CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 51, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Tichun Wang, Hongyang Zhang, Lei Tian 
Copyright © 2016, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-43-3; ISSN 2283-9216 

A Real-time Bus Traveling Speed Optimization Model for 
Reducing bus delay and CO2 Emission in Connected Vehicle 

Environment  
Wei Wua*, Qianru Chena, Youfang Wanga, Yi Zhangb 
a Key Laboratory of Highway Engineering of Ministry of Education, Changsha University of Science & Technology, 
Changsha 410114, Hunan, China 
b School of Naval Architecture Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China 
jiaotongweiwu@csust.edu.cn 

Public transportation plays an important part in sustainable motorization and urbanization. This research 
presents a novel bus speed operation strategy to reduce bus delay and CO2 emission within connected 
vehicle environment. Most previous work merely focuses on optimization of signal timings to decrease bus 
signal delay by assuming that the speed of buses is given as a constant input and the acceleration and 
deceleration processes of buses can be neglected. This paper explores the benefits of bus speed control 
strategy to minimize the total cost that includes bus signal delay and bus travel delay caused by adjusting 
speed due to frequent stops and intense driving. A set of formulations are developed to capture the benefits of 
bus speed control. Experimental analyses have shown that the proposed model outperforms the traditional 
control strategy in terms of reducing average bus delay and CO2 emission. 

1. Introduction 

In 2010, congestion caused urban Americans to travel 4.8 billion hours more and to purchase an extra 1.9 
billion gallons of fuel for a congestion cost of $101 billion. Vehicles are responsible for almost all of the Carbon 
Monoxide emissions, for about the 75% of the Hydrocarbon emissions and volatile organic compounds, and 
for about the 65% of the Nitrogen Oxide emissions (Tzirakis et al., 2006). Traffic congestion and vehicle 
emissions have emerged as a pressing issue during the process of motorization and urbanization. An 
increasing number of researchers have recognized that developing public transportation and improving the 
level of service of buses are potentially sustainable strategies to relieve traffic-related problems (Khandker et 
al., 2011; Bigerna and Polinori, 2015; Chen et al., 2014; Shi et al., 2011). 
In order to improve the level of service of buses, Transit signal priority (TSP) is a promising option (Hickman, 
2001, Zhao et al., 2006, Xuan et al., 2011; Daganzo, 2009). However, most existing models for transit signal 
priority are developed on the basis of the assumption that the travel speed of buses is constant and given as 
exogenous input, the acceleration and deceleration processes of buses can be neglected (Koehler and Kraus, 
2010; Ma et al., 2013; Liu et al., 2011). Based on these assumptions, signal settings are determined to 
minimize the delay (Zeeshan and Bruce, 2011; Xu et al., 2010). Moreover, most of TSP methods only try to 
minimize the delay, but the fuel consumptions, pollution emissions are also the critical parameters to measure 
the level of service of transit system. These parameters are affected by the driving patterns which mainly 
depend on accelerations and decelerations of buses. 
Technical difficulties in reliable bus location, speed, acceleration detection and real time communications 
between buses and intersection controllers may have been obstacles to use holding and speed control in 
transit system. But with the development of the wireless communication technology, vehicle infrastructure 
integration environment have progressed significantly and changed the way we operate the transit systems 
(Abu-Lebdeh and Chen, 2010).  
Under connected vehicle environment, buses and the intersection controller can communicate with each other 
through wireless communication technology like Dedicated Short Range Communication (DSRC). Buses 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1651034

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Wu W., Chen Q.R., Wang Y.F., Zhang Y., 2016, A real-time bus traveling speed optimization model for reducing bus 
delay and co2 emission in connected vehicle environment, Chemical Engineering Transactions, 51, 199-204  DOI:10.3303/CET1651034 

199



automatically send the real time information like bus location, speed and acceleration to the controller. Then 
the intersection controller will issue driving order to buses such as when and where to accelerate, decelerate, 
start to move, begin to stop and so on, based on the signal timing and traffic conditions. 
In response to aforementioned concern, this research focuses on developing a bus speed control strategy to 
improve the level of service of transit systems within connected vehicle environment.  

2. General notations 

The notations used hereafter are summarized in Table 1. 

