ChangiNOW A New Queueing Model for Efficient

Transcription

1 ChangiNOW A New Queueing Model for Efficient Taxi Allocation Afian Anwar, Mikhail Volkov, Daniela Rus Intelligent Transportation Systems Conference October 7, 2013 The Hague, Netherlands

2 MOTIVATION

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6 PROPOSED APPROACH Find out how many flights arrive at each terminal, and how many tourists they bring Establish a relationship between tourist arrival flows and the taxi queue time at each terminal Using this data, build a queuing model to predict the expected queuing time for a taxi about to join the queue at each terminal Develop mobile applications to share this information with taxi drivers, directing them to terminals with the highest demand FCL

7 PROPOSED APPROACH Find out how many flights arrive at each terminal, and how many tourists they bring Establish a relationship between tourist arrival flows and the taxi queue time at each terminal Using this data, build a queuing model to predict the expected queuing time for a taxi about to join the queue at each terminal Develop mobile applications to share this information with taxi drivers, directing them to terminals with the highest demand FCL

8 PROPOSED APPROACH Find out how many flights arrive at each terminal, and how many tourists they bring Establish a relationship between tourist arrival flows and the taxi queue time at each terminal μ Using this data, build a queuing model to predict the expected queuing time for a taxi about to join the queue at each terminal Develop mobile applications to share this information with taxi drivers, directing them to terminals with the highest demand FCL

9 PROPOSED APPROACH Find out how many flights arrive at each terminal, and how many tourists they bring Establish a relationship between tourist arrival flows and the taxi queue time at each terminal Using this data, build a queuing model to predict the expected queuing time for a taxi about to join the queue at each terminal Develop a mobile app to direct taxis to high demand terminals FCL

10 RELATED WORK Mobility on Demand Parragh (2008) Berbeglia (2010) Double Ended Queueing Pavone (2011) Taxi System Optimization Kendall (1951) Sasieni (1961) Larson (1981) Yuan (2010) Hu (2010) Wu (2011)

11 RELATED WORK Assumes Steady State Conditions Parragh (2008) Berbeglia (2010) Pavone (2011) Kendall (1951) Sasieni (1961) Larson (1981) Yuan (2010) Hu (2010) Wu (2011)

12 RELATED WORK Parragh (2008) Berbeglia (2010) Pavone (2011) Uses Hotspot Analysis Kendall (1951) Sasieni (1961) Larson (1981) Yuan (2010) Hu (2010) Wu (2011)

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15 SERVICE MODEL flight +5 Ltrans... Step 1 Taxi queries the ChangiNOW server LQ u

16 SERVICE MODEL flight +5 Ltrans LQ... Step 2 Server checks for μ(t), L trans (t) and L Q (t) u

17 SERVICE MODEL flight +5 Ltrans... LQ u Step 3 Server returns the predicted waiting time, the probability of entering the queue and a bounded estimate of the wait for each terminal.

18 SERVICE MODEL flight +5 Ltrans... LQ u Step 4 Taxi accepts the server s recommendation (terminal with the shortest waiting time)

19 SERVICE MODEL flight +5 Ltrans... LQ u Step 5 Taxi is immediately added to L trans (t) for the terminal he chose

20 ASSUMPTIONS flight +5 Ltrans... LQ u Commitment Implies that taxis arrive at the terminal with probability 1 Order Taxis do not overtake each other on the way to the terminal

21 ESTIMATING PASSENGER ARRIVALS Passengers u(t) 1200 flight(t) am 3 am 6 am 9 am 12 pm Time 3 pm 6 pm 9 pm 12 am

22 ESTIMATING PASSENGER ARRIVALS Passengers u(t) 1200 flight(t) term(t) am 3 am 6 am 9 am 12 pm Time 3 pm 6 pm 9 pm 12 am

23 ESTIMATING PASSENGER ARRIVALS Passengers u(t) 1200 flight(t) term(t) am 3 am 6 am 9 am 12 pm Time 3 pm 6 pm 9 pm 12 am

24 ESTIMATING PASSENGER ARRIVALS Passengers u(t) 1200 flight(t) term(t) u(t) am 3 am 6 am 9 am 12 pm Time 3 pm 6 pm 9 pm 12 am

25 ! QUEUEING MODEL AND PREDICTION ENGINE L Q (t) : #taxis in queue at time t L virtual (t) = L transit (t) + L Q (t) L transit (t) L Q (t)...

26 ! QUEUEING MODEL AND PREDICTION ENGINE L Q (t) : #taxis in queue at time t L transit (t) : #taxis in transit to the airport terminal at time t L max : taxi queue capacity L virtual (t) = L transit (t) + L Q (t) L transit (t) L Q (t)... L max

27 ! QUEUEING MODEL AND PREDICTION ENGINE L Q (t) : #taxis in queue at time t L transit (t) : #taxis in transit to the airport terminal at time t L max : taxi queue capacity L virtual (t) = L transit (t) + L Q (t) L transit (t) L Q (t)...

