## 3 Model
### Revenue Models for All Parties  
The revenue of ride-hailing platforms comes from the commission on passenger fares and the commission on penalty fees paid by passengers for canceling orders. With a revenue-sharing ratio of \(\beta\), the single-order revenue for orders assigned to taxis, \(U_{T}\), and the single-order revenue for orders assigned to ride-sharing vehicles, \(U_{C}\), can be expressed as Equations (18) and (19), respectively. \[U_{T}=(1-P_{T})M_{T}L\beta+P_{T}F_{P}\beta\omega \tag{18}\]  
\[U_{C}=(1-P_{C})M_{C}L\beta+P_{C}F_{P}\beta\omega \tag{19}\]  
where \(\omega\) is a 0-1 variable:  
\[\omega=\left\{ \begin{array}{cc}0&T_{X}<T_{P}\\ 1&T_{X}\geq T_{P}\end{array} \right. \tag{20}\]  
The revenue for a single order on the ride-hailing platform \(U\) can be expressed as Equation (21). \[U=\alpha U_{T}+(1-\alpha)U_{C} \tag{21}\]  
For passengers, their travel utility is influenced by the expected travel cost per unit, \(M_{E}\), the penalty for canceling an order, \(F_{P}\), the disutility associated with canceling an order, \(G_{T}\), and the emotional cost incurred by paying the penalty, \(G_{M}\). Specifically, \(G_{T}\) refers to passengers' dissatisfaction with the inconvenience caused by cancellation, which arises when passengers cancel their orders. \(G_{M}\) represents passengers' impatience and low willingness to pay the penalty, which occurs when passengers pay the cancellation penalty. By denoting both the taxi fare, \(M_{T}\), and the ride-hailing fare, \(M_{C}\), collectively as \(M\), the utilities for passengers who do not cancel their orders, passengers who cancel their orders without incurring a penalty, and passengers who cancel their orders and incur a penalty can be expressed as shown in Equations (21) to (23), respectively. \[W_{1}=(M_{E}-M)L-RT \tag{22}\]  
\[W_{2}=(M_{E}-M_{T})L-RT_{X}-G_{T} \tag{23}\]  
\[W_{3}=(M_{E}-M_{T})L-RT_{X}-G_{T}-G_{M}-F_{P} \tag{24}\]  
In summary, when the probability of a passenger canceling a taxi order, \(P_{T}\), is denoted, and the probability of canceling a ride-hailing order, \(P_{C}\), collectively as \(P\), the passenger utility \(W\) for a single order can be expressed as Equation (25). \[W=(1-P)W_{1}+P[\omega W_{2}+(1-\omega)W_{3}] \tag{25}\]  
For drivers on the ride-hailing platform, their earnings consist of the commission from the passenger's order payment and the commission from any penalty fees paid by passengers for canceling orders. Simultaneously, the driver's patience decreases with an increase in the pick-up time, \(T\), resulting in a negative utility with a coefficient of \(f\). Additionally, drivers experience an emotional loss, \(H\), due to passengers' order cancellation behavior, characterized by feelings of disappointment and frustration. The driver's earnings for a single order received through the platform can be expressed as Equation (26). Drivers experience emotional loss H due to passengers' order cancellation behavior, characterized by feelings of disappointment and frustration. \[K_{1}=(1-P)(M-fT)L(1-\beta)+P[F_{P}(1-\beta)\omega-H] \tag{26}\]  
For taxi drivers who operate both on the street and through ride-hailing platforms, the earnings for a single order are given by Equation (27), where \(\mu\) represents the additional offline customer-seeking costs. \[K_{2}=\theta(M_{T}-\mu)L+(1-\theta)K_{1} \tag{27}\]  
Denote \(\varepsilon\) as the proportion of taxi drivers in the travel market relative to the total number of taxi drivers and ride-hailing drivers. Then, the average earnings, \(K\), per order for drivers can be expressed as Equation (28). \[K=(1-\varepsilon)K_{1}+\varepsilon K_{2} \tag{28}\]  
This paper studies the scenario of excessive order demand in the general travel market, where taxis can accept rides through both cruising and ride-hailing platforms, and it discusses passenger order cancellation behavior and ride-hailing platforms' order dispatch strategies. The uniqueness of our model lies primarily in taxis' ability to accept orders through both online and offline channels.