TML-KUL Lunch Seminar on Transport Policy
Leuven, 31st May 2012
Multimodal pricing and optimal
design of public transport services
The interplay between traffic congestion and bus
crowding
Alejandro Tirachini, David Hensher and John Rose
Institute of Transport and Logistics Studies
The University of Sydney
Email: [email protected]
Introduction
• Decisions on urban public transport provision
-
Network design
-
Technological choice (bus, tram, light rail, metro, etc.)
-
Investment in infrastructure
-
Number of services per hour and day
-
Fare collection method
-
Location of stations or bus stops
› Choices have a profound impact on the cost of the system and the level of
service provided (accessibility, waiting time, in-vehicle time, comfort, etc.)
› Microeconomic literature on public transport operations: Several papers
that attempt to find optimal values of:
-
Frequency (veh/h)
-
Vehicle size (pax/veh)
-
Network density (lines/km2)
-
Stop spacing (stops/km)
2
The basic model (Mohring, 1972)
Operator cost
Users cost (waiting time)
Cop  c  f  T
Y
Cu  Pw
2f
c: bus operating cost
f: frequency, T: cycle time
Pw: Value of waiting time savings
Y: demand
3
The basic model (Mohring, 1972)
Operator cost
Users cost (waiting time)
Cop  c  f  T
Y
Cu  Pw
2f
c: bus operating cost
f: frequency, T: cycle time
Pw: Value of waiting time savings
Y: demand
Cost C
operator
users
Frequency f
4
The basic model (Mohring, 1972)
Operator cost
Cop  c  f  T
c: bus operating cost
f: frequency, T: cycle time
Cost C
Users cost (waiting time)
+
Y
Cu  Pw
2f
Pw: Value of waiting time savings
Y: demand
total
operator
users
Frequency f
5
The basic model (Mohring, 1972)
Y
Ctot  c  f  T  Pw
2f
Cost C
dCtot
Y
 c  T  Pw
df
2f 2
Pw
f*
Y
2cT
total
operator
users
f*
Frequency f
6
Optimisation of public transport systems
Model
Mohring (1972)
Jansson (1980)
Kocur and Hendrickson
(1982)
Oldfield and Bly (1988)
Kuah and Perl (1988)
Chang and Schonfeld
(1991)
Chien and Schonfeld
(1998)
Jara-Diaz and Gschwender
(2003)
Tirachini and Hensher
(2011)
Freq
*
*
*
*
*
Bus
size
Dist
Route
stops density
*
*
*
*
*
*
*
Stop spacing in feeder system
*
*
*
Elastic demand, number of
lines
Waiting time not constant
*
*
*
*
Square root formula, scale ec
*
Vehicle size
*
*
*
Fare
Run
Fare Special feature/contribution
level speed payme
nt tech
Multiperiod analysis, elastic
demand
Rail line length optimization
*
*
Crowding cost effect
*
*
*
*
Bus congestion, queuing
delays at bus stops
7
This work
› Objective: Social welfare maximisation (e.g., De Borger et al., 1996; Proost and Van
Dender, 2004; Wichiensin et al., 2007; Ahn, 2009; Parry and Small, 2009; Basso and Silva,
2010; Jansson, 2010)
› Three modes (bus, car, walk), single corridor, single period.
› It uncovers the trade-off between bus crowding and traffic congestion under
several modelling assumptions.
› It includes a large number of variables on the bus supply side:
- Frequency
- Bus size
- Fare collection technology
- Number of doors per bus
- Boarding and alighting policy (simultaneous or sequential)
- Bus design (number of seats)
- Fare level
- Congestion toll
8
Bus crowding
Montréal
Delhi
9
http://www.chinawhisper.com/passengers-climb-into-overcrowded-bus
10
Before things get that bad, what you can do is…
11
http://www.columbiamissourian.com/stories/2008/09/17/columbia-transit-adds-more-buses-students/
12
That sounds good, but what if…
13
…Congestion!
Sydney
Guangzhou
Santiago
14
Congestion/crowding trade-off
Congestion pushes
frequency down
(Tirachini and Hensher, 2011, for bus congestion)
Trade-off needs to be accounted for
Crowding pushes
frequency up
(Jara-Díaz and Gschwender, 2003)
15
Crowding cost modelling
• People dislike crowding
• People dislike standing
Increase in valuation of in-vehicle time
Data comes from SP survey for Metro project in Sydney (Hensher et al., 2011)
› Two crowding variables:
- Proportion of seats occupied
- Density of standees per m2
› Three demand models are estimated
- M1: No crowding cost
- M2: Only the density of standees
- M3: Density of standees plus proportion of seats occupied.
16
Value of in-vehicle time savings
Travel comfort
depends on
number of seats
AUD/h, MNL models
17
Optimal number of seats inside a bus
› Travel comfort depends on number of seats.
› Number of seats and allocation of space:
- Pax sitting: 0.50 m2
- Standee: 0.15-0.20 m2
› More seats: Comfort and the expense of capacity
18
Number of seats as a decision variable:
not a crazy idea
Different allocation of space for seating and standing
19
Physical setting: Transport corridor
Zone 2
Zone 1
Zone P
Zone i
f a11
f
f a12
f a22
f ai2
L1
L2
Li
2
a1
f ai1
Direction 1
Direction 2
f aP1 1
f aP21
LP 1
› Corridor divided in short sections (e.g., 300 m), one bus stop per
section.
› Spatially disaggregated demand along corridor, origin-destination
matrix at section level.
› Calculation of crowding cost per section.
› Congestion modelling: BPR function for mixed traffic (buses and cars):
Travel time
1
i