Table 1: List of key variables used in the formulations 

Notations  Explanation 
𝑎𝑚𝑖𝑛, 𝑎𝑚𝑎𝑥  The maximum and minimum accelerations for the bus (m/s2) 
𝑎𝑡  Acceleration/ deceleration of buses(m/s2) 
𝐶𝑎  Acceleration cost 
𝐶0  The cycle length of the signal timing (s) 
𝐷𝑏𝑢𝑠  Bus delay cost 
𝑑𝑠  Bus signal delay(s) 
𝑑𝑡   Bus travel delay(s) 
𝐿  The distance from bus stop to the intersection (m) 
𝑙𝑣  The average vehicle length (m) 
𝑞  The constant arrival flow rate ( #. of vehs/s) 
𝑠  Saturation flow rate ( #. of vehs/s) 
𝑇𝑐  Time for bus to close the door at the bus stop and ready to move(s) 
𝑇𝑔  Time for green light starts (s) 
𝑇𝑗  Time for buses stopped by red (s) 
𝑇𝑠  Time for bus to clear the intersection(s) 
𝑇𝐴𝐵 , 𝑇𝐵𝐶 ,  𝑇𝐶𝐴 The boundary point for scenario A, B, and C (s) 
𝑡𝑔  Green time duration  (s) 
𝑡0_𝑣  Time duration for a bus accelerates from zero to bus traveling speed(s) 
𝑉𝑏𝑢𝑠  Bus traveling speed (m/s) 
𝑉𝑚𝑖𝑛, 𝑉𝑚𝑎𝑥  The maximum and minimum bus speed limits (m/s) 

3. Problem description 

The fundamental idea for bus speed control can be illustrated in Figure 1. When the red light begins, a queue 
will be formed and accumulated until the green light is turned on. Trajectory 1 represents the common bus 
operation strategy without speed control. In this case, the bus departs from the bus stop at the time 𝑇𝑐 , 
accelerates to average bus speed 𝑉𝑎 , then joins in the queue formed by red. Trajectory 2 stands for the bus 
operation strategy with speed control. In this case, the bus also departs from the bus stop immediately at 𝑇𝑐, 
but it will accelerate to a relatively lower speed 𝑉𝑙 , then it can clear the intersection without stopping again.  

4. Objective function 

The objective function in this study is to minimize the total cost of the buses, including both delay cost and 
acceleration cost. It can be specified as 

min (𝐶𝑎 + 𝛽𝐷𝑏𝑢𝑠)       (1) 

Where 𝐶𝑎 is the acceleration cost caused by frequent stops and vigorous accelerations/ decelerations; 𝐷𝑏𝑢𝑠 is 
the cost caused by bus delay; 𝛽 is the weighting factor. In this paper, 𝐶𝑎 can be specified as 

𝐶𝑎 = ∑ √𝑎𝑡
2𝑇𝑠

𝑡=𝑇𝑐
  (2) 

Where 𝑎𝑡  is the second by second acceleration or deceleration;  𝑇𝑐 is the time for bus to close the door at the 
bus stop and ready to move;  𝑇𝑠 is the time for bus to clear the intersection. 
Bus delay is consisted of three parts and can be calculated by the following equation: 

𝐷𝑏𝑢𝑠 = 𝑑𝑡 + 𝑑𝑠  (3) 

200



Where 𝑑𝑡  is the bus travel delay caused by travelling with a lower speed; 𝑑𝑠 is the signal delay caused by red 
light. 

 
 

Figure 1. Space-time diagram of two different bus operations 

5. Constraints 

The operation of the system begins with the bus closing the door and ready to depart from the stop at the 
current time 𝑇𝑐 which is measured relative to the start of the cycle. As shown in Figure 2, bus departure time is 
divided into five parts, 𝐴1, 𝐵, 𝐶 and 𝐴2. We generated three separate scenarios depending on 𝑇𝑐: 

 Scenario A, when 0 < 𝑇𝑐 < 𝑇𝐴𝐵  or 𝑇𝐶𝐴 < 𝑇𝑐 < 𝐶0  (including 𝐴1 and 𝐴2); 
 Scenario B, when 𝑇𝐴𝐵 ≤ 𝑇𝑐 < 𝑇𝐵𝐶 ; 
 Scenario C, when 𝑇𝐵𝐶 < 𝑇𝑐 < 𝑇𝐶𝐴; 

 

