OPTIMAL TRAFFIC SIGNAL STRATEGY FOR FUEL CONSUMPTION AND EMISSIONS CONTROL AT SIGNALIZED INTERSECTIONS

Tsai-Yun Liao Randy B. Machemehl

The University of Texas at Austin Department of Civil Engineering

Austin, TX, U.S.A.

1. INTRODUCTION

Fuel economy is an important issue because of both energy conservation and environmental concerns. Fuel consumption and emissions in ground transportation can be reduced by increasing vehicle standards and optimizing traffic system management. Although the Corporate Average Fuel Economy Act (CAFE) has propelled fuel economy of new vehicles from 14 miles per gallon per car (mpgpc) to 28 mpgpc in 1992, more than 60% of all vehicles are at least five years old. Due to their design and maintenance needs, these older vehicles consume far more fuel and produce more emissions than the new models and they compose the majority of the vehicle fleet. Therefore, motivated by the Clean Air Act Amendments, the USEPA (U.S. Environmental Protection Agency) has initiated a number of studies to reduce automobile fuel consumption and emissions.

This paper investigates vehicle fuel consumption and emissions at signalized intersections where signal control causes vehicles to slow, stop, and accelerate consuming excess fuel and producing more emissions. Most existing fuel consumption and emissions models for signalized intersections are developed based on instantaneous data, in which vehicle speed-acceleration-deceleration profiles are utilized. However, these models are unable to directly reflect the impact of traffic control measures, such as traffic signal timing on fuel consumption and emissions. Within this study, signal parameters, vehicle characteristics, and geometric conditions of signalized intersections are considered to estimate fuel consumption and emissions. Therefore, traffic signal strategy optimization can be developed through trade-offs of fuel consumption, delay, and other measures of effectiveness.

In Section 2, criteria for signal design are briefly discussed and the trade-offs between fuel consumption and delay are addressed. An Analytical Fuel Consumption Model is described in Section 3. Field tests producing vehicle speed and acceleration/deceleration profiles as well as FTP (Federal Test Procedure) data from the USEPA are combined to calibrate the fuel consumption model. In the numerical experiments, the AFCM and Webster's delay model are used to calculate optimal signal timing on fuel consumption and delay, and the results are compared with those from the TEXAS simulation model.

2. FUEL EFFICIENCY AND OTHER OBJECTIVES IN OPTIMAL TRAFFIC SIGNAL CONTROL

2.1 Fuel Consumption and Emissions at Signalized Intersections

Vehicle fuel consumption and emissions at or near street intersections are usually higher than on other street segments because the intersection frequently causes vehicles to slow, stop, and accelerate. Excessive fuel consumption at intersections is a major concern in traffic engineering and in transportation economics as it relates to the conservation of energy. Vehicle emissions at intersections can sometimes accumulate at certain points, and concentrations in the air can make occupancy of these areas potentially dangerous to human health.

Fuel consumption can be characterized by a time-dependent instantaneous rate with respect to location along the roadway. Fuel consumption for any vehicle traveling along the roadway actually depends on the vehicle type, vehicle condition, and traffic .conditions. Vehicle source emissions, which vary with respect to time and location along the roadway, are also addressed in this study since the estimation techniques are similar.

2.2 Trade-offs of Fuel Consumption and Delay

Several criteria have been applied to evaluate the effectiveness of traffic control measures in traffic networks, including minimizing delay, minimizing a combination of delay and numbers of stops, and minimizing fuel consumption. Among these criteria, delay is probably most widely used, but fuel consumption and emissions have become important measure of effectiveness (MOE) in urban networks where fuel consumption and emissions may be more critical than delay.

A number of studies (Brohard, 1986; Cohen and Euler, 1978; Bauer, 1975; Courage and Parapar, 1975; AI-Khalili and EI-Hakeem, 1984; AI-Khalili, 1985; Reljic et al., 1992) have focused on the impact of tratfic signals on fuel consumption and delay. In the 1980s, a fund was approved for California's Fuel Efficient Traffic Signal Management (FETSIM) program to work on reducing fuel consumption through traffic signal timing. California local governments have conducted a series of studies (Brohard, 1986) by using TRANSYT to investigate the impact of traffic signals on traffic control measures. They suggested that fuel savings can be improved by signal improvement. Cohen and Euler (1978) used NETSIM to evaluate fuel consumption for different signal timing plans and found that the optimal cycle lengths for minimizing delay and for minimizing fuel consumption are the same. However, the result is different from the studies of Bauer (1975) and Courage and Parapar (1975) where the results show that the optimum cycle length for minimizing fuel consumption is much longer than the cycle length for minimizing isolated intersection delay. Al-Khalili and EI-Hakeem (1984) designed a computer control system incorporating a fuel consumption model for urban traffic network fuel consumption minimization and found that minimization of fuel consumption can be achieved by optimal signal control. Later in 1985, A1-Khalili examined the offsets

