.6%

9th 80.2% 53.7% 4.0% 10.9% 12.1% 44.4%

10th 2.0% 0.2% 1.5% 0.9% 12.07% 16.2%

Table 5 ANOVA test results.

ANOVA: Single Factor

Source of Var-iation

SS df MS F P-

value F crit

Between Groups

3.1608 9 0.3512 2.351 0.0026 2.073

Within Groups

7.4668 50 0.1493

Total 10.627 59

Table 6 GEH test results.

Intersection Direction GEH value AT W-E 3.64

E-W 1.06 S-N 0.81 N-S 1.06

AA W-E 1.66 E-W 4.84 S-N 3.43 N-S 0.41

ME W-E 4.07 E-W 3.35 S-N 1.74 N-S 0.62

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2- The delay caused by discharging the formed queues in front of an individual vehicle in each lane at the intersection.

On the ground field, the values of the parameters used in Eqn. (2) to Eqn. (7) are collected based on vehicle detectors. They record and transmit the loca-tion and the speed of each vehicle along the cover-age range.

Similarly, VISSIM-COM is also designed to pro-vide the position and the speed and the location of each vehicle in each time step.

m, 1

. / .Jajor major major major

j i arr qjd S T t N S d s

(2)

, 1. / .

Jminor minor minor minorj i arr qj

d S T t N S d s

(3)

, , ,. .major minor minor minori f i ex i clrS T S T g g t (4)

, , ,. .minor major major majori f i ex i clrS T S T g g t (5)

1

Jmajor majorjJ

D d

(6)

1

Jminor minorjJ

D d

(7)

where: dj

major, djminor: the delay of an individual vehicle in

the major and the minor approach respectively; S.T major, S.T minor: the time point when the green time of the major and the minor starts at an intersec-tion (i) respectively;

,majori arrt , ,

minori arrt : the time point when each individual

vehicle on the major and the minor arrives at the stop line of an intersection (i) respectively;

1

J

qjN

: the total number of queueing vehicles in

the formed queues in front of vehicle (j) at an inter-section (i); S: the saturation flow rate at an intersection (i) (veh/ln/s);

. majord s , . minord s : the delay saved because of the ex-tension green time in the major and the minor ap-proach at an intersection (i) respectively in seconds (s);

,majori fg , ,

minori fg : the fixed green time of major and

minor approach at intersection (i) respectively in seconds (s);

,majori exg , ,

minori exg : the extension green time of major and

minor approach at an intersection (i) respectively in seconds (s);

,i clrt : the clearance time at intersection (i) in seconds

(s); majorD , minorD : the total delay in major and minor

approach at an intersection (i) respectively in sec-onds (s); J: the total arriving vehicles at an intersection (i); a) The stopped delay estimation

The stopped delay is calculated as the time differ-

ence between the time point when the green time of the subjected phase starts at an intersection and the arrival time point for each vehicle to reach the stop line. The speed and the position of each vehicle up-stream the main intersection, the estimated arrival time point for each vehicle to reach the stop line is calculated. By recording the exact time point when the green time of the running stream starts, the delay time of the other stopping approach at an intersec-tion (i) can be calculated as shown in Fig.5. Since there are only two phases control the DLTs main intersection, the green time of major approach will start when the green time of the minor approach ends and vice versa. Therefore, during the same cy-cle, the major and the minor approach delays are dependent. The delay of each stopped vehicle during the red time in both major and minor approach at intersection (i) is calculated as shown in Eqn. (2) and Eqn. (3) respectively.

Although, the stopped delay that is defined as the delay occurred when a vehicle is totally immobi-lized, in this study a vehicle when moving at 5 km/h experiences the stopped delay. b) The formed queues discharging delay estima-

tion The total number of queuing vehicles in the

formed queues in front of each stopped vehicle at the intersection could be determined as Fig.5 de-picts. The standing queue discharging delay could be estimated by dividing the number of formed ve-hicles in front of each stopped vehicle by the satura-tion flow rate at the subjected intersection as shown in Eqn. (2) and Eqn. (3). Although each approach is divided into three lanes as VISSIM provided its links, however, in order to estimate the position of each vehicle is updated per each time step in order to fulfill the non-lane base traffic conditions. Hence, for this study context the time step iteration was set as (0.1) seconds, therefore the data is collected for each time step. Accordingly, the total number of queued vehicles is estimated for each time step, ac-cordingly the non-lane based traffic is considered.

