A Time Series Approach to Forecast Highway Peak Period Spreading and Its Application in Travel Demand Modeling Sabya Mishra (University of Memphis) Timothy F. Welch (Georgia Institute of Technology) Subrat Mahapatra (Maryland State Highway Administration) Innovations in Travel Modeling Conference -2014 Monday, April 28, 2014, 1:30PM - 3:00PM
Background Peak traffic congestion periods commonly occur in urban areas (mostly AM and PM) AM peaks are typically more pronounced (or vice versa in other cases) Evening peaks can span for longer time period Shoulder peak occur immediately before and after the peaks 2
A Typical Example: HBW Trips Source: Data collected from joint HTS by MWCOG-BMC 3
Need for Peak Spreading Analysis Congestion Management Programs Identification of Highway System Problems Transportation demand management strategies Time of day travel choices Pricing or other strategies 4
Peak Spreading Types Active When travelers adjust their behavior in an effort to avoid the negative impacts of the congestion during the most heavily congested time of the peak, the type is referred as active peak spreading. Passive passive peak spreading on the other hand occurs as peak period travellers experience delays to their trip due to congested traffic conditions. 5
Modeling Peaks (After Mode Choice) Trip Generation Trip Distribution Mode Choice Daily Trip Tables (By Purpose and Mode) Time of Day Factors Time of Day (ToD) Model Assignment with ToD Trip Tables Directional Split Factors Note: ToD is possible in other steps as well 6
Trip Based Peak Spreading Trip Generation Trip Distribution Mode Choice Daily Transit Trips Revise Peak Hour Trips Stop Over Congested Links Daily Auto Trips Peak Hour Auto Trips Peak Hour Assignment Other approaches: link based and system based peak spreading 7
Opportunity for Research Determine the diurnal distribution for future years How to take advantage of existing data in obtaining peak spreading Apply various methods in travel behavior Examine impacts of proposed models for various applications 8
Time Series Modeling Time Series Smoothing Methods No Trend? Yes Trend Models Moving Average Exponential Smoothing Linear Quadratic Exponential Auto- Regressive 9
Time Series Modeling X t = θ 0 + k 1 X t 1 + k 2 X t 2 + + k p X t p + ε t X t, X t 1, X t 2 + + k p X t p are the observations in periods t, t-1,,t-p; p is the number of periods (lags) considered; k i are the autoregressive coefficients; θ 0 is the constant term and is the disturbance for period t. E(X t ) = μ = θ 0 1 k 1 k 2 k p + k 1 X t 1 + k 2 X t 2 + + k p X t p + ε t Var(X t ) = γ 0 = σ α 2 1 k 1 ρ 1 k 2 ρ 2 k p ρ p 10
Time Series Model Steps Step 1 Identify orders of the model p, q, d Step 2 Determine auto correlation function (ACF) and partial auto correlation function (PACF) If: any patterns evolved use p,d,q, Else: differentiate observations Obtain ACF and PACF of differentiated observations Step 3 Estimate model parameters Step 4 Examine disturbances of fitted models If: residuals are random and test is significant; go to step 5 Else: go to step 2 Step 5 Model is suitable for forecasting Note: p-number of autoregressive terms; d-number of non-seasonal variations; q-number of lagged forecast errors in the prediction equation 11