of optimal cycle length green split on traffic management measures and commented that optimum performance is obtainable by manipulating the green split. Reljic et al. (1992) presented an optimization procedure for calculating the signal plan which minimizes a selected optimization criterion such as total delay, total number of stops, total cost of losses, and total fuel consumption at an intersection subject to certain constraints.

The important issue is how to determine the trade-offs of different criteria. Fuel consumption can be related to delay, stops, and travel time; however, the objective of signalized intersection delay minimization is not necessarily synonymous with fuel consumption minimization. In subsequent sections, experimental study and numerical results of signal cycle length versus different traffic flow cases are presented. Also, results of the optimal cycle length for minimizing fuel consumption and delay are discussed and compared.

3. ANALYTICAL FUEL CONSUMPTION MODEL (AFCM)

Most existing fuel consumption models for signalized intersections are developed based on instantaneous data, in which vehicle speed-acceleration-deceleration profiles are defined. In this study, the relationship between fuel consumption, traffic characteristics, and signal parameters is explicitly considered in the development of an alternative model called the Analytical Fuel Consumption Model (AFCM). Thus, the model can estimate the fuel consumption by directly considering the impact of signal control and traffic conditions.

3.1 Modeling Approach

In this model, the three major fuel consumption modeling elements are traffic characteristics, signal control strategies, and geometric configurations. Traffic characteristics, including vehicle arrival distributions, flow rates, turning percentages, vehicle desired speeds, and traffic mixes, are essential factors in determining roadway geometric configurations and traffic control measures. Pretimed signal control parameters include the phase sequence pattern, cycle length, and G/C ratios, which are based on roadway geometric conditions and traffic demands. Within this work, the number of phases is defined as P; cycle length is defined as C; and the G/C ratio for phase i is defined as GCi, V i ~ P. Thus, the effective green time and effective red time for an approach i can be defined as

gi = GCi. C [1] ri = C - Y~gj [2]

jeP\{i} Roadway geometric configurations include numbers of approaches and lanes, turning bay, inbound and outbound lane lengths, intersection size, and grades. The turning bay length is an important factor when turning movement demand is very high. Uphill grades cause vehicles to consume more fuel than level or downhill grades.

In addition to the three basic elements described above, travel time, vehicle speed, and acceleration/deceleration profiles are also important in developing a fuel consumption

model. Assume Vij and aij represent the velocity and acceleration (deceleration) of a vehicle i at time j, respectively. The total fuel consumption for the intersection can be expressed as:

N Ti ~ fij( Vii, aij) [3]

i=lj=t where f~j is the fuel consumption rate for vehicle i at time j, Ti is the total time for vehicle i in the considered system, and N is the total number of vehicles. Ti, the time for an individual vehicle in the system, can thus be expressed as:

TLi Ti = - - + Di [4] Vi

where Vi is the average speed without signal delay; Di is the delay caused by signal control; and TLi is the total traversed roadway length, which is expressed as:

TLi = LIBj + LOBk + LINTjk V i ~ Njk [5] where Njk is a subset of vehicles traveling from inbound approach j to outbound approach k; and lengths of inbound approach, outbound approach, and the intersection are expressed by LIBj, LOBk, and LINTjk, respectively.

Fuel consumption rate f~j, corresponding to individual vehicle speed and acceleration (deceleration) profiles, is critical in fuel consumption estimation. Individual vehicle profiles describing Vij and aij, were obtained through on-road measurement. Fuel consumption rates were determined through laboratory experiments. Consequently, fuel consumption at a signalized intersection can be estimated incorporating signal control strategies, traffic characteristics, travel time, and fuel consumption rates.

