Evaluating Alternative Operations Strategies to Improve Travel Time ...

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SHRP 2 L11: Final Appendices Step 3 – Evaluate the Change that Affects Unreliability A. Estimate the expected reduction in speed variability achieved through the implementation of the strategy. B. Calculate the certainty-equivalent value for the new scenario. Step 3 – Evaluate the Change that Affects Unreliability A. “Smart” systems, including collision-warning systems and systems that automatically adjust cruise-control speed based on the relative distance of the car ahead, can reduce speed variability and travel-time unreliability as they are widely adapted in vehicles. It is estimated that the new system would reduce the speed variability,α, by 50%. Assumptions for the new scenario: • Vehicle volume remains constant over time • Unknown speed ( V T ) = 32.67 mph • Guaranteed speed (I) = 32.67 mph • α = 0.5× 0.3635 = 0.1817 B. The European Put option and a 5.00% risk-free interest rate are chosen. Thus, r = 0.05 The lowest 1% speed is now 20.18 mph due to the change in the travel-time variability. Therefore, the new contract length is given by ⎛ 60 / 20.18 ⎞ T -t = ⎜ ⎟× 10 = 0.0000566 years ⎝365× 24× 60 ⎠ Sigma is calculated using the formula for volatility in finance, which is the standard deviation of the log speed divided by the square root of the contract length: α 0.1817 σ = = = 24.17 T − t 0.0000566 Perform intermediate and final option value calculation: 2 ln( VT / I) + ( r+ σ / 2)( T −t) d1 = σ ( T − t) 2 ⎛32.67 ⎞ ⎡ ⎛24.17 ⎞⎤ ln ⎜ ⎟ + ⎢0.05 + ⎜ ⎟⎥ × 0.0000566 ⎝32.67 ⎠ ⎝ 2 ⎠ = ⎣ ⎦ = 0.09089 24.17× 0.0000566 DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-45
SHRP 2 L11: Final Appendices d2 = d1 −σ ( T −t) = 0.09089 − 24.12 0.0000566 =−0.09086 Nd ( ) = N(0.09089) = 0.4638 1 Nd ( ) = N( − 0.09086) = 0.5362 2 PV t = Ie Nd −VNd −rT ( −t) ( T,) ( 2) T ( 1) = e − −0.05(0.0000057) 32.67 (0.5362) 32.67(0.4638) = 2.37 mph Thus, new certainty-equivalent value in minutes per mile is 1 1 PV ( , ) ( ) 60 0.14 minutes per mile T t = − × = 30.3 32.67 Step 4 – Calculate the Road User Value of Reliability Change A. Determine the value of time for different vehicle classes. B. Calculate the value of the reliability improvement for each vehicle class. C. Calculate the value of reliability improvement for the average a.m. peak hour. D. Calculate the total annual value of the reliability improvement over the length of the highway for all user groups for the average a.m. peak hour only. DETERMINING THE ECONOMIC BENEFITS OF IMPROVING TRAVEL-TIME RELIABILITY Page B-46
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