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MIT1_258JS10_lec18

# MIT1_258JS10_lec18 - Vehicle Scheduling Outline 1 Timetable...

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Outline 1. Timetable Development 2. Fleet Size 3. ehicle Scheduling Vehicle Scheduling Nigel H.M. Wilson 1.258J/11.543J/ESD.226J Spring 2010, Lecture 18 1 Vehicle Scheduling

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Can translate frequency into timetable by specifying headways as: equal -- appropriate if demand is uniformly distributed across period balanced load -- appropriate if there is substantial variation in demand ver period over period clockface or not -- do headways repeat every hour Cumulative Passenger Flow Time of Day P b1 P e1 h e1 h b1 9:00 6:00 2 Nigel H.M. Wilson 1.258J/11.543J/ESD.226J Spring 2010, Lecture 18 Timetable Development
If we have N departures in peak period: qual headway solution: equal headway solution: balanced load solution: Nigel H.M. Wilson 1.258J/11.543J/ESD.226J Spring 2010, Lecture 18 3 Timetable Development

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Salzborn’s Fleet Size Theorem: iven: Given: l(k,t,s) = # of departures from terminal k by time t following schedule s (k,t,s) = # of arrivals at terminal k by time t following schedule s a(k,t,s) of arrivals at terminal y time llowing schedule and: d(k,t,s) = l(k,t,s) - a(k,t,s) , deficit function at terminal k at time t following schedule s Nigel H.M. Wilson 1.258J/11.543J/ESD.226J Spring 2010, Lecture 18 4 Fleet Size Requirement
for T terminals Salzborn’s Fleet Size Theorem: hen: Then: N(s), the minimum size fleet to serve schedule s , is given by: Also, N(s) Max # of trips in simultaneous operation. Nigel H.M. Wilson 1.258J/11.543J/ESD.226J Spring 2010, Lecture 18 5 Fleet Size Requirement

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The deficit function, or minimum required fleet size, may be reduced by: shifting de parture and/or arrival times adding deadhead trips between terminals Schedule m m m u u m u u m v v u u m v m 1 5 4 3 2 Fixed S n m v v u 7 6 10 9 8 it Functio n erminal m 4 -- 3 -- 2 -- Defic for T 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4
Input: --A set of vehicle revenue trips to be operated, each

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MIT1_258JS10_lec18 - Vehicle Scheduling Outline 1 Timetable...

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