3.2 Vehicle Behavior on Fuel Consumption and Emissions

The Analytical Fuel Consumption Model (AFCM) is developed based on the relationship of the variables described above. The model only considers pretimed signalized intersections. The estimation of fuel consumption at signalized intersections is divided into three street segments (inbound approach, intersection, and outbound approach) in three cycle stages (effective red time, time from green onset to time to, where to is the time after the start of green until the queue is dissipated, and time from to to the end of the effective green).

The conceptual approach of estimating intersection fuel consumption assumes second-by- second individual vehicle data are available. At any instant in time, fuel consumption is the product of the number of vehicles and their corresponding fuel consumption rates as expressed by equation 3. For example, Figure 1 indicates fuel consumption at any instant in a signal cycle and cumulative fuel consumption on the inbound approach. During the effective red time (0 < t _< r ), vehicles decelerate and stop. Individual vehicle fuel consumption is decreasing with elapsed time because vehicles consume less fuel during deceleration and idle than during acceleration and cruise (Figure 1.a). However, the cumulative fuel consumption increases due to the increased number of vehicles (Figure

1.b). After the green starts, vehicles accelerate to pass the intersection. The most fuel is consumed with high acceleration rates at high speeds (Akcelik and Biggs, 1987). Therefore, fuel consumption at any instant in time increases with elapsed effective green time and remains stable when vehicles reach cruise speeds (Figure 1.a). Maximum fuel consumption, depends on speeds and acceleration rates and the vehicle discharge distribution, and could occur in the first stage ( r _< t < r + t0) or in the second stage of the effective green time (r + to -< t _< r + g = c ).

The curve in Figure 1.b illustrates the cumulative fuel consumption at any instant in time. The smooth curve in the effective green time (r _< t < r + g = c ), corresponding to typical speed profiles during on-road driving when initial speed is zero in Akcelik and Biggs' work, is a typical fuel consumption profile during the effective green time. It can be used to describe fuel consumption profiles for other cycle stages.

Descriptions of fuel consumption profiles for the intersection itself and the outbound approach can be derived in a similar way. Hence, the fuel consumption model can be developed and total fuel consumption can be estimated. A more detailed discussion is given in Liao and Machemehl (I 995).

4 EXPERIMENTAL STUDY AND SETUP

4.1 Experimental Design

In all experiments, a two by two intersection (one inbound and one outbound lane on each leg) is used. Two major factors considered in numerical experiments are traffic volume and cycle length. Low through high traffic volumes ranging from 300 to 750 vehicles per hour (vph) will be used to reflect different traffic conditions. Cycle length is varied from 20 to 180 seconds with an interval of 10 seconds. Each cycle length has 50%-50% green splits and 3 second clearance intervals.

In these experiments, results from the analytical model and the TEXAS simulation model are compared across different cycle lengths. The Webster delay model and the AFCM are used to estimate delay and fuel consumption, respectively.

4.2 The TEXAS Simulation Model

TEXAS model (Traffic EXperimental and Analytical Simulation model) is a micro simulation model developed at The University of Texas at Austin, U.S.A. In the TEXAS simulation model, an emissions and fuel consumption processor, EMPRO (Lee et al, 1983), provides instantaneous fuel consumption and emissions models for an intersection. It uses instantaneous vehicle speed and acceleration/deceleration with respect to time and location along the road section provided by the simulation processor of the TEXAS model.

4.3 AFCM and Webster ' s Delay Model

AFCM is used to estimate aggregate fuel consumption with respect to different traffic signal timing. The aggregate fuel consumption is estimated by fuel consumption rates fij along street segment k. Total fuel consumption at street segment k (TFk) thus is estimated by

N Ti TFk = X ~.fij(Vij, aij) [6]

i=lj=l where k is equal to 3 in the AFCM. Finally, total fuel consumption for an intersection can be estimated by accumulating total fuel consumption at street segments and an optimal cycle length for minimizing total fuel consumption can be derived.

Webster (1958) derived optimal cycle time using his empirically developed delay equation. For delay minimization, optimal cycle time is given by the following equation:

1.5L+5 Co - - - seconds I - Y [7]

where, Y: the sum for all signal phases of the highest ratios of flow to saturation flow, L: n l + R ,

n: the number of phases, 1: the average lost time per phase (excluding all-red times), and R: all-red times.

