Improving Travel Efficiency by Parking Permit Distribution and Trading Xiaoning Zhang Tongji University, Shanghai, China Email:
[email protected]
Introduction • Parking is becoming an increasingly important aspect of traffic planning and management. • In the past, the traffic pattern of morning commute with inadequate parking space at the destination has not been investigated. • We study the behavior of competition for parking spots at the destination. • We study the policies of parking permit allocation and free trading of parking permits, in the spirit of tradable credit scheme for managing network mobility (Yang et al, 2010).
Contributions First, we derive a model to compute the morning commuting pattern when the city center has inadequate parking space to accommodate potential private cars. Second, we propose and compare the following three schemes to distribute parking permits to different origins: uniform, Pareto improving, and system optimum distribution of parking permits. Third, we consider tradable parking permits and examine the efficiency and fairness of the policy of parking permit trading. Forth, numerical examples show that parking permit distribution and trading are very efficient in traffic management.
Vickrey Model n C
N αs α +β
æ g ö N ÷ ç t0 = t - ç ÷ ÷s çè b + g ø *
æ b ÷ öN ç t1 = t + ç ÷ çèb + g ÷ øs *
B
αs α −β
0
A t0
dN Individual travel cost: ; s
dN 2 Total scheduale delay cost: ; 2s 2 dN Total waiting time cost: ; 2s 2 dN Total travel cost: . s
s
t
*
t1
t
Vickrey Model with Positive Free Flow Travel Time n C
nc
r2 B
r1
0
A t1
D t2
F
r2
E
s
r1
t t3
t4
t*
t5
Improved Vickrey Model with Inadequate Parking Spots
n
n C
nc
G
F
r2
B
B
D t2
t t3
r1
r1
s
s
s
r1
A t1
E
E
nc
0
D
t4 t5
t6
t
*
t7
Ending time of parking spots: Extended inverse
0
A t1
t
C t2
te ( n ) = t * −
t3
t4
t5
C ( n ) − α T0 n + β s
0 t ≤ te ( 0 ) function：π ( t ) = te−1 ( t ) t ∈ te ( 0 ) , te ( N ) t ≥ te ( N ) N
(
)
t
*
A Many-to-One Bi-Modal Transportation Network Oi
O2
ai b2 O1
bi
O|w|
a2 a|w| b1 b|w| a1 D
Determination of Parking Spots Ending Time Parking Spots Available n
n=
w π ∑ (tend )
w∈W
Parking Spots Ending Time t end
Determination of Private Car Travelers of Each OD Parking Spots Ending Time t end
tend
w w w w P ( N − n ) − α T n r 0 = t* − + r s β
Number of Private Car Travelers n w r
Traffic Pattern of Each OD (Improved Vickrey Model Inadequate Parking Spots) n
n C
nc
G
D t2
r2
E
B
r1
t t3
t4 t5
t6
t*
t7
0
A t1
Parking Permit
D t2
F
r2
E
s
s
r1
A t1
C
nc
r2 B
0
F
s
r1
t t3
t4
t*
t5
Uniform Parking Permit Assignment Parking permits are distributed evenly among all commuters. For each OD, the number of parking spots allocated is w N nuw = n i ∑N i∈W
The travel cost of an OD may increase in comparison with the original case without parking permit distribution, thus this scheme may not be Pareto improving. Parking permits may be wasteful for some ODs.
Pareto improving Parking Permit Assignment Parking permits are assigned according to the number of auto commuters computed by the original bi-modal equilibrium model with parking restraint. In this scheme, no parking space is wasted, since there is no excessive parking spot assigned to any OD pair. This scheme is Pareto improving. The travel cost of all transit commuters remain the same as before, and the auto commuters enjoy a reduction of travel cost.
Optimal Parking Permit Assignment Parking permits are allocated to minimize the total travel cost in the network. Model: min ns ,N,N
s .t .
( )
w w w w ∑ pw ( N ) N + Pw N N w∈W
Nw + Nw = Nw w ∑ ns = n
w∈W
N w ≤ nsw nsw ≤ N mw Nw ≥ 0
Nw ≥ 0
Parking Permit Trading Parking permits are allowed to trade among commuters of all OD pairs in a competitive market. w w p N ( For an OD, travel cost of auto travelers is, t ) + λ. The equilibrium solution of triple (N tw , N tw , λ ) can be found from the following model: min
Nt , Nt ,λ
Ntw 0
∑ ∫
w∈W
s .t .
Ntw 0
p (ω)d ω + λn + ∑ ∫ w
N tw + N tw = N w w ∑ Nt = n
w∈W
N tw ≥ 0
N tw ≥ 0
w∈W
P w (ω)d ω
Setting of Numerical Example
The Ending Time of Parking Spots Given the Amount of Total Parking Spots Available Clock time of parking ending time .
10:00 09:30 09:00 08:30 08:00 07:30 07:00 06:30
Coordinates of the turning points:
06:00
A: (0, 5:40); B: (700, 6:30); C: (2725, 8:00); D: (5437, 9:09:14); E: (5604, 9:16:40); F: (5628, 9:19:08)
05:30 0.0
1.0
2.0
3.0
4.0
5.0 3
Total parking spots available n (10 )
6.0
Parking Spots Occupied by Each OD
3
Parking spots occupied by different Ods (10 ) .
