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Transportation Research Record
OPTIMAL DESIGN OF BUS ROUTES FOR DIFFERENT VEHICLE TYPES
CONSIDERING VARIOUS DRIVING REGIMES AND ENVIRONMENTAL FACTORS
--Manuscript Draft--
Full Title: OPTIMAL DESIGN OF BUS ROUTES FOR DIFFERENT VEHICLE TYPES
CONSIDERING VARIOUS DRIVING REGIMES AND ENVIRONMENTAL FACTORS
Abstract: As a major part of public transportation system, bus transit has been regarded as an
effective mode to alleviate the traffic congestion and solve vehicle emission problem.
The performance of bus transit system depends largely on its design of proper stop
locations. In this reasearch, we proposed a multi-period continuum model (peak hour
and off-peak hour) to optimize the design of a bus route for four different vehicle types
(i.e., supercharge bus, Compressed Natural Gas (CNG) bus, Lithium-ion battery bus,
and diesel bus) considering driving regimes and the pollutant cost. Inter-stop driving
regimes, including acceleration, cruising, coasting, and deceleration, are explicitly
introduced into the optimization to determine whether and how the coasting regime
should be undertaken in the tradeoff between vehicle’s commercial speed and the
operating cost. The comparison for the cost effectiveness of each alternative has been
investigated in a life span with respect to different vehicle types. The method has been
implemented in the real-word bus route 7 in Yaan City (China). The numerical
experiments suggest that through optimization, the total system cost has been saved
by more than 50%. The results of continuum model are validated by the comparison
with the discretized results, and the outcomes are closely located in neighborhood
(with error less than 3%). The life-cycle cost of four vehicle types is finally analyzed,
and the result indicates that due to the high purchase prices, it’s difficult for clean-
energy buses to outperform conventional buses in a life cycle (normally 8 years),
unless with subsidies provided.
Manuscript Classifications: Public Transportation Planning and Development AP025; Model; Transit; Transit
Management and Performance AP010; Planning; Public Transportation
Manuscript Number:
Article Type: Publication & Presentation
Order of Authors: Yue Su
Xiaobo Liu
Guo Lu
Wenbo Fan
Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation
OPTIMAL DESIGN OF BUS ROUTES FOR DIFFERENT VEHICLE TYPES
1
CONSIDERING VARIOUS DRIVING REGIMES AND ENVIRONMENTAL FACTORS
2
3
4
5
Yue Su
6
School of Transportation and Logistic, Southwest Jiaotong University
7
No.999, Xi’an Street, ChengDu, SiChuan, China, 611756
8
Tel: +86-13908214147 Email: yuesu@my.swjtu.edu.cn
9
10
Xiaobo Liu, Ph.D.
11
School of Transportation and Logistic, Southwest Jiaotong University
12
No.999, Xi’an Street, ChengDu, SiChuan, China, 611756
13
Tel: +86-13688002461 Email: xiaobo.liu@swjtu.cn
14
15
Guo Lu
16
School of Transportation and Logistic, Southwest Jiaotong University
17
No.999, Xi’an Street, ChengDu, SiChuan, China, 611756
18
Tel: +86-18620366066 Email: 496069232@qq.com
19
20
Wenbo Fan, Ph.D., Corresponding Author
21
School of Transportation and Logistic, Southwest Jiaotong University
22
No.999, Xi’an Street, ChengDu, SiChuan, China, 611756
23
Tel: +86-13658082981 Email: wbfan@swjtu.edu.cn
24
25
26
Word count: 6,127 words text + 5tables x 250 words (each) = 7,377words
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Submission Date: August 1, 2018
34
Manuscript Click here to download Manuscript TRB Paper_SU V6.docx
Su, Liu, Lu, Fan 2
ABSTRACT
1
As a major part of public transportation system, bus transit has been regarded as an effective mode
2
to alleviate the traffic congestion and solve vehicle emission problem. The performance of bus
3
transit system depends largely on its design of proper stop locations. In this reasearch, we proposed
4
a multi-period continuum model (peak hour and off-peak hour) to optimize the design of a bus
5
route for four different vehicle types (i.e., supercharge bus, Compressed Natural Gas (CNG) bus,
6
Lithium-ion battery bus, and diesel bus) considering driving regimes and the pollutant cost.
7
Inter-stop driving regimes, including acceleration, cruising, coasting, and deceleration, are
8
explicitly introduced into the optimization to determine whether and how the coasting regime
9
should be undertaken in the tradeoff between vehicle’s commercial speed and the operating cost.
10
The comparison for the cost effectiveness of each alternative has been investigated in a life span
11
with respect to different vehicle types. The method has been implemented in the real-word bus
12
route 7 in Yaan City (China). The numerical experiments suggest that through optimization, the
13
total system cost has been saved by more than 50%. The results of continuum model are validated
14
by the comparison with the discretized results, and the outcomes are closely located in
15
neighborhood (with error less than 3%). The life-cycle cost of four vehicle types is finally
16
analyzed, and the result indicates that due to the high purchase prices, it’s difficult for clean-energy
17
buses to outperform conventional buses in a life cycle (normally 8 years), unless with subsidies
18
provided.
19
20
21
22
23
Keywords: Bus Route Design, Pollution, Driving Regimes, Continuum Model, Different Vehicle
24
Types
25
26
Su, Liu, Lu, Fan 3
INTRODUCTION
1
With the astounding growth in automobile ownership, most cities in China have to face a number
2
of transportation related issues such as rapid environmental deterioration and serious congestion
3
problem in urban area. The pollutants emitted such as CO, VOC, and , bring unpleasant
4
impacts on the air quality as well as the public health. Zero-emission buses, such as battery electric
5
buses and supercharge buses, entail environmental friendliness, and have been recognized as a
6
new solution of environmental problem and traffic congestion. Supercharge bus is the newest bus
7
type in the market and it utilizes super capacitor as power source, which has the advantages of fast
8
charging and discharging ability. Compared with battery electric bus, supercharge bus takes far
9
less time to charge, and it doesn’t need to replace batteries in a life cycle. Many cities in China
10
have spared no effort in developing a new transit network with clean-energy buses. For instance,
11
all the conventional buses (i.e., 16,000 CNG and diesel buses) in Shenzhen will be replaced with
12
electric buses by the end of 2018 (1). Despite the environmental advantages of the new-energy
13
buses, the expensive purchase price is an obstacle that impedes the progress of the shifting to clean
14
energy. For example, the unit vehicle price of an electrical bus is almost three times more
15
expensive than conventional bus (2). In order to yield a scientific assessment between
16
clean-energy buses and conventional buses, it is necessary to take the technical and economical
17
characteristics of different bus types into consideration to assess their cost competiveness.