4.4 Data Col lect ion and Analys i s

In order to provide empirical evidence in this work, a field study was conducted to collect travel time, speed, and acceleration/deceleration profiles at various points between two intersections. The site is a medium-volume six-lane urban street in Austin, Texas. The portion of the road tested starts at an intersection with a medium volume street and continues unconstrained by traffic control for approximately 1700 feet downstream. The data was collected through videotaping from the 32nd floor of a building which is approximately 1200 feet from the test section.

Speed distribution for vehicles departing from the stop line at a signalized intersection is plotted in Figure 2. To specify major and significant factors which dominate traffic behavior at signalized intersections, analysis of variance (ANOVA) is used to identify the effect of prevailing traffic conditions, signal control methods, and geometric configurations on vehicle acceleration/deceleration and speed profiles. Fuel consumption and emissions data from the FTP revised by USEPA are used to calibrate fuel consumption and emissions based on speed and acceleration/deceleration values. Since more fuel is consumed and more emissions are released when speed and acceleration rates are high, vehicle profiles downstream from the intersection are more critical for analyzing fuel consumption and emissions than for delay.

5. RESULTS

Since vehicle characteristics and traffic control measures have different impacts on delay and fuel consumption, the optimal strategies for setting signals might be different. Based on the results of the TEXAS model, Webster's delay equation, and the AFCM model, Table 1 shows optimal cycle lengths for delay and fuel consumption for various volumes from 300 vph to 750 vph.

Volume (vph)

Table 1. Optimal Cycle Lengths vs. Volume for Fuel Consumption and Delay Minimization

Optimal Cycle Lengths for Total Delay (seconds) TEXAS Model Webster's Model 20 20 20 20 40 30

40 50 60 60 80

Optimal Cycle Lengths for Fuel Consumption (seconds)

~ TEXAS Model AFCM 300 20 30 400 30 50 500 40 60 600 40 60 80 700 70 90 750 70 100

The results from Table 1 show that the optimal cycle lengths for minimization of delay and fuel consumption are not the same. It also indicates that for signal setting there might be a trade-off between delay and fuel consumption. The trade-off involves the value of time and the value of fuel. Figures 3 through 6 depict the relationship of optimal cycle length and delay and fuel consumption, respectively. Optimal cycle length increases with respect to volume. It indicates that longer cycle length is preferred in a high volume situation. Furthermore, the optimal cycle lengths for fuel consumption minimization are higher than for delay minimization. For both fuel consumption and delay minimization, the analytical models tend to require higher cycle lengths compared to the TEXAS simulation model.

Also, the optimal cycle lengths from AFCM are higher than those from the TEXAS model. One major reason might be that the fuel consumption data in the TEXAS model was calibrated and tested in 1975, therefore, the effects of speed and acceleration/deceleration on fuel consumption could not be captured for new vehicles.

Delay is a complex measure and only reflects the possible traffic situations on upstream from the intersections (inbound approach) due to the signal control. However, both inbound and outbound approaches are important for estimating intersection fuel consumption. According to Liao and Machemehl (1995), the total fuel consumption appears higher on outbound approaches than inbound approaches because there are more speed and acceleration fluctuations.

From the experimental results, optimal cycle lengths for fuel consumption minimization are 50% higher than delay minimization. Figures 5 and 6 show optimal cycle lengths versus traffic volume for fuel consumption and delay minimization for both simulation and

analytical models. It indicates that higher cycle lengths are needed for minimizing fuel consumption although there might be some instances where the cycle lengths are about the same as the TEXAS simulation results.

The analytical methodology for minimizing fuel consumption can be derived through the same approach for minimizing delay. Figure 7 depicts fuel consumption as a function of signal cycle length for the 600 vph case. Since the curve is convex, an optimal cycle length can be identified. Generally speaking, optimal cycle lengths for fuel consumption minimization are much higher than for delay minimization (80 vs. 40 seconds). Vehicle emissions, which behaves much like fuel consumption, could be reduced through long cycle lengths under high volume situations.

A common issue, therefore, is how to determine the trade-otis between fuel consumption, emissions, and delay. Fuel economy is an important issue due to both energy conservation and environmental concerns. Vehicle fuel consumption and emissions at or near street intersections are usually higher than on other street segments due to frequent vehicle deceleration, stops, and acceleration. Fuel consumption and emissions at intersections should be included in designing signal strategies.

