## 3 Model  
### Distribution Model for Taxi Arrival Time Intervals  
The symbols used in this article and their meanings are shown in Table 2. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Study** & **Relevance** & **Differences from Our Study** \\ \hline [PERSON] et al. (2018) [PERSON] et al. (2018) [18] & Both studies consider taxis accepting orders online and offline and the impact of cancellation penalties. & We focus on peak-hour offline order acceptance strategies by taxis, while [PERSON] et al. focus on platform pricing strategies. \\ \hline [PERSON] et al. (2019) [PERSON] et al. (2019) [17] & Both studies consider the impact of traditional taxis on passenger cancellation behavior. & We extend the analysis to peak-hour scenarios and discuss taxi strategies under such conditions. \\ \hline [PERSON] and [PERSON] (2023) [PERSON] and [PERSON] (2023) [11] & Both studies address order allocation under road network congestion. & They propose an algorithm for optimal matching intervals and distances, while we develop a vehicle arrival probability model to study order allocation between taxis and ride-hailing vehicles. \\ \hline [PERSON] and [PERSON] (2022) [PERSON] and [PERSON] (2022) [PERSON] and [PERSON] (2022) [25] & Both studies examine the impact of taxi search behavior on the ride-hailing market during peak hours. & They focus on the effects of peak-hour and congestion surcharges on passenger and taxi decisions, while we focus on order allocation strategies during peak hours. \\ \hline [PERSON] and [PERSON] (2019) [PERSON] and [PERSON] (2019) [24] & Both studies investigate taxi order acceptance behavior during peak hours and the impact of peak pricing. & They analyze whether taxis remain in high-demand areas during peak hours, while we focus on changes in taxi order acceptance modes. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative Research. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline
**Symbol** & **Meaning** \\ \hline \(N\) & Total number of taxis \\ \(t_{i}\) & Any given moment \\ \(N_{i}\) & Number of taxis operating offline at any given moment \\ \(D\) & Total number of orders received by the ride-hailing platform at any given moment \\ \(\alpha\) & Proportion of orders allocated to taxis by the ride-hailing platform \\ \(\theta\) & Proportion of taxis accepting offline orders at any given moment \\ \(E\) & Number of taxis operating vacant due to canceled orders at any given moment \\ \(S\) & Total mileage of urban roads (km) \\ \(v\) & Average operating speed of taxis (km/h) \\ \(\eta\) & Taxi vacancy rate \\ \(T_{P}\) & Critical time for imposing penalties on order cancellations by the platform \\ \(F_{P}\) & Penalty amount for order cancellation by the customer on the platform \\ \(L\) & Passenger-carrying distance of the order \\ \(R\) & Passenger time cost \\ \(\delta_{I}\) & Time preference coefficient of Passenger \(i\) \\ \(M_{C}\) & Ride-hailing platform unit cost \\ \(M_{T}\) & Taxi unit cost \\ \(M_{E}\) & Passenger’s expected unit cost for the travel \\ \(\beta\) & Revenue sharing ratio of the ride-hailing platform \\ \(G_{T}\) & Distrust towards the platform caused by passenger order cancellations \\ \(G_{M}\) & Disutility experienced by passengers when need to pay cancellation penalties \\ \(f\) & Coefficient of driver disutility from pick-up time \\ \(H\) & Emotional loss experienced by drivers due to passenger order cancellations \\ \(\mu\) & Additional offline customer-seeking costs of taxis \\ \(\varepsilon\) & Proportion of taxi drivers in the travel market \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Definition of Symbols. At any given time, \(t_{i}\), the number of offline cruising taxis, \(N_{i}\), is influenced by several factors, including the total number of taxis in the city, \(N\), the number of taxis assigned to online orders, \(\alpha D\), and the number of taxis whose status changes due to passenger order cancellations at a particular time, \(E\). This is represented as \(N_{i}=N-\alpha D+E\).