# Smart Recommendations for Renting Bikes in Bike-Sharing Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Station-Based BSSs

## 4. User-Centred Station Recommendation

#### 4.1. Standard Strategies

#### 4.1.1. Shortest Distance

#### 4.1.2. Informed Shortest Distance

#### 4.1.3. Distance Resources

#### 4.2. Distance Expected Resources

#### 4.3. Expected Cost

#### 4.3.1. Demand Estimation

#### 4.3.2. Probability Calculation

#### 4.3.3. Expected Cost Recommendation

## 5. Evaluation of User-Centred Recommendation

#### 5.1. Simulation Experiment Setup

- Data on the trips: Including, for each trip, the time of taking a bike, origin station, destination station, travel time, and approximate route. However, in order to anonymize the data, only the day and hour of the pick-up time of each trip are given (without minutes). Each trip includes a user type, with possible values representing regular or occasional users, BiciMAD staff, or unidentifiable users;
- Situation of the stations: including the number of available bikes and slots, and whether or not a station was active.

- ShortestDistance (SD);
- InformedShortestDistance (ISD);
- DistanceResources (DR);
- DistanceExpectedResources (DER);
- ExpectedCost (EC(x,y)), where $x=RentFailCost$ and $y=ReturnFailCost$.

- A user ${u}_{k}$ appears at a geographical location ${l}_{k}$ at time $t$ and asks the recommendation system for a rental recommendation (with request $ren{t}_{k}=\langle {l}_{k},t,md\rangle $). The maximum acceptable distance in the experiments is set to $md=600$ m;
- The recommendation system applies its strategy and returns a ranking of possible stations;
- Given the ranking, the user filters out all stations that they have already tried. If no stations are left, the user will abandon the system without renting a bike. Otherwise, they walk towards the first station in the list of recommendations in order to rent a bike;
- In case the user gets to a station and there are no available bikes, they repeat the whole process until they either abandon the search or finally find a bike. In this case, the value of the maximum acceptable distance ($md$) is reduced by the distance the user has walked already.

- In the moment a user ${u}_{k}$ has rented a bike at a station ${s}_{i}$, they issue a return request $retur{n}_{k}=\langle {l}_{k},t,{l}_{d}\rangle $, where ${l}_{k}$ and $t$ are the current position and time, and ${l}_{d}$ is their final destination location;
- The recommendation system returns a ranking of stations for returning the bike;
- Given the ranking, the user filters out any stations that they have already tried, and selects the first remaining station for returning the bike;
- In case the user gets to a station and there are no available slots, they repeat the whole process until they finally find a station to leave the bike (there is no possibility to abandon the attempt).

#### 5.2. Simulation Results

- #a: number of users who dropped out (abandoned) the system, and percentage with regards to users that finished;
- #fh: number of failed user rental attempts and percentage over all user rental attempts;
- #fr: number of failed user return attempts and percentage over all user return attempts;
- tt: average total time of users in the system; this is based on the time a user requires to go from their origin to a bike rental station, to cycle from there to a station to return the bike and, finally, to walk to their final destination. The value is averaged over all users who were able to rent a bike (i.e., who did not abandon the attempt);
- AET: average station empty time; this is the time for which a station has been empty (without available bikes) and, thus, would potentially have been denying service. The value is the average over all 169 stations for the whole simulation period.

## 6. Recommendation Based on Local and Global Utility

#### 6.1. Calculating the Future Impact of Rentals and Returns

#### 6.2. Recommendation Based on Expected Cost and Future Impact

- $md$—the maximum distance to rental stations;
- $RentFailCost$ and $ReturnFailCost$—the penalization costs applied if a user is unsuccessful when trying to rent or return a bike;
- $tf$—the timeframe for predicting the future impact of a rental or return action;
- $FRentFC$ and $FReturnFC$—the penalization costs applied when estimating the costs of local alternative stations for users who cannot find a bike or slot at station ${s}_{i}$ in the future;
- $MD$—the maximum distance to consider alternative stations for users who cannot find a bike or slot at station ${s}_{i}$;
- $f$—the factor applied to the global impact on the cost estimation.

## 7. Evaluation of ExpectedCostFutureImpact Recommendation

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Example of the evolution of the number of bikes at a station. Values of $changes\left({s}_{i},t,{t}_{exp}\right)$, $commitedBikes\left({s}_{i},{t}_{exp}\right)$, and $commitedSlots\left({s}_{i},{t}_{exp}\right)$ are shown.