6. CONCLUSION

In this paper, several issues regarding signal control are discussed, and a new fuel consumption model is proposed to estimate fuel consumption at signalized intersections. Field data as well as FTP data are collected and used in calibrating the AFCM model.

The investigation in this paper seeks fundamental insights into optimal traffic signal strategy for fuel consumption and emissions minimization. The numerical analysis, the results indicate that fuel consumption and emissions are major concerns at intersections and thus they might be important traffic signal design objectives. Differences between optimal cycle lengths for fuel consumption and delay minimization are significant and generally longer cycle times are needed for fuel consumption minimization. Furthermore, to reduce fuel consumption and emissions, longer cycle lengths are preferred for high volume situations.

ACKNOWLEDGMENTS

This paper is based on work supported by the U.S. Department of Transportation through the Southwest Region University Transportation Center under contract UT#96-0145 (96826) titled "A Fuel Consumption Model for Optimizing Intersection Traffic Control". Of course, the authors are solely responsible for the contents of this paper.

REFERENCES

Akcelik, R. and Biggs, D.C. (1987). Acceleration Profile Models for Vehicles in Road Traffic, Transportation Science, Vol. 21, No. 1, pp. 36-54.

A1-Khalili, A.J. and E1-Hakeem, A.K. (1984). Computer Control System for Minimization of Fuel Consumption in Urban Traffic Network. 1EEE, New York, U.S.A., pp. 249-254.

A1-Khalili, A.J. (1985). The Optimum Green Split of a Cycle Time, 1985 1EEE Transactions on Systems, Man, and Cybernetics, Vol. SMC-15, No. 15.

Bauer, C.S. (1975), Some Energy Considerations in Traffic Signal Timing, Traffic Engineering, Vol. 45(2), pp. 19-25.

Biggs, D.C. (1988). ARFCOM - Models for Estimating Light to Heavy Vehicle Fuel Consumption, Australian Road Research Board, Research report ARR No. 152.

Brohard, T. (1986). Signal Improvements Save Time and Fuel, Public Works, Vol. 117, No. 2, pp. 52-53.

Cohen, S.L. and Euler, G. (1978). Signal Cycle Length and Fuel Consumption and Emissions, Transportation Research Record, No 667, pp. 41-48.

Courage, K.G. and Parapar, S.M. (1975). Delay and Fuel Consumption at Traffic Signals, Traffic Engineering, Vol. 45(11), pp. 23-27.

Johns, L.S. and Blair, P.D. (1991). Improving Automobile Fuel Economy: New Standard, New Approaches, U.S. Congress, Office of Technology Assessment, OTA-E-504 (Washington, DC: U.S. Government Printing Office).

Lee, F.P:, Lee, C.E., Machemehl, R.B., and Copeland, C.R.(1983). Simulation of Vehicle Emissions at Intersections, Center for Transportation Research, the University of Texas at Austin, U.S.A., research report 250-1.

Liao, T.Y. and Machemehl, R.B (1995) Fuel Consumption Based Optimal Traffic Signal Timing, 37th TRF Annual Meeting Proceedings, pp. 527-544.

Reljic, S., Kamhi-Bama, M. and Stojanovic, S. (1992). Multicriteria Signal Plan Choice at an Isolated Intersection, Mathematics in Transport Planning and Control (Institute of Mathematics & its Applications Conference Series 38), pp. 81-93.

Webster, F. V. (1958). Traffic Signal Setting, Her Majesty's Stationery Office, London, Road Research Technical Paper No. 39.

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Figure 1.a Fuel Consumption at any Instant in a Cycle Time

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Figure 1 .b Cumulative Fuel Consumption at any Instant in a Cycle Time

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Figure 2. Speed vs. Time Interval from the Start o f Green at a Signalized Intersection

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F igure 3. Opt imal Cycle Lengths vs. Traff ic Volume for Delay

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F igure 4. O p t i r r ~ Cyele Lengths vs, Traff ic Volume for Fuel Consumpt ion

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Figure 5. Optimal Cycle Lengths vs. Traffic Volume for Fuel Consumption and Delay Minimization - TEXAS Model

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Figure 6. Optimal Cycle Lengths vs. Traffic Volume for Fuel Consumption and Delay Minimization - Analytical Model

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Figure 7 Fuel Consumption and Total Delay as a Function of Signal Cycle Length