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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

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May 24, 2017 1 / 15

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Bike-sharing systems (BSS)

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

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Forecasting : what and why?

What is forecasting : Present (time t) Future (time t+xhours) Historical data

May 24, 2017 3 / 15

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Forecasting : what and why?

What is forecasting : Present (time t) Future (time t+xhours) Historical data Why forecasting :

Operator perspective (rebalancing) User perspective (will I find a bike?) This talk May 24, 2017 3 / 15

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Outline

1

Is forecasting easy?

2

Probabilistic forecasts

3

Conclusion and Perspectives

May 24, 2017 4 / 15

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V´ elib’ data

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

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First attempt: deterministic forecasts

Output of forecasting method : Xt(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

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Is this good enough?

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

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Is this relevant for users?

(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

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Outline

1

Is forecasting easy?

2

Probabilistic forecasts

3

Conclusion and Perspectives

May 24, 2017 9 / 15

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Output of forecasting method : Prob

• Xt(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

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Queueing network representation

κ1

X1(t) λ1(t) λ2(t) λ3(t) µ1(t)

p12(t) p13(t)

Z21(t) τ31 =

1 µ31

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

Tribastone (CIKM 2015) May 24, 2017 11 / 15

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Mean-field analysis → independence of the stations

µ(t) λ(t)

⇓ 1 2 . . . . . . κ µ(t) λ(t) µ(t) λ(t) µ(t) λ(t) µ(t) λ(t)

Probabilistic predictor

p(j|i, t, h) = exp h Q(t + s)ds

• i,j

where Q(t) is the kernel of the Markov chain at time t.

May 24, 2017 12 / 15

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Application to V´ elib’ Data

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

2 4 6 8 10 prediction horizon (in hours) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 score of predictor (for the success)

Queue QMP Historic HP Last-value LVP always go

May 24, 2017 13 / 15

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Application to V´ elib’ Data

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

2 4 6 8 10 prediction horizon (in hours) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 score of predictor (for the success)

Queue QMP Historic HP Last-value LVP always go

May 24, 2017 13 / 15

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Outline

1

Is forecasting easy?

2

Probabilistic forecasts

3

Conclusion and Perspectives

May 24, 2017 14 / 15

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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