18
To make the transit system more efficient, it is necessary for designers to provide a
19
delicated transit system with stops being well located. There are two basic approaches for tackling
20
Transit Route Design (TRD) problem. One is discrete approach which has been frequently used in
21
the TRD problem. Studies (3-6) applied discrete approach to decide the optimal stop locations.
22
The basic idea of discrete model is to determine optimal set of stops for a given OD matrix and
23
predict travel time per link on the route (7). Dynamic programming is largely used in the
24
optimization. The disadvantage of this approach is the computational inefficiency because of the
25
numerous decision variables.
26
Another approach is the Continuum Approximation (CA) approach. Previous studies (8-18)
27
employed CA approach to obtain the optimal design of a transit system, where a small number of
28
continuous functions are inputed; e.g., lines and stations are specified in terms of the spacing
29
between them (19). Some other parameters including headway, bus capacity, fleet size, have also
30
been used in the optimization model (20-21). The pioneering work of CA approach employed in
31
transit route design seems to be the study of Newell (8), in which the mechanics of CA approach
32
was elaborated. After that, Vaughan and Cousins (14) took advantage of a continuous stop density
33
function to determine the number of stops so as to minimize user’s travel time on a single corridor.
34
The demand pattern is a “many-to-many” demand pattern to reflect the spatial heterogeneity of
35
demand and is also presented in a continuous form. Later, Wirashinghe and Ghoneim (12)
36
proposed a more general continuous model to minimize the total system cost which consists of
37
user cost and operator cost with respect to a “many-to-many” demand pattern. The stop density is
38
expressed as a function of location and the integral of stop density function is firstly used as the
39
method to find optimal stop locations. Recently, Medina-Tapia et al. (16) employed CA-based
40
transit design model to a single bus corridor considering multiple periods (peak hour and off-peak
41
hour). A bi-directional stop density functions and multi-period headways are obtained. Further,
42
Amirgholy et al. (22) proposed a CA model to minimize user cost, agency cost, and pollutant cost
43
in a congested network. It seems to be the only CA-based work that considering environmental
44
impacts into transit route design.
45
The theme of this study is to optimize the bus route design for a single corridor considering
46
Su, Liu, Lu, Fan 4
different bus types of which the inter-stop driving regimes are explicitly modeled. In the proposed
1
model, the objective function is to minimize the total system cost, as a sum of user cost, operator
2
cost, as well as pollutant cost. The model is based on continuum approximation and its accuracy is
3
verified by a discrete approach. A case study is furnished on a bus route in Yaan City (China). The
4
contributions of this work include: the environmental factors and inter-stop driving regimes are
5
considered in transit route design model to analyze the system cost of different vehicle types. By
6
intergrating the optimized system cost (on a per day basis) with life-cycle cost analysis, it can
7
provide operator insight to choose appropriate vehicle type. Furthermore, the optimized coasting
8
speeds for different bus types have been analyzed as well as the effect of coasting regimes on
9
operation cost, which can be implemented in practical selection of driving regimes for different
10
bus types.
11
The remainder of this paper is organized as follows. Next section introduces the
12
optimization model, with variables’ definitions and formulations of the CA model, respectively. In
13
the section, a non-linear total cost minimization problem is introduced. After that, the numerical
14
application is conducted by using the real demand data, and the obtained results are analyzed. In
15
the end of section 3, a cost-effectiveness analysis among different vehicle types has been
16
elaborated. Last section concludes the findings and indicates further extensions.
17
18
METHODOLOGY
19
The proposed model contains a bus corridor of length L, operating in two directions (denoted by
20
, indicating eastbound and westbound, respectively). The bus travelling in each
21
direction of the corridor stops at each stop. The studied periods are: peak hour period and off-peak
22
hour period (denoted by , indicating peak-hour period and off-peak hour period,
23
respectively) whose service headways are different to reflect the demand variation but equal in
24
both directions. To facilitate organization, the developed model is based on a few assumptions as
25
follows:
26
27
1. The value of time for all passengers is assumed to be the same, regardless the citizen’s
28
status, income, etc.
29
2. Passengers choose the nearest stop to board or alight bus.
30
3. There is no congestion on the corridor, so bus acceleration or deceleration results from
31
whether it has to stop or start at bus stop. For the segment between two stops, different driving
32
regimes could be adopted regarding whether coasting occurs, for instance. In addition, the
33
acceleration and deceleration rates are constant in this study.
34
4. No bus congestion is assumed to occur at bus stops, so each bus opens its door as soon as it
35
arrives at a stop.
36
37
In this section, we will first introduce the objective function , which represents the
38
total system cost (on a per day basis), with , representing supercharge,
39
CNG, Lithium-ion, and diesel buses, respectively. contains user cost , operator cost ,
40
and pollutant cost :
41
42
43
, (1)
44
45
Su, Liu, Lu, Fan 5
1
2
The user cost includes three parts: the cost that passengers have to access or egress the stop
3
(), the cost that passengers spent waiting at the stop (), and the in-vehicle cost ().
4
5
6
, (1a)
7
8
9
10
The operator cost entails those of: the stop construction and maintenance cost ; the
11
Vehicle Hour Traveled (VHT) related cost (i.e., the cost associated with fleet size
, the cost
12
associated with driver salary
, and idling cost
); Vehicle Kilometer Traveled (VKT)
13
related cost (i.e., the cost associated with distance under cruising regime
, coasting regime
14
, and acceleration and deceleration regimes
). The operator cost is thus given by:
15
16
17
, (1b)
18
19
20
21
The expression of pollutant cost will be formulated later in Equation 30 and 31.