**Figure 4.**ExpectedCost strategy with increasing equal values of RentFailCost and fixed ReturnFailCost.

**Figure 5.**Impact of different prediction timeframes on the behaviour of ExpectedCostFutureImpact (with $RentFailCost$= 3000, $ReturnFailCost$ = 2500, $FutRentFailCost$= 3000, $FutReturnFailCost$= 1000, and $f$= 1).

**Figure 6.**Impact of different factors $f$ with ExpectedCostFutureImpact (with $RentFailCost$= 3000, $ReturnFailCost$= 2500, $FutRentFailCost$= 3000, $FutReturnFailCost$= 1000, and $tf$= 60 min).

Symbols | Description |
---|---|

$S=\left\{{s}_{1},\dots ,{s}_{n}\right\}$ | Set of stations |

$l\left({s}_{i}\right)$ | Location of station s_{i} |

$c\left({s}_{i}\right)$ | Capacity of station ${s}_{i}$ |

$bikes({s}_{i},t)$ | Number of available bikes at time $t$ |

$slots({s}_{i},t)$ | Number of empty slots at station ${s}_{i}$ at time $t$ |

${u}_{k}$ | User k |

$ren{t}_{k}=\langle {l}_{k},t,\text{}md\rangle $ | Rental request of user k, with: ${l}_{k}$ (initial user location), t (time the request is issued), md (maximum distance the user is willing to walk to get a bike) |

$retur{n}_{k}=\langle {l}_{k},{d}_{k},t\rangle $ | Return request of user k, with: ${l}_{k}$ (initial user location), d_{k} (location of the user’s final destination), t (time the request is issued) |

$wtime\left(x,y\right)$ | Expected walking time from x to y |

$btime\left(x,y\right)$ | Expected cycling time ¡ from x to y |

$wdist\left(x,y\right)$ | Expected walking distance from x to y |

$bdist\left(x,y\right)$ | Expected cycling distance from x to y |

$RentStation\left(ren{t}_{k}\right)$ | Ordered sequence of recommended rental stations $\left({s}_{1},\dots ,{s}_{m}\right)={\left({s}_{i}\right)}_{i=1}^{m}$ |

$ReturnStation\left(retur{n}_{k}\right)$ | Ordered sequence of recommended return stations $\left({s}_{1},\dots ,{s}_{m}\right)={\left({s}_{i}\right)}_{i=1}^{m}$ |

t_{exp} | Expected arrival time of a user at a station |

t_{x} | Time of the last known expected event |

changes (s_{i}, t, t_{exp})
| Expected change in the number of bikes at station s_{i} in interval [t, t_{exp}] with respect to the number of bikes at time t (e.g., +2 indicates there will be two more bikes at time t_{exp}) |

committedSlots (s_{i}, t)
| Maximum number of “committed” slots at station s_{i} after time t. This value is ≥ 0 |

committedBikes (s_{i}, t)
| Maximum number of “committed” bikes at station s_{i} after time t. This value is ≥ 0 |

$estimatedBikes\left({s}_{i},ren{t}_{k}\right)$ | Number of expected available bikes at s_{i} at the time user k is expected to arrive and taking into account the expected changes and “committed” bikes |

$estimatedSlots\left({s}_{i},retur{n}_{k}\right)$ | Number of expected available slots at s_{i} at the time user k is expected to arrive and taking into account the expected changes and “committed” slots |

Symbols | Description |
---|---|

$rentDemand\left({s}_{i},{t}_{a},{t}_{b}\right)$ | Number of expected rent attempts at s_{i} between ${t}_{a}\text{}\mathrm{and}\text{}{t}_{b}$ |

$returnDemand\left({s}_{i},{t}_{a},{t}_{b}\right)$ | Number of expected return attempts at s_{i} between ${t}_{a}\text{}\mathrm{and}\text{}{t}_{b}$ |

${\pi}^{i}\left(t\right)$ | (Transient) state probability distribution of the number of bikes at station s_{i} at time t |

${\pi}_{j}^{i}\left(t\right)$ | Probability that there are $j$ available bikes at station s_{i} at time $t$ |

$bikeProb\left({s}_{i},ren{t}_{k}\right)$ | Probability that ${u}_{k}$ would find an available bike at station ${s}_{i}$ when they arrive |

$slotProb\left({s}_{i},retur{n}_{k}\right)$ | Probability that ${u}_{k}$ would find an available slot at station ${s}_{i}$ when they arrive |

λ | Average bike arrival rate |

μ | Average bike rental rate |

$RentFailCost$ | Cost of getting to a station and finding no available bike |

$ReturnFailCost$ | Cost of getting to a station and finding no available slot |

localRentCost(s_{i}, rent_{k}, RentFailCost)
| Estimated cost for user u_{k} to rent a bike at s_{i}, resulting from combining the walking time to the station and the probability of finding an available bike |

localReturnCost(s_{i}, return_{k}, ReturnFailCost)
| Estimated cost for user u_{k} to return a bike at s_{i}, resulting from combining the cycling time to the station, walking time to the final destination, and the probability of finding an available slot |

