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Sonoma Marin Area Rail Transit (SMART)
Analysis on the Effectiveness of the Proposed Rail System
MS&E 220 – Probabilistic AnalysisFall 2008 – Professor Samuel Chiu
Prepared By:Samuel GambrellPaul JonesDavid Williams
December 4, 2008
Overview
• This analysis will examine the probabilities related to making a decision on whether to support the Sonoma Main Area Rail Transit system
• This includes:– Creating a decision analysis tool – Examining input probabilities to the model
• Ridership• Costs & Revenue
Decision Analysis
• This process used decision trees, to structure the probability inputs
• Values of different outputs are assigned by the user
• Feedback on whether they should or should not support the decision is provided
• So is a measure of how much change is required for them to change their position
Decision Tree: Yes or No to the TrainValue Measure U-Value
0.39 Costs overrun >15 %20 20
Daily trips reduced0.25 15,403 0.29 Costs delta <>15%
25 2524.6104
0.31 Cost underrun of >15%30 30
0.39 Costs overrun >15 %10 10
Build SMART Train 0.5 11,210 0.29 Costs delta <>15%15 15
14.0709 14.6104
0.31 Cost underrun of >15%20 20
0.39 Costs overrun >15 %0 0
16 0.25 7018 0.29 Costs delta <>15%3 3
2.45226
0.31 Cost underrun of >15%5 5
>>> Do not build SMART Train16 16
Value from User
Costs Relative valueGreater than 87,184,492 Greater than 15,403 Costs overrun >15 % 20Greater than 87,184,492 Greater than 15,403 Costs delta <>15% 25Greater than 87,184,492 Greater than 15,403 Cost underrun of >15% 30around 63,453,133 around 11,210 Costs overrun >15 % 10around 63,453,133 around 11,210 Costs delta <>15% 15around 63,453,133 around 11,210 Cost underrun of >15% 20Less than 39,721,774 Less than 7,018 Costs overrun >15 % 0Less than 39,721,774 Less than 7,018 Costs delta <>15% 3Less than 39,721,774 Less than 7,018 Cost underrun of >15% 5
Relative value of 1/4 percent sales tax 16
Reduced cars on 101Pounds of GW gas reduced
Recommended Decision
If your prefence for saving the 1/4 % of sales tax changed by the value below, your preference would change
Vote against the train -1.929144516
Results and change of preference required to alter position
RIDERSHIP PROJECTIONS
Distance between Santa Rosa Stations = 1.18 milesTotal area of Santa Rosa within 1 mile of train station is = 5.36 square miles (see spreadsheet for calcs)
Population Density for Santa Rosa = 3844 people per square mileSanta Rosa Residents within 1 mile of SMART station is = 3,844 x 5.3564 = 20590
Population within 1 mile of station
Larkspur
San Rafael (2)
Novato (2)
Petaluma (2)
Cotati
Rohnert Park
Santa Rosa (2)
Windsor
Healdsburg
Cloverdale
0 10000 20000 30000
11721
21074
11812
24812
12001
19792
20590
11787
9114
10166
Population within 1 mile of SMART Station
Calculation for Santa Rosa (special case overlapping station radii) Commuters within 1 mile of station are
significantly more likely to use SMART
Low Projection:Assessed Ridership Conditioned on
Proximity to Station and Commuter Status
High Projection:Assessed Ridership Conditioned on
Proximity to Station and Commuter Status
A.
B.C. D.
Scenario Gas PriceRegular [$/gal.]
Projected Riders
Ridership as % of target Max of 6,200 riders
A. $0 per gallon equates to zero riders*** 0.00 0 0.00 %
B. June 2006 (actual)**** 3.21 5000 80.6 %
C. Hypothetical Case 1 * 5.00 5750 92.7 %
D. Hypothetical Case 2 * 6.00 5950 96.0 %
E. Maximum Target Riders ** Infinity 6200 100.0 %
E.