22
23
Continuum Approximation Models
24
User Cost
25
Seeing in Equation 1a, each cost item will be explained in brief expression in this part.
26
For users who access and egress at point x on the corridor, the access/egress cost is
27
computed by multiplying the number of users, the value of access time, and the average walking
28
time. Assuming that the distribution of demand in the neighborhood of x is uniformed, the
29
expected walking distance can be formulated as
, thus the access/egress cost is:
30
31
32
, (2)
33
34
35
36
where
37
: value of access time (dollar per passenger hour);
38
Su, Liu, Lu, Fan 6
: number of passengers who would like to alight at point x (). Noting that
1
, (passenger per kilometer per hour);
2
: number of passengers who would like to board at point x (). Noting that
3
, (passenger per kilometer per hour);
4
: duration of period i, with (hour);
5
: stop density function, with , (number of stops per
6
kilometer);
7
: average walking speed for passengers accessing and egressing bus stop; (kilometer per hour);
8
The daily waiting cost is considered as the product of average waiting time per passenger,
9
the number of boarding passengers, and the value of waiting time. Considering that waiting
10
passengers will get on the first bus that passes by, the waiting time of passengers will increases
11
linearly with average headway between buses, . The expected passenger’s waiting time will be
12
half of headway if bus’s arrival is perfectly regular. Therefore, the expression for user waiting cost
13
is given as follow:
14
15
16
, (3)
17
18
19
20
where:
21
: value of waiting time (dollar per passenger hour);
22
: the average headway, with (hour);
23
The in-vehicle cost is the cost generated by all on board passengers when bus is operating
24
between stops. It contains the cost accounted for bus travelling and for bus idling. Different driving
25
regimes might be conducted while bus is moving to next stop and it is essential to fully understand
26
the driving scenarios that could happen. Generally, there are four basic driving regimes (i.e.,
27
acceleration, cruising, coasting, and deceleration).
28
The bus’s travel time between stops depends on whether a transit vehicle can reach its
29
maximum speed or not. Supposed to be the critical distance for completing a perfect
30
acceleration to cruising speed and a perfect deceleration from the cruising speed. For a stop
31
spacing (represented as
), here are four driving scenarios:
32
Scenario 1: No coasting and cruising,
33
In this case, the inter-stop travel time consist of two parts, the time for accelerating to
34
some speed (, is the cruising speed, with ) and time for braking; The
35
time items are expressed as follows:
36
37
38
(4)
39
40
41
Su, Liu, Lu, Fan 7
(4a)
1
2
3
(4b)
4
5
6
where, , indicate the acceleration and deceleration rates, respectively, in unit km/h2;
7
We can calculate as following expression:
8
9
10
,
, (5)
11
;
12
13
14
Noting that the sum of acceleration and deceleration distance is
, which represents
15
the stop spacing. The per-kilometer travel time
can be determined by substituting
16
Equation 5 in Equation 4 and then dividing the spacing. Thus, per-kilometer travel time (in unit of
17
hour) in scenario 1 can be formulated as:
18
19
20
, (6)
21
;
22
23
24
Scenario 2: No coasting,
25
In this scenario, there are three intervals in an inter-stop traveling: the time for accelerating
26
to cruising speed (); the time for cruising (); and the time for braking(). The travel
27
time for each regime and the total travel time in a stop spacing for this scenario () are:
28
29
30
(7)
31
32
33
(7a)
34
Su, Liu, Lu, Fan 8
1
2
(7b)
3
4
5
(7c)
6
;
7
8
9
Thus, the per-kilometer travel time, denoted as
, in unit of hour, is formulated as:
10
11
12
,
, (8)
13
;
14
15
16
Scenario 3: No cruising,
17
Similarly, there are three intervals composed in this scenario: accelerating, coasting to
18
speed with deceleration rate (km/h2), and then braking regime is applied to reach the stop.
19
Thus, we can determine the inter-stop travel time for each regime as follows:
20
21
22
(9)
23
24
25
(9a)
26
27
28
(9b)
29
30
31
(9c)
32
with ;
33
Su, Liu, Lu, Fan 9
1
2
Thus, the per-kilometer travel time (hour) in this scenario is formulated as:
3
4
5
,
, (10)
6
;
7
8
9
With (indicating the speed at the end of coasting with , ,
10
, at point x) expressed as below, which is derived from the work of Vuchic
11
(23):
12
13
14
, (11)
15
;
16
17
18
Scenario 4: With coasting and cruising,
19
In this scenario, buses can accelerate to cruising speed, then keep constant speed, coast
20
from cruising speed, and brake. Thus, four intervals are included in the inter-stop travel time.
21
22
23
(12)
24
25
26
The distance for an inter-stop cruising is:
27
28
29
, (13)
30
;
31
32
33
We denote the inter-stop cruising time as , and present it in the following equation:
34
35
36
Su, Liu, Lu, Fan 10
, (14)
1
;
2
3
4
Thus, the inter-stop travel time is:
5
6
7
, (15)
8
with ;
9
10
11
It should be mentioned that, even though it exists four different operation scenarios, the
12
scenario 1 to 3 can be regarded as the special situations of scenario 4 (explained later), which the
13
per-kilometer travel time
and the time covered by each driving regime in per-kilometer
14
distance are:
15
16
17
(16)
18
19
20
Where
21
22
23
(16a)
24
25
26
(16b)
27
28
29
(16c)
30
31
32
(16d)
33
Su, Liu, Lu, Fan 11
1
2
, (17)
3
;
4
5
6
In scenario 2, which doesn’t contain coasting regime, it means that the coasting speed
7
equals to the cruising speed, . Thus, Equation 17 can be converted into Equation
8
8. As for scenario 3, which has no cruising regime, the cruising time is zero (
), and
9
we can find the expression of the same as Equation 11. Scenario 1 is the combination
10
of two conditions ( and
) and the Equation 6 can be yielded.