Fig.5 Time-space diagram.

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(2) The control algorithm structure

This algorithm was built and developed based on the advanced detection and communication technol-ogies of the adaptive signal control systems to pro-vide control strategies in response to the real-time traffic conditions. Although the hourly traffic vol-umes are not direct inputs in this proposed algo-rithm, the dependent gap out time as well as the total number of queuing vehicles in the formed queues is thedirect inputs of the proposed algorithm. The needed real-time data including the gap out time between two passing vehicles in major and minor approach at an intersection (i), the speed and posi-tion of each vehicle are obtained at the 5 seconds before the end of the previouscycle time in order to execute the proposed algorithm. Consequently, the objective function is predicted, the extension green time is calculated and the appropriate decision is taken. The mechanism of the provided algorithm is shown in Fig.6 and explained as follows:

First, the initial input design parameters of the en-tire proposed control algorithm were calculated based on Webster delay function (1966) is shown in Eqn. (8) and Eqn. (9). The cycles’ times as well as the green splits of each phase for different signal groups of each intersection on the studied corridor were estimated as a fixed-time cycle.

1.5 5 1C LT FR (8)

max maxig C LT FR FR (9)

where: C: optimal signal cycle time (s); LT: total lost time per cycle (s); FR: critical flow ratio for each phase (Q/S). These variables were assigned as initial input for the proposed algorithm as Fig.6 illustrates; where: Q.Lmax

major, Q.Lmaxminor: Max. queue length in the

major and minor approach at an intersection (i) re-spectively in meters (m); Gpmajor, Gpminor: Gap out time between two passing vehicles in major and minor approach at an intersec-tion (i) respectively in seconds (s). Stg. Ln.: Storage length at an intersection in major and minor approach (i) in meters (m). Second, in order to provide and ensure a smooth flow along the coordinated corridor, the proposed control algorithm prioritized the flow continuity during the green time of each phase. Therefore, the gap out time condition prioritized over the queue length condition statement at each intersection as the Fig.6 depicts. During the green time of an approach, the gap out time of each two passed consecutive vehicles of the running stream are detected. Simul-taneously, the queue length of the stopped standing queues during the red time of the other approach for both standing queue lengths upstream the main in-tersection as well as upstream the crossovers. To keep the functionality of DLTs operation perfor-mance emphasized, the standing queue length up-stream the main intersection as well as upstream the crossovers should not exceed the storage length. For this end, the DLTs capability for both approaches would not be influenced and the continuous flow is ensured along the corridor.

Finally, the original time plan would be operated based on the initial design if one of the abovemen-tioned conditions are satisfied, otherwise, the opti-mization problem is executed to find out the optimal extension green time that fulfill the minimum delay at the intersection for both major and minor ap-proach.

(3) The detectors’ positions

As mentioned earlier in the previous section, that the delay of each vehicle is calculated based on its position and the speed of each individual vehicle by utilizing the wireless vehicle detectors. However, as an importantdesign element that achieves the pro-posed control algorithm, detectors are crucial to de-tect the gap out time between two passing vehicles as well as the total number of queuing vehicles in

Fig.6 The control algorithm framework.

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the formed queues to estimate the queue length as Fig.5 depicts. The positions of the detectors used in this design were precisely determined and installed carefully upstream the main intersection along the major and minor approach. The detectors’ positions were installed 10 meters downstream of each cross-over lane at each approach to emphasize enough storage length for the stopped standing queues dur-ing the red time of the other approach as shown in Fig.7. Thus, the delay of the vehicles between the detectors and the stop lines is calculated upon their real-time positions and speeds.