2.5
2.0
OD 1 OD 2 OD 3
1.5
1.0
0.5
0.0 0.0
1.0
2.0
3.0
4.0
5.0 3
Total parking spots available n (10 )
6.0
Individual and System Travel Costs Given the Amount of Parking Spots Available 1.9
180 OD 1 OD 2 OD 3 System travel cost
1.7
6
140
1.8
1.6
120
1.5
100
1.4 1.3
80
1.2 60
1.1
40
1.0 0.0
1.0
2.0
3.0
4.0
5.0 3
Total parking spots available n (10 )
System travel cost (10 )
Travel cost of different ODs .
160
6.0
Number of Auto Commuters of Each OD and the Whole Network
5.0
Number of auto commuters of OD 1 Number of auto commuters of OD 2&3 Number of total auto commuters
3
Number of auto commuters (10 ) .
6.0
4.0
3.0
2.0
1.0
0.0 0.0
1.0
2.0
3.0
4.0
5.0 3
Total parking spots available n (10 )
6.0
5.0
20.0
4.0
0.0
3.0 2.0
-20.0
1.0 -40.0 Change of driving cost of OD 1 Change of driving cost of OD 2 Change of driving cost of OD 3 Change of riding cost of OD 1 Change of riding cost of OD 2 Change of riding cost of OD 3 Change of system cost
-60.0 -80.0 -100.0
0.0 -1.0 -2.0 -3.0
-120.0
-4.0 0.0
1.0
2.0
3.0
4.0
5.0 3
Total parking spots available n (10 )
6.0
4
40.0
Change of system cost (10 ) .
Change of travel cost .
Change in Individual Travel Costs from Scheme NM to Scheme UD
Change in Individual and System Travel Cost from Scheme NM to Scheme PD 0.0
0.0 2.0
3.0
4.0
5.0
6.0
-20.0
-2.0
-40.0
-4.0
-60.0
-6.0
-80.0
Change of driving cost in OD 1 Change of driving cost in OD 2 Change of driving cost in OD 3 Change of system travel cost
4
1.0
-8.0
-100.0
-10.0
-120.0
-12.0 3
Total parking spots available n (10 )
Change of system travel cost (10 )
Change of driving cost .
0.0
Allocation of Parking Permits to Each OD and the Corresponding System Cost in Scheme SD 2.0 Parking permits of OD 1 Parking permits of OD 2 Parking permits of OD 3 System travel cost
2.5
1.9 1.8 1.7
2.0
1.6 1.5
1.5 1.4
1.0
1.3 1.2
0.5
1.1 0.0
1.0 0.0
1.0
2.0 3.0 4.0 5.0 3 Total parking spots available n (10 )
6.0
System travel cost (106)
Parking permits for each OD (103) .
3.0
20
2.0
0
0.0
Change of travel cost
1.0
2.0
3.0
4.0
5.0
6.0
4
0.0 -20
-2.0
-40
-4.0
-60 -80 -100
Change of driving cost for OD 1 Change of driving cost for OD 2 Change of driving cost for OD 3 Change of riding cost for OD 1 Change of riding cost for OD 2 Change of riding cost for OD 3 Change of system cost
-120
-6.0 -8.0 -10.0 -12.0
3
Total parking spots available n (10 )
Change of system cost (10 )
Change in Individual and System Travel Costs from Scheme NM to Scheme SD
Parking Permits of Each OD and Its Price at Market Equilibrium 120.0 Parking permits of OD 1 Parking permits of OD2
2.5
100.0
Parking permits of OD 3 Price of a parking permit
2.0
80.0
1.5
60.0
1.0
40.0
0.5
20.0
0.0
0.0 0.0
1.0
2.0
3.0
4.0
5.0 3
Total parking spots available n (10 )
6.0
Price of a parking permit .
3
Parking permits held by each OD (10)
3.0
Change in Travel Cost from Scheme NM to Scheme TP 20
Change of travel cost
0 0.0
1.0
2.0
3.0
4.0
5.0
-20 -40 -60 -80 -100
Change of driving cost of OD 1 Change of driving cost of OD 2 Change of driving cost of OD 3 Change of riding cost of OD 1 Change of riding cost of OD 2 Change of riding cost of OD 3
-120 3
Total parking spots available n (10 )
6.0
System Travel Cost in Scheme TP Minus that in Schemes NM, PD and SD 0.0
4
Difference of system cost (10 ) .
2.0
0.0 -2.0 -4.0
1.0 2.0 3.0 4.0 5.0 System cost in scheme TP minus that in scheme WM System cost in scheme TP minus that in scheme PD System cost in scheme TP minus that in scheme SD
-6.0 -8.0 -10.0 -12.0 3
Total parking spots available n (10 )
6.0
Conclusions • Benefit of parking permit assignment Avoid competition for parking spots Adjust numbers of auto travelers among ODs Control total auto travelers.
• Parking permit trading Obtains nearly optimal parking permit distribution.
Thank you！