11
Therefore, Equation 17 is the generalized formula with four scenarios included. We can
12
make an assumption that scenario 4 is conducted in every inter-stop trip. By plugging
13
into optimization, we can finally yield the profile of . Once we get the
14
profile, the effect of coasting regime on operation cost can be explored.
15
After bus finishes its inter-stop travel, the bus dwell time will generate for passengers
16
boarding and alighting and for opening and closing doors. Supposing that an onboard fare payment
17
method is applied and one door is used for boarding and one or more doors are used for alighting,
18
the dwell time at each stop is dominated by the process that takes longer. To facilate modeling, we
19
convert dwell time at each stop to dwell time on per kilometer basis, denoted as
. The
20
expression of
is:
21
22
23
(18)
24
25
26
Where
27
28
29
, (19)
30
31
;
32
33
34
is the dead time for opening and closing doors, and are the average boarding and alighting
35
time (hour) per passenger, respectively.
36
To summarize, the expression for in-vehicle cost is presented as follow:
37
38
39
Su, Liu, Lu, Fan 12
, (20)
1
;
2
3
4
Where
5
: the number of passenger load at point x in direction r, in period i (passengers per hour);
6
: bus’s per-kilometer travel time (hour) with , ,
7
;
8
: bus’s per-kilometer dwell time (hour) with , ,
9
;
10
: the value of in-vehicle time (dollar per hour);
11
12
Operator Cost
13
Each cost item in Equation 1b will be discussed in this part. The cost for stop construction and
14
maintenance is determined by and , which represent the daily cost for stop construction
15
($/day) and the hourly cost for stop maintenance ($/hour), respectively. Thus, the per-day cost for
16
stops on the corridor is:
17
18
19
(21)
20
21
22
23
Where, T presents the total operating time of a stop (hour).
24
The cost associated with fleet size is closely related to the maximum fleet size required,
25
which is correspondent to peak hour fleet size, denoted as . is determined as the quotient of
26
peak hour cycle time
and peak hour headway . Thus:
27
28
29
(22)
30
31
32
(23)
33
34
35
(24)
36
;
37
Su, Liu, Lu, Fan 13
1
2
Where, is the fixed cost per bus (dollars per vehicle per day).
3
To determine the cost associated with driver wage, we suppose that a fixed wage is paid
4
hourly for each on-duty hour, and the cost item for labor is expressed as:
5
6
7
(25)
8
;
9
10
11
Where is the hourly salary for driver (dollar per hour).
12
The cost associated with idling
is presented as:
13
14
15
(26)
16
;
17
18
19
Where is the per hour cost of idling per vehicle(dollar per vehicle per hour);
20
Then, we discuss the VKT related cost:
21
The cost associated with distance travelled by buses at cruising speed for daily bus flow is
22
presented as the integral of the product of vehicle flow over day
, the per vehicle-kilometer
23
cruising distance
, and the per vehicle-kilometer cost . And the cost related is
24
expressed as:
25
26
27
(27)
28
;
29
30
31
Where, is the vehicle cost per unit distance covered at cruising speed (dollar per vehicle per
32
kilometer).
33
Similarly, the cost associated with distance coasted
, the cost associated with
34
acceleration and deceleration
are expressed as follows, respectively:
35
36
37
(28)
38
Su, Liu, Lu, Fan 14
1
2
(29)
3
;
4
5
6
Where
7
: the unit cost per kilometer traveled by coasting (dollar per vehicle per kilometer);
8
: the unit cost per kilometer covered at accelerating from bus station or braking to bus station
9
(dollar per vehicle per kilometer);
10
11
Pollutant Cost
12
In this model, we primarily take HC, CO, and NOx into account. The nth pollutant volume can be
13
determined as the product of emission rate for pollutant n (n=1: HC; n=2: CO; n=3: NOx) and the
14
per-kilometer travel time of different driving regimes, as expressed below:
15
16
17
(30)
18
;
19
20
21
where ,,, , and represent the emission rates for pollutant n, under acceleration,
22
cruising, coasting, deceleration, and standing regimes, respectively, in unit of (ton/hour).
23
Therefore, the pollutants cost generated while buses are operating on the corridor is:
24
25
26
(31)
27
;
28
29
30
where, is the unit vehicle-related damage cost of pollutant ($/ton).
31
32
Model Optimization
33
In this model, the objective function is the generalized cost, which is the sum of user cost, operator
34
cost, and pollutant cost. The expression of minimization problem is:
35
36
37
(32)
38
39
Su, Liu, Lu, Fan 15
1
Subject to:
2
(33)
3
4
5
6
The first constraint indicates that the bus’s capacity must feed the total passenger demand
7
(). The second constraint is the stop capacity should satisfy the total demand of
8
boarding and alighting. In addition, the optimal results of headway, stop density, and coasting
9
speed should be positive.
10
The objective function has three variables/functions: , , , and the
11
constrains are nonlinear. Those factors increase the complexity of the optimization. To obtain the
12
analytical expression of each variable/function, two alternative procedures are proposed. Firstly,
13
we introduced an initial value of headway to reduce the dimension. We can obtain the expression
14
of coasting speed and stop density by solving first order condition and
15
. Through this approach, the model is transformed into a problem
16
that has variables.
17
The second procedure contains two steps: in the first place, and are
18
replaced by the optimal expression
and . As the optimal function of headway
19
also contains stop density and coasting speed, which is , the next
20
step is to iterate the analytical expression of headway, stop density, and coasting speed until the
21
convergence is reached under constraints.
22
The first-order-condition expressions of stop density in each direction is:
23
24
25
(34)
26
;
27
28
29
Where
30
31
32
;
33
34
35
Su, Liu, Lu, Fan 16
1
;
2
3
4
;
5
6
7
;
8
9
10
;
11
12
13
It should be mentioned that the stop density function is different on two sides of corridor to
14
reflect the flexibility of locating curbside bus stops.
15
The expressions of optimal headway in peak hour and off-peak hour are as follows,
16
respectively:
17
18
19
(35)
20
21
22
(36)
23
;
24
25
26
Where
27
28
29
30
;
31
32
33
.