f


s
f

a1
b b
i
i
i
i
tvb1  f a1 , fb   tb 0 1   0 
   ts1
Kr


 

20
Objective: Social Welfare Maximisation
Max
SW 

ij
y ij
U mij
ln  e
Iu
m
Users’ benefit (logsum)

ij
ij
y


y
 a a  b b
ij

Co
ij
Bus and toll revenue
Bus op cost
Subject to constraints:
Capacity
max  ybi 1 , ybi 2    fb K  sb , nseat 
i
min
seat
max
 nseat  nseat
Number of seats
n
Frequency
fbmin  fb  fbmax
Bus size
sb sb1 ,..., sb 4 
Solution programmed in Matlab
21
Application: Military Road in Sydney
22
Application: Military Road in Sydney
Zone 2
Zone 1
Zone P
Zone i
f a11
f
f a12
f a22
f ai2
L1
L2
Li
2
a1
f ai1
Direction 1
Direction 2
f aP1 1
f aP21
LP 1
Zone 12
3.4 km,
2 lanesdirection
Zone 1
23
Application: Military Road in Sydney
› OD matrix, morning peak (7.30 to 8.30am), 19,231 trips total
› Mode choice: bus, car, walk
O/D
1
2
3
1
0
856 1324
2
165
0
192
3
829 93
0
4
50
12
0
5
146
0
0
6
235
9
3
7
87
13
4
8
18
1
0
9
396 22
5
10
7
0
0
11 119 11
1
12 1780 277 54
4
54
15
0
0
0
0
0
0
1
0
0
21
5
23
4
0
0
0
0
0
0
1
0
0
16
6
8
1
0
0
0
0
0
0
3
0
0
27
7
74
20
0
1
0
0
0
0
24
0
12
151
8
99
19
0
3
0
3
12
0
9
0
0
65
9
10
11
12
419 71
16 1405
68
14
3
326
0
0
0
0
13
1
0
91
1
0
0
11
9
0
0
17
48
12
0
187
3
9
0
8
0
27
3
763
0
0
12 1511
3
123
0
1027
207 3763 1685
0
24
Base results (Total demand=19,231 trips)
Optimal value
Bus length [m]
Frequency [veh/h]
Fare [$]
Toll [$]
Number of seats
Bus capacity [pax/bus]
Seating area/ (seating plus standing area)
M1
8
21.7
0.1
2.0
24
36
0.80
M2
8
23.7
0.1
2.0
24
36
0.80
M3
12
26.1
0.4
2.0
39
58
0.80
Average occupancy rate (over number of seats)
0.57
0.52
0.30
1.08
521
129,544
114,290
-671
15,925
0.83
11
7.1%
60.0%
32.9%
0.98
569
122,984
107,721
-645
15,908
0.83
12
7.0%
59.9%
33.1%
0.56
1,017
122,897
107,454
-467
15,909
0.46
13
7.0%
60.0%
33.0%
Max. occupancy rate (over number of seats)
Seat capacity bus route (seats/h)
Social welfare [$]
Consumer surplus [$]
Bus operator profit [$]
Toll revenue [$]
Subsidy/bus operator cost
Fleet size [buses]
Modal split bus
Modal split car
Modal split walk
25
Demand scaling
Uniform increase of total demand (up to 50%) to analyse evolution of key variables
Frequency [bus/h]
Average speed [km/h]
26
Seat supply and total bus capacity
Seat supply [seat/h]
Total supply (seat+stand) [pax/h]
M1 (No crowding): Remove seats from buses
27
Mixed traffic vs bus lane, M1 (No crowding)
28
Modal Split
Modal split – Total demand
Modal split – Trip length
29
The case with increased bus-induced congestion
Bus equivalency factor is doubled (from 1.6 - 3.0 to 3.2 – 6.0 cars/bus)
Frequency – M1 (No crowding)
Frequency – M2 (Crowding)
30
What if suboptimal number of seats is provided?
Frequency – number of seats, M3
31
Summary
1. Methodological contributions
- Crowding/Congestion trade-off is exposed and analysed.
- Number of seats (bus design) is endogenous.
2. Policy implications
- Result on number of buses, size of buses, number of seats, fare and