Autoregressive Modeling Used for forecasting trend Like regression model Independent variables are lagged response variables X t-1, X t-2, X t-3 etc. Assumes data are correlated with past data values 1 st Order: Correlated with prior period Estimate with ordinary least squares Identifying p-number of autoregressive terms; d-number of non-seasonal variations; q-number of lagged forecast errors 12
Plotting Time Series Data: I-95 SB 6AM-7AM 7AM-8AM Volume 3000 4000 5000 6000 0 200 400 600 800 1000 Volume 3000 5000 7000 0 200 400 600 800 1000 Time Periods (Weekday:2000-2013) Time Periods(Weekday:2000-2013) 8AM-9AM 9AM-10AM Volume 3000 5000 7000 0 200 400 600 800 1000 Volume 3000 5000 7000 0 200 400 600 800 1000 1200 Time Periods(Weekday:2000-2013) Time Periods(Weekday:2000-2013) 13
Plotting Time Series Data: I-95 NB 3PM-4PM 4PM-5PM Volume 3000 5000 7000 0 200 400 600 800 1000 1200 Volume 3000 5000 7000 0 200 400 600 800 1000 1200 Time Periods (Weekday:2000-2013) Time Periods(Weekday:2000-2013) 5PM-6PM 6PM-7PM Volume 3000 5000 7000 0 200 400 600 800 1000 1200 Volume 3000 5000 7000 0 200 400 600 800 1000 1200 Time Periods(Weekday:2000-2013) Time Periods(Weekday:2000-2013) 14
Maryland and Major Corridors 15
Count Locations 16
Time Series for AM Peak Peak Time Period Model Type Coefficients (t-stat) ar1 ar2 ar3 ma1 ma2 ma3 ma4 drift 6AM-7AM ARIMA(1,1,1) 0.144 (3.488) -0.810 -(31.521) 1 AM Peak (North Bound) PM Peak (South Bound) 7AM-8AM 8AM-9AM 9AM- 10AM 3PM-4PM 4PM-5PM 5PM-6PM 6PM-7PM ARIMA(2,1,2) with drift ARIMA(3,1,4) with drift ARIMA(1,1,3) with drift ARIMA(3,1,2) with drift ARIMA(3,1,3) with drift ARIMA(2,1,3) ARIMA(3,1,4) with drift 0.975 (16.069) 0.440 (2.728) 0.879 (20.741) 0.2236 (0.984) -0.3948 -(3.002) -1.5006 - (66.991) 0.0547 (0.569) -0.048 -(1.108) -0.177 -(1.542) 0.0363 (0.627) -0.3958 -(3.588) -0.9708 - (53.933) -0.0299 -(0.396) 0.550 (5.125 ) 0.142 8 (4.394 0.220 ) 8 (6.456 ) 0.660 6 (7.142 ) -1.702 -(32.796) -1.173 -(7.690) -1.571 -(29.875) -0.9974 -(4.337) -0.4336 -(3.255) 0.6237 (25.251) -0.9654 -(8.721) 0.706 (13.986) 0.421 (2.715) 0.486 (8.831) 0.008 (0.035) 0.0085 (0.066) -0.3958 - (16.630) 0.0389 (0.260) - 0.801 - (5.10 0.090 (2.60 6) - 0.475 1-0.882 1 - - 0.509 4 - (4.00 2) 0.55 8 (7.54 7) 0.44 32 (4.14 2) 1.096 (2.005) 0.584 (1.720) 0.754 (2.810) 0.4606 (1.821) 1.0615 (1.750) 0.4487 (1.666) 17
I-95 NB 18
I-95 SB 19
Topological Map of Maryland 20
Study Area 21
Three Level Modeling Regional Statewide MPO Washington Baltimore 22
MSTM Structure NHTS National/State/MPO Land Use Forecasts SE Data Reconciliation FAF3 Person Long-Distance Travel Model Trip Generation Destination Choice Trip Generation Trip Distribution Flow Estimation Disaggregation Person Travel Mode Choice II trips II trips Trucks EI/IE/EE trips Regional Model Statewide Model Time of day split Urban Model Reconciliation Multiclass Assignment EI/IE/EE trips 23
% VMT 2030 AM Peak Facility Type VMT 35% 30% 25% 20% 15% 10% 5% 0% Interstate Freeway Expressway Major Arterial Minor Arterial Collector Medium Speed Ramps 24
% VMT With and Without Peak Spreading 35% 30% Vehicle Miles Traveled Increase in VMT by Peak Spreading 25% 20% 15% 10% 5% 0% Interstate Freeway Expressway Major Arterial Minor Arterial Collector Medium Speed Ramps 25
Four Corridors Between Beltways 26