34
35
Su, Liu, Lu, Fan 17
1
Once the optimal value of headway is obtained, we can determine . The first
2
order condition is applied to obtain the unconstrained optimal as follows:
3
4
5
(37)
6
;
7
8
9
Where
;
10
Considering the constraint (), the optimal expression of
11
is given by:
12
13
14
(38)
15
;
16
where function return the middle value among , and .
17
18
As for supercharge bus and Lithium-ion bus, the pollutant emitted can be neglected, so
19
the optimal expressions of stop density, headway, and coasting speed are simplified as follows:
20
21
22
(39)
23
24
25
(40)
26
27
28
(41)
29
30
Su, Liu, Lu, Fan 18
1
(42)
2
3
4
(43)
5
;
6
7
8
NUMERICAL APPLICATION
9
System Inputs
10
In this section, we apply continuum model to the 7th bus route, Yaan (City), China, where the first
11
supercharge bus route is in operation. The studied corridor is approximately 11 km in length, 21
12
stops in the east direction and 22 stops in the west, as shown in Figure 1. The bus’s peak-hour
13
cruising speed and off-peak hour cruising speed are given by Shu Tong Transportation Agency.
14
All the operator cost items are shown in Table 1 as follows:
15
16
17
18
FIGURE 1 The No.7 bus route, Yaan (China)
19
20
21
TABLE 1 Cost Parameters of Four Transit Modes
22
23
Supercharge Cost Parameters
Parameters
Value
Source
$I-S infrastructure stop cost
($/stop/h)
$0.47
Derived from Gu et al (2016), with additional
construction cost 2,590,000 yuan for charging
facilities.
Su, Liu, Lu, Fan 19
Operating Costs (Distance)
Maintenance cost per veh-km
$0.012
Shu Tong Transpotation Agency
Energy cost per km ($/km)
$0.088
Electricity price 2018
$v, Cost per veh-km ($/veh-km)
$0.1
Operating Costs (Time)
Employees per vehicle
1.5
Average wage ($/h)
$6.15
Yaan City average wage standard
Labour cost per hour
$9.225
Vehicle cost ($)
$257,353
Vehicle lifespan (years)
8
Depreciation cost per hr ($/hr)
$6.3
Assumed straight-line depreciation, work 14 hr
per day
CNG Cost Parameters
Parameters
Value
Source
$I-S infrastructure stop cost
($/stop/h)
$0.35
Derived from Gu et al (2016)
Operating Costs (Distance)
Maintenance cost per veh-km
$0.02
Shu Tong Transpotation Agency
Energy cost per km ($/km)
$0.238
CNG price 2018
$v, Cost per veh-km ($/veh-km)
$0.258
Operating Costs (Time)
Employees per vehicle
2
Average wage ($/hr)
$6.15
Yaan City average wage standard
Labor cost per hour
$12.3
Vehicle cost ($)
$73,529
Vehicle lifespan (years)
8
Depreciation cost per hr ($/hr)
$1.8
Assumed straight-line depreciation, work 14 hr
per day
Lithium-ion battery Bus Cost Parameters
Parameters
Value
Source
$I-S infrastructure stop cost
($/stop/h)
$0.58
Derived from Gu et al (2016), with an
additional cost 5,000,000yuan for supplement
equipment
Operating Costs (Distance)
Maintenance cost per veh-km
$0.242
Shu Tong Transpotation Agency
Energy cost per km ($/km)
$0.088
Electricity price 2018
$v, Cost per veh-km ($/veh-km)
$0.33
Operating Costs (Time)
Employees per vehicle
1.7
Average wage ($/hr)
$6.15
Yaan City average wage standard
Labour cost per hour
$10.455
Vehicle cost ($)
$235,294
Vehicle lifespan (years)
8
Su, Liu, Lu, Fan 20
Depreciation cost per hr ($/hr)
$5.76
Assumed straight-line depreciation, work 14 hr
per day
Diesel Bus Cost Parameters
Parameters
Value
Source
$I-S infrastructure stop cost
($/stop/h)
$0.35
Derived from Gu et al (2016)
Operating Costs (Distance)
Maintenance cost per veh-km
$0.025
Shu Tong Transpotation Agency
Energy cost per km ($/km)
$0.512
Diesel price 2018
$v, Cost per veh-km ($/veh-km)
$0.537
Operating Costs (Time)
Employees per vehicle
2
Average wage ($/hr)
$6.15
Yaan City average wage standard
Labor cost per hour
$12.3
Vehicle cost ($)
$73,529
Vehicle lifespan (years)
8
Depreciation cost per hr ($/hr)
$1.8
Assumed straight-line depreciation, work 14 hr
per day
1
In this analysis, four different vehicle types are considered, among which two of them are
2
clean-energy bus (i.e., supercharge bus and Lithium-ion bus), the others are conventional buses
3
(i.e., CNG buses and diesel buses). It should be mentioned that all the vehicles are 12m in length.
4
The emission standard for CNG bus and Diesel bus is both of China National IV standard. The
5
emission rates of conventional buses at different driving regimes are given in Table 2, the data is
6
adopted from previous studies (24-25) and is summarized below.
7
8
TABLE 2 Emission Rates of Pollutants at Different Driving Cycles
9
10
12m China National IV CNG bus
Pollutant
Idling
Acceleration
Deceleration
Constant velocity
(g/s)
0.0036
0.0152
0.0071
0.0115
HC(g/s)
0.0012
0.0034
0.0021
0.0027
CO (g/s)
0.0211
0.0473
0.0303
0.0363
12m China National IV Diesel Bus
(g/s)
0.0226
0.0973
0.0503
0.0766
HC (g/s)
0.0013
0.0022
0.0014
0.0018
CO (g/s)
0.0070
0.0212
0.0069
0.0137
11
The boarding and alighting density function is obtained by using the on and off data which
12
is collected on 6th April, 2017 by Shu Tong Transportation Agency. All the programming process
13
is performed on Matlab platform. Figure 2 shows the boarding and alighting densities along the
14
corridor in terms of different time periods (i.e., peak hour and off-peak hour).
