**4. Analysis Results**

### *4.1. The Analysis Result of Areas Expected to Be Marginalized in Ridesharing Services*

In order to identify the indices to be applied to reinforcement learning, the taxi operation data in Seoul were categorized into different zones according to 25 districts (gu), and the OD matrix was formed on the basis of the volume of pick-ups and drop-offs using district codes. Consequently, the study analyzed centrality and tried to identify a standardized index for each zone to be applied to reinforcement learning. The origin (the number of pick-ups) was compiled by matching administrative districts through the GIS spatial join function, while the destination (the number of drop-offs) was compiled by using the district(gu) code information for each vehicle departure. Any data including areas surrounding Seoul were excluded.

Using the OD matrix, degree centrality analysis for each zone was conducted, and the average in-degree and out-degree centrality was calculated for weekdays and weekends from 10:00 p.m. to 4:00 a.m. (Figures 4 and 5). According to the analysis, in-degree centrality displayed similar patterns for both weekends and weekdays, whereas the regional deviation was smaller than seen for out-degree centrality. Out-degree centrality was high in the Central Business Districts(CBDs) on weekdays and similarly high on weekends.

**Figure 4.** Results of centrality analysis between 10:00 p.m. and 4:00 a.m. on weekdays: (**a**) average in-degree centrality; (**b**) out-degree centrality.

**Figure 5.** Results of centrality analysis between 10:00 p.m. and 4:00 a.m. on weekends: (**a**) average in-degree centrality; (**b**) out-degree centrality.

Areas located on the outskirts of the city had a lower degree centrality. In particular, outskirt areas showed lower out-degree centrality on weekdays. Residential areas on the outskirts of Seoul showed higher in-degree centrality. On the other hand, central and subcentral regions of the city showed higher out-degree centrality (Figure 6). The patterns were similar to those found in previous studies showing the concentration of taxi pick-ups during late-night hours near CBDs [39]. There were large differences in out-degree centrality by zone before and after midnight when most public transportation services were suspended, with the difference growing as the night went on.

**Figure 6.** Results of out-degree centrality versus in-degree centrality analysis between 10:00 p.m. and 4:00 p.m.: (**a**) weekday; (**b**) weekend.

### *4.2. Results of Reinforcement Learning Simulation*

The algorithm presented in Figure 3 was used in the learning of 600 OD cells. When the reward function was defined by a simple matching rate, there was a limitation in comparison among regions as the fare and travel time for each OD were different. Therefore, the simulation implemented a reward value considering travel time and cost. Moreover, analysis was conducted depending on the application of a negative reward value in the unmatched condition. The matching rate for each learning step when a waiting time with a negative reward was applied (alt1) or not (alt2) is depicted in Figure 7.

**Figure 7.** Matching rate comparison depending on time value.

When the negative reward was considered, the matching rate increased before converging as learning was reiterated. When it was not considered, the matching rate decreased before converging. According to this result, it can be concluded that the application of a negative reward was necessary when the reward function used the travel cost but not the matching rate. However, the current negative reward for the waiting time used a fixed value from a previous study; thus, for real-world applications, the expected waiting time according to a driver's choice probability should be calculated for each OD.

Using the deduced average surge, when a fare was calculated for each OD, the distribution could be expressed as shown in Figure 8, where the *x*-axis is the travel distance between origin and destination, and the *y*-axis is the price. Then, price levels were compared in terms of the base fare, base fare with late-night surcharge (additional 20% to base fare), late-night surcharge + ride-hail fee (KRW 3000, the highest fee charged by existing platform companies), and surge price (the outcome of learning for each OD). For travel distances shorter than 10 km, the differences among fares were not severe. However, the gap grew wider when the distance increased (see Figure 8a). This is because the late-night surcharge + ride-hail fee (yellow dotted line) was a flat fare regardless of traveling distance, while the surge fare (blue dotted line) was determined using a certain ratio, increasing the absolute price with traveling distance. Table 1 displays the three average prices for different distances, showing the price gap widening as the distance increased.

**Figure 8.** Price distribution for different OD when a surge was applied (using the average surge for different OD): (**a**) total range; (**b**) short distance.


**Table 1.** Tra ffic volume and average price (KRW) for di fference distances.

1 The late-night surcharge is surge 1.2 of the base amount and an additional Hail Fee of 3000 KRW (based on the existing platform price).

### *4.3. Changes in Centrality after Surge-Driven Supply Increase*

Centrality analysis was carried out after recalculating the tra ffic volume in accordance with the surge previously identified for each OD matrix and time slot. The tra ffic volume was recalculated as follows: 

$$Nvol\_{i,j} = \left(Ovol\_{i,j} \times S\_{i,j}\right) \times \frac{\sum\_{i,j} Ovol\_{i,j}}{\sum\_{i,j} Ovol\_{i,j} \times S\_{i,j}} \tag{7}$$

where *i*, *j* are the origin and destination, *Nvoli*,*<sup>j</sup>* is the recalculated tra ffic volume, *Ovoli*,*<sup>j</sup>* is the previous tra ffic volume, *Si*,*<sup>j</sup>* is the optimal surge for travel (optimal surge for di fferent OD as identified from reinforcement learning), and *i*,*j Ovoli*,*<sup>j</sup>* is the sum of tra ffic volume. In centrality analysis, the indicator evaluating the volume of vehicles traveling to a certain zone was the in-degree centrality. When in-degree centrality increases, it can be said that supply is increasing toward that region.

According to the level of improved spatial equity by region, in-degree centrality decreased in the central and subcentral regions of the city, such as Gangnam-gu and Jongno-gu, while the in-degree centrality increased in residential areas on the outskirts of the city, such as Songpa-gu, Gangseo-gu, Dongjak-gu, and Nowon-gu (Figure 9). When this was overlaid on top of the previous hotspot analysis, it was found that the in-degree centrality was drastically improved in districts (gu) located on the outskirts of Seoul Metropolitan City where the number of drop-o ffs or vacant vehicles was greater compared to the number of pick-ups (Figure 10b). As a result, it can be expected that vehicle supply would be enhanced by as much as 7.5% when applying a higher surge to the region predicted to have a lower choice probability from the perspective of drivers. At the same time, equity in service supply would be improved by reducing the waiting time of passengers in marginalized regions with low taxi demand.

**Figure 9.** Change in in-degree centrality: (**a**) before; (**b**) after.

**Figure 10.** (**a**) Rate of change in in-degree centrality; (**b**) comparison between in-degree centrality and hotspot analysis.