subsidy is very sensitive on assumptions regarding crowding and
congestion cost functions.
- Relevance of non-motorised alternative for short trips, more people
walk as corridor (city) gets congested.
32
Dank u wel
33
References
› Ahn, K., 2009. Road pricing and bus service policies. Journal of Transport Economics and Policy 43(1), 2553.
› Basso, L. J. and Silva, H. E., 2010. A microeconomic analysis of congestion management policies. 5th
Kuhmo Nectar Conference in Transport Economics Valencia, Spain, July 8-9.
› Chang, S. K. and Schonfeld, P. M., 1991. Multiple period optimization of bus transit systems. Transportation
Research Part B 25(6), 453-478.
› Chien, S. and Schonfeld, P., 1998. Joint optimization of a rail transit line and its feeder bus system. Journal
of Advanced Transportation 32(3), 253-284.
› De Borger, B., Mayeres, I., Proost, S. and Wouters, S., 1996. Optimal pricing of urban passenger transport:
a simulation exercise for Belgium. Journal of Transport Economics and Policy 30(1), 31-54.
› Hensher, D. A., Rose, J. M. and Collins, A., 2011. Identifying commuter preferences for existing modes and
a proposed Metro in Sydney, Australia with special reference to crowding. Public Transport 3(2), 109-147.
› Jansson, J. O., 1980. A simple bus line model for optimization of service frequency and bus size. Journal of
Transport Economics and Policy 14(1), 53-80.
› Jansson, K., 2010. Public transport policy with and without road pricing 5th Kuhmo-Nectar Conference on
Transport Economics, Valencia, Spain, July 8-9.
34
References
› Jara-Díaz, S. R. and Gschwender, A., 2003. Towards a general microeconomic model for the operation of
public transport. Transport Reviews 23(4), 453 - 469.
› Kocur, G. and Hendrickson, C., 1982. Design of local bus service with demand equilibration. Transportation
Science 16(2), 149-170.
› Kuah, G. K. and Perl, J., 1988. Optimization of feeder bus routes and bus-stop spacing. Journal of
Transportation Engineering 114(3), 341-354.
› Mohring, H., 1972. Optimization and scale economies in urban bus transportation. American Economic
Review 62(4), 591-604.
› Oldfield, R. H. and Bly, P. H., 1988. An analytic investigation of optimal bus size. Transportation Research
Part B 22(5), 319-337.
› Parry, I. W. H. and Small, K. A., 2009. Should urban transit subsidies be reduced? American Economic
Review 99(3), 700-724.
› Proost, S. and Van Dender, K., 2008. Optimal urban transport pricing in the presence of congestion,
economies of density and costly public funds. Transportation Research Part A 42(9), 1220-1230.
› Tirachini, A. and Hensher, D. A., 2011. Bus congestion, optimal infrastructure investment and the choice of a
fare collection system in dedicated bus corridors. Transportation Research Part B 45(5), 828-844.
› Wichiensin, M., Bell, M. G. H. and Yang, H., 2007. Impact of congestion charging on the transit market: An
inter-modal equilibrium model. Transportation Research Part A 41(7), 703-713.
35