# Smart Recommendations for Renting Bikes in Bike-Sharing Systems
## 5 Evaluation of User-Centred Recommendation
### Simulation Results
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Strategy** & **\#\%** & **\#fh/\%** & **\#fr/\%** & **tt (min)** & **AET (min)** \\ \hline OPTIMUM & 0 & 0 & 0 & 19.21 & \\ \hline SD & 1573/12.85 & 1834/14.67 & 5148/32.6 & 22.47 & 378.4 \\ \hline ISD & 895/7.3 & 415/3.53 & 1965/14.7 & 21.86 & 398.1 \\ \hline DR & 461/3.76 & 126/1.06 & 225/1.9 & 21.54 & 201.9 \\ \hline DER & 243/1.98 & **0/0** & **0/0** & 21.62 & 189.7 \\ \hline EC (1000/2000) & 428/3.49 & 72/0.6 & 269/2.2 & **21.12** & 362.7 \\ \hline EC (3000/2000) & 367/2.99 & 13/0.11 & 183/1.5 & 21.24 & 309.0 \\ \hline EC (70000/2000) & 240/1.96 & 3/0.02 & 260/2.1 & 21.6 & 197.5 \\ \hline EC (10\({}^{6}\)/10\({}^{6}\)) & **148/1.21** & 1/0.01 & **0/0** & 23.21 & **75.7** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results for Madrid. Bold numbers indicate the best obtained result for each metric. the recommended stations, and (2) the estimated travel time of users is the same as their actual travel time. In a real scenario, the benefit of \(DER\) with respect to \(DR\) should be somewhat smaller. The last four rows in Table 3 correspond to different instances of the _ExpectedCost_ strategy (\(EC\)), which prioritises stations with a lower cost, calculated based on travel time and the (demand-dependent) probability of finding a bike/slot at the expected time of arrival of the user. This strategy's performance varies for different values of \(RentFailCost\) and \(ReturnFailCost\). In general, higher penalizations produce a lower abandonment rate, but increase the travel time. With \(RentFailCost=ReturnFailCost=\) 1,000,000, for example, the abandonment rate is reduced to 1.21%, but the travel time increases to 23.21 min, which is considerable. A rather high value for \(RentFailCost\) and low value for \(ReturnFailCost\) obtains a good compromise. In this sense, for \(RentFailCost=\) 70,000 and \(ReturnFailCost=2000\), both dropout rate and travel time can be slightly reduced with regard to \(DER\). With rather low penalizations, the abandonment rate is higher, but the travel time can be reduced, as with \(EC\) (1000,2000). In Figures 2-4, we analyse the behaviour of \(EC\) with varying values for \(RentFailCost\) and \(ReturnFailCost\). As shown in Figure 2, the abandonment rate decreases with increasing \(ReturnFailCost\), and the travel time decreases up to a value of \(\sim\)2000, and then increases. At higher values, both travel time and abandonment rate become almost stable. The lowest travel time is obtained with a value of \(\sim\)2000. Exactly the same behaviour is observed for other values of \(RentFailCost\). We also observed in our experiments that, as the value of \(ReturnFailCost\) increases, the number of failed returns (#fr) falls rapidly towards \(\sim\)0 at the value of \(ReturnFailCost=\) 4000 (for the sake of clarity, this is not shown in the figure). In Figure 3, we show a fixed value of \(ReturnFailCost=2000\) (the value that generally obtains the lowest travel time for different values of \(RentFailCost\)), and we increase \(RentFailCost\). As can be seen, higher values of \(RentFailCost\) produce lower abandonment rates and fewer failed rent attempts, but lead to increased travel times. It seems that the values remain almost stable at a certain point. Figure 2: _ExpectedCost_ strategy with fixed \(RentFailCost=\) 50,000 and varying \(ReturnFailCost\). If we increase \(RentFailCost\) and \(ReturnFailCost\) at the same time, as shown in Figure 4, the abandonment rate reduces continuously and considerably, but at the cost of an increase in travel time. The failed rental attempts tend towards 0. Comparing the _ExpectedCost_ strategy with _DistanceExpectedResources_, the former can be parametrised in order to prioritise abandonment rate or travel time. However, it is interesting to observe that for the same ratio of travel time, both methods obtain almost the same dropout rate, and vice versa. In other words, the rather simple \(DER\) strategy performs as well as the much more sophisticated \(EC\) strategy.