15
16
Su, Liu, Lu, Fan 21
1
FIGURE 2 Boarding and alighting densities along the corridor in different time periods
2
3
The values of walking time, riding time, and waiting time are derived from (16), and are set
4
at 4.09$/hour, 1.64$/hour, 2.73$/hour, respectively. Passengers access/egress bus stop at 3.6km/h.
5
The time for opening and closing doors is 2s at each stop. According to the schedule provided by
6
Shu Tong Transportation Agency, in the day time, from 7:00 to 17:00, the headway in current
7
system is 7 min; and during the evening peak, which is 17:00-19:00, the service headway is 12min;
8
for 19:00-20:00, the service headway is 15 min; 20:00-21:00, the service headway prolonged to
9
20min.
10
11
Optimal Design Solution Analysis
12
Figure 3 presents the discretization of the bi-directional stop density functions for four transit
13
modes. We discretize the bi-directional stop density functions by locating stops when the integral
14
of its left boundary and right boundary is 1. Here, we take the center line of each stop spacing as
15
the left/right boundary. The detailed description of the discretization method is derived from (16).
16
In the Figure, the circles on the stop density curves represent the optimal location of stops and the
17
dash lines represent the boundaries of each stop coverage market. The system characteristics of
18
current and optimized 7th route in Yaan (City) are summarized in Table 3.
19
20
0 1 2 3 4 5 6 7 8 9 10 11
location at the corridor,km
1000
800
600
400
200
0
1000
800
600
400
200
transit demand
peak
eastbound
westbound
boarding number
alighting number
0 1 2 3 4 5 6 7 8 9 10 11
location at the corridor,km
200
150
100
50
0
200
150
transit demand
off peak
eastbound
westbound
boarding number
alighting number
Su, Liu, Lu, Fan 22
(a) Supercharge bus stop locations
(b) CNG bus stop loactions
(c) Li-thium-ion bus stop locations
(d) Diesel bus stop locations
1
FIGURE 3 Optimal stop locations
2
3
In Table 3, we compare the optimal system costs of four vehicle types. The optimal results
4
indicate that when CNG buses are operating on the route, the system cost is the lowest. Note that
5
the cost gap between CNG buses system and supercharge buses system is slight (8080.9$/day vs.
6
8127.4$/day). Then, we discretize the optimal results based on CA approach and we obtain the real
7
results when CA models are applied practically, which are shown in the third row. Comparing with
8
the optimal results with discretized results, the outcomes of discrete models are in neighborhood
9
with that of CA models, with error less than 3%. In other words, if we employ the discretized
10
results on a real bus route, the system cost will be closed to optimal value, which verified the
11
applicability and accuracy of CA models. Finally, we compare the current system costs (detailed in
12
user cost, operator cost, and pollutant cost for conventional buses), with optimal results and
13
discretized results. Remarkably, the optimal results have saved more than 50% of the system cost,
14
especially in user cost.
15
0 2 4 6 8 10 12
location at the corridor,km
0
1
2
3
4
stop density, stop/km
eastbound stop locations
0 2 4 6 8 10 12
location at the corridor,km
0
1
2
3
4
stop density, stop/km
westbound stop locations
0 2 4 6 8 10 12
location at the corridor,km
0
1
2
3
4
5
6
stop density, stop/km
eastbound stop locations
0 2 4 6 8 10 12
location at the corridor,km
0
1
2
3
4
5
6
stop density, stop/km
westbound stop locations
0 2 4 6 8 10 12
location at the corridor,km
0
1
2
3
4
stop density, stop/km
eastbound stop locations
0 2 4 6 8 10 12
location at the corridor,km
0.5
1
1.5
2
2.5
3
3.5
stop density, stop/km
westbound stop locations
0 2 4 6 8 10 12
location at the corridor,km
0
1
2
3
4
5
6
stop density, stop/km
eastbound stop locations
0 2 4 6 8 10 12
location at the corridor,km
0
1
2
3
4
stop density, stop/km
westbound stop locations
Su, Liu, Lu, Fan 23
In terms of system design, comparing with the current route configuration, the average stop
1
spacing is increased by up to 31.3%. As for the service headway, the optimal headway in peak hour
2
is ranging from 6.55 min to 8.30 min with respect to vehicle type. Among them, CNG is the most
3
frequently emited bus type. According to optimal design, the optimal headway in peak hour has
4
been decreased by up to 31%, while in off-peak hour, the optimal headways are approximately
5
equal to the observed values in current system.
6
7
TABLE 3 System Characteristics of Current and Optimized 7th route in Yaan
8
9
Supercharge Bus Route Design
System metrics
Current corridor
Optimal results
Real results
, min
9.50 (weighted)
7.76
7.76
,min
9.64 (weighted)
8.12
8.12
, km
0.52
0.65 (17 stops)
0.65
,km
0.55
0.61 (18 stops)
0.61
, $/day
14,081.0
5,567.4
5,540.5
, $/day
2,624.2
2,559.9
2,359.4
, $/day
16,706.2
8,127.3
7,899.9
Cost Saving, %
na
51.3%
52.7%
Difference% (CA and
discrete models)
na
2.8%
CNG Bus Route Design
System metrics
Current corridor
Optimal results
Real results
, min
9.50 (weighted)
6.55
6.55
,min
9.64 (weighted)
10.68
10.68
, km
0.52
0.65 (17 stops)
0.65 (17 stops)
,km
0.55
0.61 (18 stops)
0.61 (18 stops)
, $/day
15,365.0
5,594.7
5,796.2
, $/day
2,165
2,398.2
2,412.7
, $/day
252.1
88.0
91.3
, $/day
17,782.1
8,080.9
8,300.2
Cost Saving, %
na
54.6%
53.3%
Difference% (CA and
discrete models)
na
2.7%
Lithium-ion Battery Bus Route Design
System metrics
Current corridor
Optimal results
Real results
, min
9.50 (weighted)
8.3
8.3
,min
9.64 (weighted)
10.3
10.3
, km
0.52
0.69 (16 stops)
0.69 (16 stops)
,km
0.55
0.65 (17 stops)
0.65 (17 stops)
, $/day
14,320.0
5,911.1
6,054.6
, $/day
3,223.1
2,818.0
2,880.2
, $/day
17,543.1
8,729.1
8,934.8
Cost Saving, %
na
50.2%
47.8%
Su, Liu, Lu, Fan 24
Difference% (CA and
discrete models)
na
2.3%
Diesel Bus Route Design
System metrics
Current corridor
Optimal results
Real results
, min
9.50 (weighted)
7.60
7.60
,min
9.64 (weighted)
12.89
12.89
, km
0.52
0.69 (16 stops)
0.69 (16 stops)
,km
0.55
0.65 (17 stops)
0.65 (17 stops)
, $/day
16,130.0
6,305.8
6,146.9
, $/day
2,542.2
2,688.9
2,534.7
, $/day
248.9
62.5
106.5
, $/day
18,921.1
9,057.2
8,788.1
Cost Saving, %
na
52.1%
53.6%
Difference% (CA and
discrete models)
na
3%
1
The Effect of Coasting Regime
2
Previously, we have discussed the optimal values of stop density functions, service headways
3
(peak and off-peak hour), and system costs for different bus types. This part will focus on
4
analyzing the optimal value of coasting speed in different periods (peak hour and off-peak hour)
5
for four vehicle types and investigating the interrelationship of coasting regime on system cost.
