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www.quanticol.eu Probabilistic forecasts for bike-sharing systems N. Gast (Inria) joint work with G. Massonnet (Inria / Mines Nantes), D. Reijsbergen (U. Edinburgh), M. Tribastone (IMT Lucca) May 24, 2017 quan�col . ........ . . . ... ... ... ... ... ... ... May 24, 2017 1 / 15

Bike-sharing systems (BSS) www.quanticol.eu Figure: V´ elib’ stations in the centre of Paris � Each station has a given number of parking slots. � Users enter the system by picking up a bike at a station and making a trip to another station, where they drop the bike on an available parking spot. May 24, 2017 2 / 15

Forecasting : what and why? www.quanticol.eu What is forecasting : Present (time t ) Future (time t+ x hours) Historical data May 24, 2017 3 / 15

Forecasting : what and why? www.quanticol.eu What is forecasting : Present (time t ) Future (time t+ x hours) Historical data Why forecasting : � Operator perspective (rebalancing) � User perspective (will I find a bike?) This talk May 24, 2017 3 / 15

Outline www.quanticol.eu Is forecasting easy? 1 Probabilistic forecasts 2 Conclusion and Perspectives 3 May 24, 2017 4 / 15

V´ elib’ data www.quanticol.eu V´ elib’ Data (Paris) : availability at stations + trips info from September 2013 to December 2014 Figure: Evolution of the average departure rate from V´ elib’ stations during the day May 24, 2017 5 / 15

First attempt: deterministic forecasts www.quanticol.eu Output of forecasting method : X t ( t + h ). Examples - Last-Value (LVP) : availability at t + h is equal to the availability at t . - Historical (HP) : distribution of the bikes availability at t + h , based on historical observations. - Machine learning tools (ARIMA, Bayesian network,...) May 24, 2017 6 / 15

Is this good enough? www.quanticol.eu Figure: Comparison of the RMSEs for different predictors. Average error : � 3 bikes for h = 30 min � 5 bikes for h = 2h. May 24, 2017 7 / 15

Is this relevant for users? www.quanticol.eu (a) Empty station (b) Full station Figure: Shortage and blocking stations Predict blocking situtations - Warn the users - Rebalance the system - Improve traffic flow → Need for good forecasting tools May 24, 2017 8 / 15

Outline www.quanticol.eu Is forecasting easy? 1 Probabilistic forecasts 2 Conclusion and Perspectives 3 May 24, 2017 9 / 15

www.quanticol.eu Output of forecasting method : � � � Prob X t ( t + h ) = k � present and historical data , � for k ∈ { 0 , . . . , capacity } . � How to evaluate a probabilistic predictor? � Scoring rule � False positive / false negative May 24, 2017 10 / 15

Queueing network representation www.quanticol.eu 1 τ 31 = µ 31 λ 3 ( t ) κ 1 p 13( t ) µ 1 ( t ) λ 1 ( t ) p 12( t ) X 1 ( t ) λ 2 ( t ) Z 21 ( t ) Figure: A BSS network with 3 stations � Moment-based Probabilistic Prediction of Bike Availability for Bike-Sharing Systems. / Feng, Cheng; Hillston, Jane; Reijsbergen, Daniel. (QEST 2016) � Probabilistic Forecasts of Bike-Sharing Systems for Journey Planning. Nicolas Gast; Guillaume Massonnet; Daniel Reijsbergen; Mirco May 24, 2017 11 / 15 Tribastone (CIKM 2015)

www.quanticol.eu Mean-field analysis → independence of the stations µ ( t ) λ ( t ) ⇓ µ ( t ) µ ( t ) µ ( t ) µ ( t ) . . . . . . κ 0 1 2 λ ( t ) λ ( t ) λ ( t ) λ ( t ) Probabilistic predictor �� h � p ( j | i , t , h ) = exp Q ( t + s ) ds 0 i , j where Q ( t ) is the kernel of the Markov chain at time t . May 24, 2017 12 / 15

0.9 Queue QMP score of predictor (for the success) Historic HP 0.8 Last-value LVP always go 0.7 0.6 0.5 0.4 0.3 0 2 4 6 8 10 prediction horizon (in hours) Application to V´ elib’ Data www.quanticol.eu We consider four trip recommendation predictors : � Queueing model � Historic predictor � Last-value � Always-go Metric: Scoring rule GO/NO-GO � 1 if prediction correct � 0 if trip could have been made but was not recommended � − 5 if trip could not been made but has been recommended May 24, 2017 13 / 15

Application to V´ elib’ Data www.quanticol.eu Metric: Scoring rule GO/NO-GO � 1 if prediction correct � 0 if trip could have been made but was not recommended � − 5 if trip could not been made but has been recommended 0.9 Queue QMP score of predictor (for the success) Historic HP 0.8 Last-value LVP always go 0.7 0.6 0.5 0.4 0.3 0 2 4 6 8 10 May 24, 2017 13 / 15 prediction horizon (in hours)

Outline www.quanticol.eu Is forecasting easy? 1 Probabilistic forecasts 2 Conclusion and Perspectives 3 May 24, 2017 14 / 15

www.quanticol.eu What’s important? � Deterministic predictors : not well-suited for users. � Stochasticity of the system must be included in forecasting tools. � Observation of the current state : useful for horizon of 2 to 5 hours but not really useful after. May 24, 2017 15 / 15