(4) Optimization problem

In this research context, one objective is consid-ered for optimization to minimize the total intersec-tion control delay for both road users, minor and major approach. The optimization problem seeks an optimal solution, the optimal extension green time, which minimizes the total intersection control delay for both road users at an intersection. The provided algorithm was formulated as a linear constraint pro-gramming problem. For processing the obtained data MATLAB optimization solver was employed to algorithmically select the optimal signal timing fast and accurate. For this purpose, the fmincon function was selected due to the fact it finds the minimum of a constrained nonlinear multivariable function. It gives the constrained local minimum point, where the function value is smaller than at nearby points but possibly greaterthan other points in the search space36). The objective function was formulated as a convex optimizationproblem to min-imize delays in both major and minor approach with respect to the extension green time as Eqn. (10) de-picts. By giving different weight coefficientdefining the relative importance of major and minor approach delay, the contradicting objectives for both road us-ers were considered. The relative importance of the major approach delay coefficient was adjusted as double as the minor approach delay coefficient as

Eqn. (10) depicts. The extension green time for both approach road users is the optimization variable that can be changed to achieve the optimum solution. The lower and upper limit of the optimization varia-ble- the extension green time- was selected as 0 and 10 seconds respectively. On the other hand, the op-timization horizon was adjusted to one cycle length. The objective function is: ,( ) min major minor

i exf x D D g (10)

where: x: the optimal total intersection control delay for both road users, minor and major approach; α, β: coefficient defining the relative importance of major and minor approach delay. gi,ex: the optimal extension green time at intersection (i).

The relative importance coefficients (𝛼, 𝛽) were selected taking into the consideration the previous Works16). The previous findings revealed that the optimal values for (𝛼, 𝛽) are 2 and 1 respectively. The objective function is subjected to one constraint for the extension green time as follow: , ,0 , 10m ajor minor

i ex i exg g (11)

where: gi,ex

major, gi,exminor: the extension green times at inter-

section (i) for both road users, major and minor ap-proach.

As indicated above in the previous equations, it can be concluded that the pre-given parameters are: a) the time point when the green time of major and minor starts at an intersection (i), b) the time point when each individual vehicle on major and minor arrives at the stop line of an intersection (i), c) the total number of queuing vehicles in the formed queues in front of vehicle (j) at an intersection (i), the saturation flow rate at an intersection (i), d) the delay saved because of the extension green time in major and minor approach at an intersection (i), and e) the fixed green time of major and minor ap-proach at an intersection (i) respectively in seconds. The objective function was utilized in order to esti-mate the extension green time for both road users major and minor approach which minimizes the to-tal intersection control delay at an intersection (i). Finally, based on the obtained value of the extension green time that ensures the optimal delay for both road users, an appropriate decision is taken and re-turned back to VISSIM through a signal controller program to execute the phasing parameters. 5. RESULTS AND DISCUSSION

The overall results are summarized to draw up this

Fig.7 A layout shows the detectors’ positions.

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research conclusion. In order to examine the effi-ciency of the proposed system, a comprehensive comparison is executed among the travel time of the conventional existing intersections, the non-coordinated DLT, the fixed pre-timed coordination algorithm and the proposed real-time demand re-sponsive signal control algorithm. The proposed system is compared to the non-coordinated DLT, the fixed pre-timed coordination algorithm that were introduced by the authors in previous works9),10). In the previous work, the authors utilized the branch-and-bound algorithm to set up the optimal offset among the same studied intersections as a fixed-time coordination system. The authors emphasized that the optimal offset values were (5) seconds between ME and AA intersections and (7) seconds between AA and AT intersections10). However, in this study context, the extension green time was found within the range (2) to (8) seconds for the studied coordi-nated DLTs.

The attained outputs revealed prominent savings in average control delays along the studied corridor. The proposed algorithm could provide a smooth flow through the coordinated intersections. The simulation results emphasized the superiority of the coordinated DLTs over the existing intersections. All performance indices such as the total travel time, average delay, queue lengths, average stopped delay per vehicle, average speeds, and the average number of stops pointed to an undoubted improvement as shown in Table 7. The total travel time shown in Table 7 is the travel time of the all traveled vehicles for the whole directions along the studied network. On the other hand, the travel time for the eastbound and the westbound corridor in 10 minutes’ time in-

terval is shown in Fig.9. As a traffic continuity indi-cation, the average number of stops dropped signifi-cantly from 20.66 to 0.55, while the average stopped delay per vehicle decreased by -91.67% as it indi-cated in Table 7. Furthermore, the minor approach performance indices also referred to as significant improvement. The minor approach travel time, north and southbound travel time was obviously enhanced as shown in Fig.8. The proposed system not only decreasing the total travel time but also could pro-vide a stable travel time as a result of the smooth operation along the subjected corridor.