6
The obtimized profiles of coasting speed with respect to different vehicle types in peak/off-peak
7
hours are presented as follows in Figure 4,5, respectively.
8
9
(a) Supercharge bus coasting profile
(b) CNG bus coasting profile
0 2 4 6 8 10 12
location at the corridor,km
33
33.5
34
34.5
35
35.5
36
36.5
37
37.5
value of coasting speed,km/h
peak-hour coasting regime eastbound
westbound
0 2 4 6 8 10 12
location at the corridor,km
20
22
24
26
28
30
32
value of coasting speed,km/h
peak-hour coasting regime eastbound
westbound
Su, Liu, Lu, Fan 25
(c) Lithium-ion bus coasting profile
(d) Diesel bus coasting profile
FIGURE 4 Coasting speed profiles in peak hours for four vehicle types
1
2
(a) Supercharge bus coasting profile
(b) CNG bus coasting profile
(c) Lithium-ion bus coasting profile
(d) Diesel bus coasting profile
FIGURE 5 Coasting speed profiles in off-peak hour for four vehicle types
3
0 2 4 6 8 10 12
location at the corridor,km
24
25
26
27
28
29
30
31
32
33
value of coasting speed,km/h
peak-hour coasting regime eastbound
westbound
0 2 4 6 8 10 12
location at the corridor,km
12
14
16
18
20
22
24
26
28
value of coasting speed,km/h
peak-hour coasting regime eastbound
westbound
0 2 4 6 8 10 12
location at the corridor,km
31.5
32
32.5
33
33.5
34
34.5
35
35.5
36
36.5
value of coasting speed,km/h
off-peak hour coasting regime
eastbound
westbound
0 2 4 6 8 10 12
location at the corridor,km
21
22
23
24
25
26
27
28
29
value of coasting speed,km/h
off-peak hour coasting regime
eastbound
westbound
0 2 4 6 8 10 12
location at the corridor,km
21
22
23
24
25
26
27
28
value of coasting speed,km/h
off-peak hour coasting regime
eastbound
westbound
0 2 4 6 8 10 12
location at the corridor,km
13
14
15
16
17
18
19
20
21
22
value of coasting speed,km/h
off-peak hour coasting regime
eastbound
westbound
Su, Liu, Lu, Fan 26
1
From the two figures above, the optimal coasting speed profiles of four different vehicle
2
types in the same period have the similar trend, but with distinguishing differences in average
3
values. By discretizating the coasting speed functions, we can obtain the average values of
4
coasting speeds in peak/off-peak hour on two directions. The results are summarized in Table 4,
5
from which supercharge bus has the highest average coasting speed regardless of the time period.
6
By contrast, diesel bus has the lowest average coasting speed. The results are reasonable because
7
the diesel bus has the highest per-kilometer energy cost. In order to conserve energy, it’s more
8
beneficial to coast, as coasting regime will have less energy consumption than cruising regime. As
9
for supercharge bus, whose per-kilometer energy cost is slight, it’s more profitable to drive at
10
cuising speed in order to save travel time.
11
12
TABLE 4 Optimal Values of Coasting Speed in Different Periods on Two Directions
13
14
Vehicle Types
in peak
(km/h)
in off-peak
(km/h)
in peak
(km/h)
in off-peak
(km/h)
Supercharge
35.23
36.12
35.42
35.00
CNG
25.00
23.07
25.57
22.80
Lithium-ion
28.79
24.95
29.23
24.71
Diesel
20.52
16.81
21.14
16.50
15
Driving regimes have direct impact on operation cost. In light of this, a system-cost
16
comparison is conducted between optimized systems that introducing coasting regime and the one
17
without considering coasting regime. The results are concluded in Table 5 and the operation costs
18
in no-coasting system increase by up to 7%, while user costs decrease more than 12.9%, mainly in
19
access/egress cost. The reason is that, introducing coasting regime will reduce the number of stops
20
along corridor, leading to an increase in access/egress cost. However, the in-vehicle costs for two
21
models are in neighborhood (with difference less than 5%), which means the travel time is closed
22
for two systems, even when coasting regime is added. As a result, the distance traveled under
23
cruising regime (with higher per-kilometer cost) will decrease. That’s the reason why operation
24
cost will decrease when introducing coasting regime in the system. Thus, coasting regime has a
25
positive impact in view of operator, but passengers should accept a higher user cost. To summarize,
26
for clean-energy buses (i.e., supercharge buses and Lithium-ion buses), it’s more profitable to
27
drive at cruising speed, while for conventional buses (i.e., CNG buses and diesel buses),
28
introducing coasting regime is justifiable, considering the cost saving in operation and energy.