Figure 2: Scenarios for the buses depart from the bus stop 

5.1  Scenario A 
In this scenario, buses could not clear the intersection without stopping by speeding up. This indicates that the 
bus will experience a stop due to the red light. Buses will depart immediately and then accelerate to 𝑉𝑏𝑢𝑠 . 
The time duration for the bus accelerating from zero to  𝑉𝑏𝑢𝑠  can be computed as: 

 𝑡0_𝑣 = 𝑉𝑏𝑢𝑠 /𝑎𝑏𝑢𝑠  (4) 

Time(s)

D
is

ta
nc

e(
m

)
B

us
 S

to
p

aV

rt gt

lV
Trajectory 1 

Trajectory 2 

Accum
ulatio

n of 

queue
Di

ss
ipa

tio
n 

of 
qu

eu
e

c
T

Time(s)

D
is

ta
nc

e(
m

)
B

us
 S

to
p

rt g
t

B C D A2A1

ABT

maxV maxV

BCT CAT

g
T

0
CqT mT

minV

201



The boundary of 𝑉𝑏𝑢𝑠 and 𝑎𝑏𝑢𝑠 can be specified as: 

𝑉𝑚𝑖𝑛 ≤ 𝑉𝑏𝑢𝑠 ≤ 𝑉𝑚𝑖𝑛  (5) 

𝑎𝑚𝑖𝑛 ≤ 𝑎𝑏𝑢𝑠 ≤ 𝑎𝑚𝑎𝑥   (6) 

Then the signal delay caused by red light 𝑑𝑠 can be computed as: 

𝑑𝑠 = 𝑇𝑠 − 𝑇𝑗  (7) 

With respect to bus travel delay𝑑𝑡   , it is caused by travelling with a lower speed, which can be computed as: 

𝑑𝑡 =
3𝑉𝑏𝑢𝑠

2𝑎𝑏𝑢𝑠
+

𝐿

𝑉𝑏𝑢𝑠
−

𝐿

𝑉𝑚𝑎𝑥
  (8) 

With regard to 𝐶𝑎 , In scenario A, the travel speed for the bus will accelerate from zero to 𝑉𝑏𝑢𝑠  after the 
departure from the bus stop. Then the bus will decelerate from 𝑉𝑏𝑢𝑠 to zero due to the red light. After the green 
light is turned on, the speed of the bus will accelerate from zero to 𝑉𝑏𝑢𝑠 again to clear the intersection. In this 
scenario, the cost  𝐶𝑎 , which is the cost caused by frequent stops and vigorous accelerations and 
decelerations, can be specified as: 

𝐶𝑎 = ∑ √𝑎𝑡
2𝑇𝑠

𝑡=𝑇𝑐
= 3𝑉𝑏𝑢𝑠  (9) 

5.2 Scenario B 
In scenario B, buses can clear the intersection without stopping if speed control is implemented. In this 
scenario, the movements of buses are consisted of three steps. The first step is that buses depart immediately 
and accelerate to a lower speed. The second step is that buses proceed with a constant velocity. Accelerating 
to a higher speed and following the last vehicle in the queue to clear the intersection is the last step. To this 
end, the constant velocity follows that: 

𝑉𝑏𝑢𝑠 = ((𝑠 − 𝑞)𝐿 − 𝑇𝑔 𝑠𝑞𝑙𝑣 )/(𝑇𝑔 𝑠 − 𝑇𝑐 (𝑠 − 𝑞))     (10) 

Then the bus travel delay in this scenario can be specified as 

𝑑𝑡 =
𝑉𝑏𝑢𝑠

2𝑎𝑏𝑢𝑠
+

𝐿

𝑉𝑏𝑢𝑠
−

𝐿

𝑉𝑚𝑎𝑥
  (11) 

There is no signal delay in this scenario, With regard to 𝐶𝑎 , there is only a complete acceleration process, 
thus can be specified as: 

𝐶𝑎 = ∑ √𝑎𝑡
2𝑇𝑠

𝑡=𝑇𝑐
= 𝑉𝑏𝑢𝑠  (12) 

5.3 Scenario C 

In scenario C, buses can clear the intersection without stopping. The time of the boundary point 𝑇𝐵𝐶  and 𝑇𝐶𝐴 
can be computed as 