The travel time indices of the proposed real-time demand responsive signal control algorithm re-vealed anobvious enhancement of both west and eastbound of the studied corridor as Fig.8 depicts. The travel time through the three DLTs along the corridor could obviously prove the efficiency of the proposed algorithm comparing to the conventional existing intersections, the non-coordinated DLT and the fixed pre-timed coordination algorithm.

On the other hand, the average stopped delay per vehicle, the total travel time, average delay as well as queue lengths could improve indisputably. The average total travel time of both east and westbound approaches through the studied three intersections along the corridor are measured and evaluated to assess the coordination provided by the proposed algorithm. Although, the obvious enhancement of the corridor performance, it was dramatically influ-enced because of the heterogeneous traffic complex-ities. The heterogeneous conditions characteristics could obviously influence the coordination of the subjected corridor. The diverse dynamic properties and the non-lane base phenomenon, especially, up-stream the crossovers could affect the gap out time. The aggressive driving behavior upstream the cross-overs could obviously influence the flow headways upstream the detectors. As a result, the restricted statement conditions in the proposed algorithm, par-ticularly, the storage length condition, could limit the extension green times. Taking into consideration the storage length limitation for both road users, major and minor approach, could restrict the optimi-zation function. As a result of considering the stor-age length upstream the main intersections as well as upstream the crossovers, the statement conditions could be satisfied, especially, under heavy traffic conditions and cross ponding short storage lengths. The designed storage length is a key design factor to ensure the continuous functionality of the provided displaced left-turn crossovers.

Fig.8 Travel time comparison of ME minor approach.

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6. CONCLUSION

This article focused on developing a real-time de-mand-responsive signal control system to minimize the total delay for consecutive DLTs traffic signals under the heterogeneous traffic conditions. In this study, the heterogeneous conditions refer to the complex operating systems occur due to the diversi-ty in the operating performance characteristics per-tain to the heterogeneous traffic system compared to the ideal conditions. As a result of these complex operating systems, platoon dispersion occurred along the arterial corridors. In order to fulfill the traffic heterogeneity needs the proposed system, therefore, estimates the delay of each vehicle indi-vidually. Based on the dynamic optimization fun-damentals, the designed system endeavors to esti-mate the delay of each vehicle individually. This study objective was accomplished by developing a mathematical model, and then PTV-VISSIM as a simulator-based approach and MATLAB as a multi-paradigm numerical computing environment was used to implement the proposed model. Utilizing VISSIM-COM interface and MATLAB, an inter-process communication and dynamic object creation were executed to manipulate the simulated model. The proposed algorithm presented in this context was applied through a real-world practical realistic case study of three intersections in central Cairo, Egypt. This researchresults emphasized the superi-ority of the coordinated DLTs over the existing in-

tersections. The proposed algorithm can produce a smooth flow through the coordinated intersections as considerable gains in performance when com-pared with the conventional existing intersections, the non-coordinated DLT, the fixed pre-timed coor-dination algorithm. The performance indices re-vealed the obvious enhancement of the subjected corridor. However, the heterogeneous traffic com-plexities could influence the control algorithm.

7. FUTURE WORK Since the optimization of this study is formulated

individually at each intersection, it is recommended to examine the optimization where it is performed in all intersections simultaneously. As a future exten-sion of this work, it would be interesting to conduct a sensitivity analysis to estimate the optimal values the relative importance coefficient of major and mi-nor approach delays. Moreover, other evolutionary algorithms with different optimizers should be ex-amined to enhance the optimization problem out-comes.

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Table 7 Operational performance indices of the studied corridor.

Performance index Conventional intersections

Non-coordinated DLTs

Pre-timed coordinated DLTs

Real-time coordinated DLTs

Total travel time (h) 2,544.14 1,335.38 1,306.38 1,206.30 Avg. delay/veh. (s) 409.11 200.518 192.17 34.03

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Avg. No. of stops/veh. 20.66 2.88 2.43 0.55 Avg. stopped delay/veh. (s) 166.30 36.44 30.72 7.07

Fig.9 Travel time comparison along the studied corridor.

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(Received February 22, 2019)

(Accepted August 26, 2019)

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