29
30
TABLE 5 System Cost with Coasting Regime vs. System Cost Without Coasting Regime
31
32
Supercharge Bus Route Design
System metrics
No coasting regime
With coasting regime
, min
7.59
7.76
,min
8.94
8.12
, km
0.50
0.65
,km
0.48
0.61
, $/day
4,850.2
5,567.4
, $/day
2,762.2
2,559.9
Su, Liu, Lu, Fan 27
, $/day
7,612.4
8,127.3
CNG Bus Route Design
, min
6.69
6.55
,min
11.92
10.68
, km
0.50
0.65
,km
0.46
0.61
, $/day
4,931.7
5,594.7
, $/day
2,596.6
2,398.2
, $/day
62.5
88.0
, $/day
7,590.8
8,080.9
Lithium-ion Battery Bus Route Design
, min
8.12
8.30
,min
11.95
10.30
, km
0.52
0.69
,km
0.50
0.65
, $/day
5,248.6
5,911.1
, $/day
2,999.9
2,818.0
, $/day
8,248.5
8,729.1
Diesel Bus Route Design
, min
7.94
7.60
,min
15.40
12.89
, km
0.52
0.69
,km
0.50
0.65
, $/day
5,456.4
6,305.8
, $/day
2,671.5
2,688.9
, $/day
270.6
62.5
, $/day
8,398.5
9,057.2
1
Cost Effectiveness Comparison
2
This part will analyze the life cycle cost for four vehicle types, which is from a macroscopic view.
3
From Table 3, we can find the most economical vehicle type is CNG buses. Historical data shows
4
that the maintenance cost for CNG and diesel bus will increase by year, even though their initial
5
capital cost is lower. As a result, the cumulative costs of conventional buses in a life span will also
6
be expensive. According to the maintenance cost data that Shu Tong Transportation Agency
7
provided, clean-energy buses have a constant maintenance cost but a high initial capital cost. Thus,
8
there exists a trade-off: which type is the most economical in a life span (8 years). Inspaired by the
9
previous studies (2, 26), which explored the varying maintenance cost by years in terms of diesel
10
buses and CNG buses by using monthly maintenance data, we can roughly analyze the life cycle
11
cost of our buses. The relationships of maintenance cost changing by year for diesel bus and CNG
12
bus are shown respectively:
13
14
, which y is presented the cost of maintenance per kilometer ($/km) for
15
diesel bus, z is the bus age (years).
16
17
Su, Liu, Lu, Fan 28
, which y is the maintenance cost per kilometer for CNG bus ($/km), z is the
1
bus age (years).
2
3
We investigated a cost comparison for four bus types as shown in Figure 6. The results present that
4
without including the pollutant cost into calculation, the cumulative costs of CNG bus will surpass
5
those of supercharge bus after 13th year. On the contrary, when pollutant costs for conventional
6
buses (i.e., CNG buses and diesel buses) are taken into consideration, supercharge bus will
7
outperform other bus types after 8 years, which is still out of a life span. Thus, clean-energy buses
8
are less competive than conventional buses unless the government provides subsidies.
9
10
(a) Life-cycle analysis without pollutant costs
(b) Life-cycle analysis with pollutant costs
FIGURE 6 Life-span cost comparison
11
12
CONCLUSION AND FUTURE EXTENSION
13
In this research, we developed a muti-period continuum approximation to optimize total cost
14
including user cost, operator cost, and pollutant cost, where environmental impact and various
15
driving regimes are explicitly considered. The proposed model is applied to four different vehicle
16
types to optimize stop locations and service headway. The optimization of a real-word bus route
17
results in significant reduction of total cost (over 50%). Comparing with current transit design, the
18
average stop spacing is increased by 31.3%, and the peak-hour headway is decreased by up to 31%.
19
The accuracy of proposed model is verified by a discrete model with error less than 3%. The huge
20
gap of total system cost between current design and optimized design indicates that current design
21
might not well fit the demand, adjustment should be done in terms of stop locations and headway.
22
To investigate the effect of coasting regime, the optimal coasting profiles and the average
23
values on two directions in multiple periods is compared in terms of different bus types. The
24
results indicate that clean-energy buses have a shorter coasting distance while conventional buses
25
need to coast longer in order to conserve energy. The analysis of the effect of coasting regime on
26
operation cost suggest that introducing coasting regime will reduce operation cost (by up to 7%)
27
but increase user cost (by up to 13%).
28
In the life-span cost effectiveness comparison amongst four different vehicle types, the
29
economic feasibility of supercharge bus has been discussed. On a life-span scale (normally 8
30
0 5 10 15
bus age
0
200
400
600
800
1000
1200
ten thousand yuan
cost comparison for 4 mode
supercharge
CNG
LI
Diesle
0 5 10 15
bus age
0
200
400
600
800
1000
1200
ten thousand yuan
cost comparison for 4 mode
supercharge
CNG
LI
Diesle
Su, Liu, Lu, Fan 29
years), the total cost of supercharge will be the lowest among four vehicle type after 8th years,
1
when pollutant costs are considered. It provides an insight that from the prespective of operator,
2
shifting conventional buses to new energy buses is not profitable unless subsidies are provided by
3
government.
4
For future extension, it is interesting to compare the stop-skip service with current all-stop
5
design. Additionally, the effect of coasting for different transit modes, such as rail and Bus Rapid
6
Transit (BRT) system can be further studied.
7
8
ACKNOWLEDGMENTS
9
This study is funded by the National Nature Science Foundation of China (NSFC 51608455). The
10
authors thank the Shu Tong Transportation Agency for providing the useful data for case study.
11
12
Author contribution statement:
13
“The authors confirm contribution to the paper as follows: study conception and design:
14
Yue Su, Guo Lu, Wenbo Fan; data collection: Yue Su; analysis and interpretation of results: Yue
15
Su, Wenbo Fan; draft manuscript preparation: Yue Su, Wenbo Fan, Xiaobo Liu. All authors
16
reviewed the results and approved the final version of the manuscript”
17
18
REFERENCES
19
1. Fastcompany:https://www.fastcompany.com/40506877/by-2018-every-bus-in-this-chines
20
e-megacity-will-be-electric
21
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