Growth Considering Peak Spreading Growth-S. of I-695 2007-S. of I-695 Growth-I-195 2007-I-195 Growth-MD 100 2007-MD 100 Growth-MD 32 2007-MD 32 US 29 I-95 US 1 MD 295 Growth-MD 198 2007-MD 198 Growth-N. of I-495 2007-N. of I-495 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% ADT 27
Choice Model Alternatives Mode of home based work trip Departure time for home based work trip Alternative 1 Drive alone Peak Alternative 2 Drive alone Off-peak Alternative 3 Shared ride Peak Alternative 4 Shared ride Off-peak Alternative 5 Transit Peak Alternative 6 Transit Off-peak Alternative 7 Walk and bicycle Peak Alternative 8 Walk and bicycle Off-peak 28
Various Nested Structures ROOT Drive Alone Shared Ride Transit Walk & Bike μ D μ S μ T μ W D P D O S P S O T P T O W P W O ROOT Peak Off-peak μ P μ O D P D O S P S O T P T O W P W O ROOT Drive Alone Shared Ride Transit Walk & Bike Peak Off-peak μ D μ S μ T μ W μ P μ O D P D O S P S O T P T O W P W O 29
Estimation Results Variables Drive alone Shared ride Transit Walk and bicycle Off-peak Peak Off-peak Peak Off-peak Peak Off-peak parameter parameter parameter parameter parameter parameter parameter Household characteristics Size1-0.01-1.48-2.38-0.16-0.14-0.18-0.15 Size3 0.05 0.12 0.38-0.03 0.07-0.03 0.05 Income1 0.16-0.01 0.65 0.04 0.12 0.01 0.12 Income3-0.17-0.16-0.30 0.01-0.18 0.07-0.19 Car1-1.27 0.46 1.43 0.72 1.02 0.76 0.98 Car3 0.05-1.24-0.89-0.21-0.17-0.21-0.10 Bicycles -0.12-0.12-0.08-0.03-0.12 0.06-0.08 Household location 0.23 0.19 0.17-0.15 0.13-0.01 0.15 Individual characteristics Gender 0.25-0.84-0.61 0.04 0.30 0.11 0.37 Age1 0.25 1.14 1.34 0.11 0.28 0.13 0.31 Age3 0.10 0.09-0.04 0.01 0.12 0.01 0.09 Race1-0.08-0.62-0.11-0.01-0.07-0.13-0.14 Race2-0.20-0.68-0.70-0.03-0.17 0.07-0.12 Occupation -0.20 0.07-0.23 0.02-0.16 0.08-0.15 Jobs 0.35 0.11 0.10-0.05 0.28-0.04 0.26 Work-related characteristics Flexibility for job 0.28-0.04 0.13-0.03 0.27-0.02 0.25 Parking cost -0.11-0.63-0.31-0.40-0.42-0.26-0.31 Subsidies for transit -0.30-0.26-0.62 0.43 0.03 0.22-0.06 Bicycle facility -0.12-0.12-0.08-0.03-0.12 0.06-0.08 Work location 0.09 0.15 0.09 0.11 0.24 0.20 0.2430
Elasticities Direct Elasticity The direct elasticities for transit are larger than that for drive alone Commuters by transit are more sensitive to travel-related attributes change than commuters by car. Commuters are more sensitive to changes in travel time than that of travel cost. Cross Elasticity Changes in travel cost and travel time for commuters by drive alone during peak period have the largest effects on probability choice of using transit during peak period. 31
Sensitivity 32
Conclusion Time series provides reasonable estimates of future peak Revised peak hours for future year models can be considered to obtain realistic travel demand results However, choice models should be developed for making models more realistic Adequate demand for each peak hour / hour can be captured in the model itself 33
Future Research The team is in the process of developing choice models (and their variations) for peak spreading Choice models will be suitable for policy and scenario analysis Variations of formulations: MNL NL CNL Others Combinations of departure time and mode choice models 34
Acknowledgment 35
Thank You! Sabyasachee Mishra, Ph.D., P.E Assistant Professor Department of Civil Engineering University of Memphis, Memphis, TN 38152, USA Email: smishra3@memphis.edu 36