**Table 3.**Experimental results for Madrid. Bold numbers indicate the best obtained result for each metric.

Strategy | #a/% | #fh/% | #fr/% | tt (min) | AET (min) |
---|---|---|---|---|---|

OPTIMUM | 0 | 0 | 0 | 19.21 | |

SD | 1573/12.85 | 1834/14.67 | 5148/32.6 | 22.47 | 378.4 |

ISD | 895/7.3 | 415/3.53 | 1965/14.7 | 21.86 | 398.1 |

DR | 461/3.76 | 126/1.06 | 225/1.9 | 21.54 | 201.9 |

DER | 243/1.98 | 0/0 | 0/0 | 21.62 | 189.7 |

EC (1000/2000) | 428/3.49 | 72/0.6 | 269/2.2 | 21.12 | 362.7 |

EC (3000/2000) | 367/2.99 | 13/0.11 | 183/1.5 | 21.24 | 309.0 |

EC (70000/2000) | 240/1.96 | 3/0.02 | 260/2.1 | 21.6 | 197.5 |

EC (10^{6}/10^{6}) | 148/1.21 | 1/0.01 | 0/0 | 23.21 | 75.7 |

**Table 4.**Experimental results for Madrid. Bold numbers indicate the best obtained result for each metric.

RentFailCost/ReturnFailCost/FutRentFailCost/FutReturnFailCost | #a | #fh | #fr | tt (min) | AET (min) |
---|---|---|---|---|---|

1000/2000/1000/2000 | 193 | 71 | 87 | 21.04 | 223.3 |

3000/2500/3000/1000 | 15 | 2 | 20 | 21.63 | 128.0 |

3000/2000/3000/2000 | 29 | 3 | 83 | 21.70 | 132.5 |

70,000/2000/70,000/2000 | 27 | 0 | 734 | 29.25 | 24.22 |

1,000,000/1,000,000/1,000,000/1,000,000 | 22 | 0 | 209 | 40.61 | 18.13 |

100,000/100,000/100,000/100,000 | 10 | 0 | 162 | 28.99 | 11.67 |

50,000/50,000/50,000/50,000 | 14 | 0 | 124 | 27.08 | 13.11 |

10,000/10,000/10,000/10,000 | 20 | 1 | 15 | 23.27 | 40.79 |

5000/5000/5000/5000 | 22 | 1 | 1 | 22.37 | 83.30 |

3000/3000/3000/3000 | 35 | 1 | 6 | 21.80 | 127.9 |

Strategy | #a | #fh | #fr | tt (min) | AET (min) |
---|---|---|---|---|---|

OPTIMUM | 0 | 0 | 0 | 19.21 | |

SD | 262 | 697 | 1613 | 20.22 | 143.75 |

ISD | 115 | 90 | 437 | 19.85 | 145.75 |

AR | 24 | 0 | 17 | 27.99 | 3.98 |

DR | 38 | 7 | 18 | 20.01 | 37.55 |

DER | 18 | 0 | 0 | 20.01 | 32.87 |

EC (3000/2000) | 41 | 0 | 1 | 19.52 | 87.89 |

$\mathrm{ECFI}\text{}(RentFailCost$$=3000,\text{}ReturnFailCost$$=2500,\text{}FutRentFailCost$$=3000,\text{}FutReturnFailCost$$=1000,\text{}tf$$=60\text{}\mathrm{min}\text{}\mathrm{and}\text{}f$ | 6 | 0 | 0 | 19.55 | 31.46 |

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**MDPI and ACS Style**

Billhardt, H.; Fernández, A.; Ossowski, S. Smart Recommendations for Renting Bikes in Bike-Sharing Systems. *Appl. Sci.* **2021**, *11*, 9654.
https://doi.org/10.3390/app11209654

**AMA Style**

Billhardt H, Fernández A, Ossowski S. Smart Recommendations for Renting Bikes in Bike-Sharing Systems. *Applied Sciences*. 2021; 11(20):9654.
https://doi.org/10.3390/app11209654

**Chicago/Turabian Style**

Billhardt, Holger, Alberto Fernández, and Sascha Ossowski. 2021. "Smart Recommendations for Renting Bikes in Bike-Sharing Systems" *Applied Sciences* 11, no. 20: 9654.
https://doi.org/10.3390/app11209654