𝑇𝐵𝐶 =
𝑇𝑔𝑠

𝑠−𝑞
− (𝐿 −

𝑇𝑔𝑠𝑞𝑙𝑣

𝑠−𝑞
)/𝑉𝑚𝑎𝑥  (13) 

𝑇𝐶𝐴 = 𝐶0 −
𝐿

𝑉𝑚𝑎𝑥
−

𝑉𝑚𝑎𝑥

2𝑎𝑚𝑎𝑥
  (14) 

In this scenario, the bus delay only contains travel delay, which can specified as 

𝑑𝑡 =
𝑉𝑏𝑢𝑠

2𝑎𝑏𝑢𝑠
+

𝐿

𝑉𝑏𝑢𝑠
−

𝐿

𝑉𝑚𝑎𝑥
   (15) 

𝐶𝑎  can be specified as 

𝐶𝑎 = ∑ √𝑎𝑡
2𝑇𝑠

𝑡=𝑇𝑐
= 𝑉𝑏𝑢𝑠    (16) 

6. Performance analysis 

In order to illustrate the applicability of the proposed model, this study employs an example intersection for 
numerical tests. The following parameters are assumed: 𝐶0 = 70𝑠  ,  𝑠 = 0.5 𝑣𝑒ℎ/𝑠 , 𝑡𝑔 = 35𝑠 , 𝑞 = 0.15 𝑣𝑒ℎ/
𝑠, 𝑙𝑣 = 6𝑚, 𝐿 = 200𝑚, 𝛽 = 1, 𝑡𝑔 = 35𝑠, 𝑉𝑚𝑖𝑛 = 5.6 𝑚/𝑠, 𝑉𝑚𝑎𝑥 = 11.1𝑚/𝑠 , 𝑎𝑚𝑖𝑛 = −3 𝑚/𝑠, 𝑎𝑚𝑎𝑥 = 3 𝑚/𝑠. 

202



With the above parameters, the boundary for each scenario can be specified as 𝑇𝐴𝐵 = 22.3𝑠, 𝑇𝐵𝐶 = 36.0, 𝑇𝐶𝐴 =
50.1𝑠. 
Considering four buses with their door closing time located in each of four time span defined by 𝑇𝑐 , Table 2 
shows the optimization and comparison results from the proposed model for the four buses. 

Table 2:  Results for buses to depart at different time 

𝑇𝑐(s) Scenario 𝐷𝑏𝑢𝑠(s) 𝐶𝑎 Vmax(m/s) CO2 emission(g) Stopped by red light 
3.0 𝐴(𝐴1) 24.5 33.3 11.1 66 Yes 

60.0 𝐴(𝐴2) 33.0 33.3 11.1 72 Yes 
28.0 𝐵 11.5 11.1 7.1 45 No 
45.0 C 1.85 11.1 11.1 36 No 

 
We can reach the following findings from Table 2: 
 After buses depart from the bus stop, they will be stopped by red light again only in scenario A. In other 

scenario, buses will clear the intersection without stopping.  
 The acceleration cost 𝐶𝑎 in scenario A is three times bigger compared with scenario B and C. It is 

because in scenario B and C, it only contains one full acceleration process after buses depart from the 
bus stop. But in scenario A, the bus will experience one more acceleration process and one more 
deceleration process because of the stop caused by red light. This result validates that the proposed 
parameter 𝐶𝑎 can be employed to represent the cost caused by frequent stops and vigorous 
accelerations and decelerations. 

 By speed control, buses can avoid unnecessary stops thus reduce CO2 emission. 
Let 𝑡𝑤 denotes the time interval in which buses close the door, and then they can clear the intersection without 
stopping. 𝑡𝑙  represents the interval length of 𝑡𝑤; 𝑡𝑠 represents the service rate for bus in the whole cycle. Then, 

𝑡𝑠 = 𝑡𝑙 𝐶0⁄   (17) 

Table 3 presents the results of bus service rate in different cases. The results clearly show that proposed 
method can provide 41.6% service rate for bus clearing the intersection without stopping and higher than the 
service rate under traditional control method. 