Projected Riders vs. Gas Price
Ridership Projections
SMART Project Cost
Sales Tax Growth
• Obtained Taxable Income from Sales for 1998 thru 2007 through California BOE
• Due to the complexity and uncertainties of a financial model a normal curve was used with the mean and SD of historical data to predict growth
• Dynamic equations were used to predict Taxable Income till 2029
Probability of Taxible Sales Income in Sonoma and Marin Counties
0
0.2
0.4
0.6
0.8
1
1.2
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84
Taxible Sales Income in Billions
Pro
ba
bili
ty
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
Probability of Accumulative Gain from Tax for Each Year
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
$0.00
$65,0
00,0
00.00
$130
,000
,000.0
0
$195
,000
,000.0
0
$260
,000
,000.0
0
$325
,000
,000.0
0
$390
,000
,000.0
0
$455
,000
,000.0
0
$520
,000
,000.0
0
$585
,000
,000.0
0
$650
,000
,000.0
0
$715
,000
,000.0
0
$780
,000
,000.0
0
$845
,000
,000.0
0
$910
,000
,000.0
0
$975
,000
,000.0
0
$1,04
0,00
0,00
0.00
$1,10
5,00
0,00
0.00
$1,17
0,00
0,00
0.00
$1,23
5,00
0,00
0.00
$1,30
0,00
0,00
0.00
$1,36
5,00
0,00
0.00
$1,43
0,00
0,00
0.00
$1,49
5,00
0,00
0.00
Total Gain from 1/4 Cent Tax
Pro
ba
bili
ty2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
Probability of Income from 1/4 Cent Sales Tax
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
$750
,000
,000
.00
$770
,000
,000
.00
$790
,000
,000
.00
$810
,000
,000
.00
$830
,000
,000
.00
$850
,000
,000
.00
$870
,000
,000
.00
$890
,000
,000
.00
$910
,000
,000
.00
$930
,000
,000
.00
$950
,000
,000
.00
$970
,000
,000
.00
$990
,000
,000
.00
$1,0
10,00
0,00
0.00
$1,0
30,00
0,00
0.00
$1,0
50,00
0,00
0.00
$1,0
70,00
0,00
0.00
$1,0
90,00
0,00
0.00
$1,1
10,00
0,00
0.00
$1,1
30,00
0,00
0.00
$1,1
50,00
0,00
0.00
$1,1
70,00
0,00
0.00
$1,1
90,00
0,00
0.00
$1,2
10,00
0,00
0.00
$1,2
30,00
0,00
0.00
$1,2
50,00
0,00
0.00
$1,2
70,00
0,00
0.00
$1,2
90,00
0,00
0.00
$1,3
10,00
0,00
0.00
$1,3
30,00
0,00
0.00
$1,3
50,00
0,00
0.00
$1,3
70,00
0,00
0.00
$1,3
90,00
0,00
0.00
$1,4
10,00
0,00
0.00
$1,4
30,00
0,00
0.00
$1,4
50,00
0,00
0.00
Income
Pro
bab
ility
Income predicted by SMART paper
Model vs Paper
• According to the model the paper has a 99.85% chance of making the predicted income from sales tax
Assumed IncomeTotal Gains Probability
Yes $11,376 $33,201 0.7290.9
Yes $2,4000.9 No $0 $21,825 0.081
0.1Yes $19,425
0.9 Yes $11,376 $30,801 0.0810.9
No $00.1 No $0 $19,425 0.009
0.1
Yes $11,376 $13,776 0.0810.9
Yes $2,4000.9 No $0 $2,400 0.009
0.1No $0
0.1 Yes $11,376 $11,376 0.0090.9
No $00.1 No $0 $0 0.001
0.1
State Transit AssistanceProgram Funds
Federal HighwayAdministration Funds NCRA Capital Offsets
Currently unable to find a source for an accurate probability.
Probability of a Cost Overrun
• Based on Transit systems built since 1994• Used to calculate the probability of a cost
overrun– Assumed normal
Study ResultsNumber of Projects 16Overage Overrun 30%Standard Deviation 39%
Translating this to the SMART ProjectTotal Cost with no buffer $1,081,076,800.00
Total Cost with 20% buffer built in to the estimates $1,351,346,000Estimated mean cost $1,405,399,840Standard deviation $527,024,940.00