28 ! QUEUEING MODEL AND PREDICTION ENGINE By assumptions (1) Order and (2) Commitment, the queue will grow by Ltransit(t) taxis When the taxi arrives at the queue minutes later, the queue will shrink by µ t taxis (avg service rate x time interval) L virtual (t) = L transit (t) + L Q (t) L transit (t) L Q (t)...

29 ! QUEUEING MODEL AND PREDICTION ENGINE Theorem 1 The queue is expected to be free if and only if E[L q ] < L max. where E[L q ] = L q (t)+l trans (t) t µ t = L v (t) t µ t L virtual (t) = L transit (t) + L Q (t) L transit (t) L Q (t)...

30 QUEUEING MODEL AND PREDICTION ENGINE How sure are we that the taxi will be able to enter the queue? Theorem 2 The queue is expected to be free with probability Pr[entry] = Pr[L q (t + t) < L max ]= Proof: Z t+t Z t µ t e µ t x ( µ tx) (L v(t) L max ) (L v (t) L max )! dx. (5) The probability that the queue will be free is Proof: The probability that the queue will be free is equal to Pr[L q (t +t) < L max ] (i.e., at least L q (t +t) L max +1 taxis will have left the terminal with a passenger during the time t). 3) What is the waiting time?: The other crucial parameter

31 QUEUEING MODEL AND PREDICTION ENGINE Case 1 Case 3 Case 2 Pr[taxi entered the queue] L max = E[L ] (taxis) q

32 QUEUEING MODEL AND PREDICTION ENGINE What guarantees can we make for expected waiting time? Theorem 3 The expected waiting time E[W]= minw s.t. Z t+t+w t+t µ(x)dx L q (t + t). (6) Proof: Define the waiting time service rate µ W as the average service rate while the taxi is waiting in the queue, given by µ W = µ s.t. µ = 1 W Z t+t+ Lq(t+t) µ t+t µ(x)dx. (7) Simplify using W = L q(t+t) µ and solving for W, first substituting W : 1 L q (t + t) Z t+t+w t+t µ(x)dx = 1 and then multiplying across: Z t+t+w µ(x)dx = L q (t + t) (8) t+t

33 QUEUEING MODEL AND PREDICTION ENGINE What is the probability that the taxi s expected waiting time is less than some wmax? Theorem 4 The waiting time W will be less than the maximum acceptable waiting time W max with probability Pr[W < W max ]= Z Wmax 0 µ w e µ wx ( µ wx) L q(t+t) L q (t + t)! dx. (9) Theorem 5 a This is equivalent to the probability that at least take place within an interval wmax L q (t + t) services will

34 QUEUEING MODEL AND PREDICTION ENGINE What is the minimum Z waiting time wα that the taxi will experience a wait of less than wα with probability α? Theorem 5 The a-certainty waiting time W a = minw s.t. Z W 0 µ w e µ wx ( µ wx) L q(t+t) L q (t + t)! dx a We choose the smallest possible wmax such that the probability computed through the integral is greater than or equal to α

35 QUEUEING MODEL AND PREDICTION ENGINE We designate two groups of drivers, Group A (risk loving) and Group B (risk averse). Group A is content to specify wmax = 40 min while Group B specifies wα with probability α = 0.9 ChangiNOW prediction: Pr[entry] 0.76 no. taxis entered = 75, 431/100, 000 Group A: avg. Pr[W < 40] = 0.18 Group B: avg. W a,a = 0.9 = 57 min Simulation results: no. Group A with W < W max = 13,695/75,431 = 0.18 no. Group B with W < W a = 70,243/75,431 = 0.93

36 LARGE SCALE SIMULATION Simulation results showed 51% improvement in taxi waiting time Minutes 60 Observed Smart Rebalancing am 3 am 6 am 9 am 12 pm 3 pm 6 pm 9 pm 12 am 70 Time

37 LARGE SCALE SIMULATION Simulation results showed 31% improvement in passenger waiting time 70 Time Minutes Observed Smart Rebalancing 12 am 4 am 8 am 12 pm 4 pm 8 pm 12 am Time

38 CONCLUSIONS + FUTURE WORK 1 Theory Non stationary queueing model formally validated 2 Simulation 51% and 31% Decrease in Taxi and Passenger Waiting Times 3 Research Prototype Collaboration between SUTD and Changi Airport to build app

39 ACKNOWLEDGEMENTS Co Author: Mikhail Volkov Advisors: Prof Daniela Rus (EECS) & Prof Amedeo Odoni (Aero Astro) Data Partners: Comfort Delgro & Changi Airport Group SMART Innovation Center: Howard Califano Web: This project was funded in part by ONR grant N , the Future Mobility project at MIT and SMART Innovation Center Explorer Grant No