Table 3:  Results of the bus service rate for different cases 

Cases 𝑡𝑤 𝑡𝑙  𝑡𝑠 
traditional control method [36.0,50.1] 14.1 20.1% 

proposed method [21.0,50.1] 29.1 41.6% 

7. Conclusion 

This paper presents a novel approach for optimization of bus travelling speed to reduce bus delay and  CO2 
emission. The objective of the proposed model is to minimize the total cost that includes bus signal delay and 
bus travel delay caused by adjusting speed and acceleration cost due to frequent stops and intense driving. A 
set of formulations are developed to capture explicitly the interaction between bus speed and signal timing. 
Experimental analyses have shown that the proposed integrated operational model outperforms the traditional 
control in terms of reducing average bus delay and CO2 emission.  
Note that this paper has presented preliminary theoretical analysis and evaluation results for the proposed 
model. More extensive numerical experiments or field tests will be conducted to assess the effectiveness of 
the proposed model under various traffic and transit demand patterns. Another possible extension of this study 
is to optimize signal timings, holding time duration and recommended bus speed together to further improve 
the level of service of buses. 

Acknowledgments  

The research has been supported by the National Natural Science Foundation of China under Grant No. 
51408065 and No. 51308336, the Natural Science Foundation of Hunan Province under Grant No. 
2015JJ6001, the Research Foundation of Education Bureau of Hunan Province under Grant No. 14B003, and 
the Open Fund of the Key Laboratory of Highway Engineering of Ministry of Education (Changsha University 
of Science & Technology) under Grant No. kfj140205. 
 

203



Reference 

Abu-Lebdeh G., Chen H., 2010, Exploring the potential benefits of Intellidrive-enabled dynamic speed control 
in signalized networks, Compendium of papers CD-ROM of 89th Transportation Research Board Annual 
Meeting, National Research Council, Washington, D.C., the United States of American. 

Bigerna S., Polinori P., 2015, Willingness to pay and public acceptance for hydrogen buses: a case study of 
Perugia. Sustainability, 7(10):13270-13289. 

Chen X., Wang X., Zhang H., Li J., 2014, The diversity and evolution process of bus system performance in 
Chinese cities: an empirical study. Sustainability, 6(11):7751-7767. 

Daganzo C., 2009, A headway-based approach to eliminate bus bunching: systematic analysis and 
comparisons, Transportation Research Part B: Methodological, 43(10):913-921. 

Hickman M., 2001, An analytic stochastic model for the transit vehicle holding problem. Transportation 
Science, 35(3):215-237. 

Khandker M., Nurul H., Lina K., Tazul I., 2011, Model of personal attitudes towards transit service quality. 
Journal of Advanced Transportation, 45(4): 271-285. 

Koehler L., Kraus W., 2010, Simultaneous control of traffic lights and bus departure for priority operation. 
Transportation Research Part C: Emerging Technologies, 18(3):288-298. 

Liu Y., Chang G., Yu J., 2011, An integrated control model for freeway corridor under non-recurrent 
congestion. IEEE Transactions on Vehicular Technology, 60(4)1404-1418. 

Ma, W., Liu, Y., Yang, X., 2013, A dynamic programming approach for optimal signal priority control upon 
multiple high-frequency bus requests. Journal of Intelligent Transportation Systems, 17(4):282-293. 

Shi J., Wu Z., Jin J., 2011, Reform Beijing to a public transit oriented city – from the view of transportation 
equity. Journal of Advanced Transportation, 45(2):96-106. 

Tzirakis E., Pitsas K., Zannikos F., Stournas S., 2006, Vehicle emissions and driving cycles: comparison of the 
athens driving cycle (ADC) with ece-15 and european driving cycle (EDC). Global NEST Journal, 8(3): 
282-290. 

Xuan Y., Argote J., Daganzo C., 2011, Dynamic bus holding strategies for schedule reliability: optimal linear 
control and performance analysis. Transportation Research Part B: Methodological, 45(10):1831-1845, 
2011. 

Xu H., Sun J., Zheng M., 2010, Comparative analysis of unconditional and conditional priority for use at 
isolated signalized. Journal of Transportation Engineering, 136(12):1092-1103. 

Zeeshan R., Bruce R., 2011, Analytical method for estimating the impact of transit signal priority on vehicle 
delay. Journal of Transportation Engineering, 137(8):589-600. 

Zhao J., Dessouky M., Bukkapatnam S., 2006, Optimal slack time for schedule-based transit operations, 
Transportation Science, 40(4):529-539.  

 

204