2.1.1 Assumptions

The following is a summary of the assumptions used for the simulation:

1. (1) All aircraft taxi along the prescribed taxiing paths.

2. (2) The taxiing route of ETT-towed aircraft is the same as that of conventional self-taxiing aircraft. Due to the slow initial speed of ETT, to ensure operational efficiency and safety, it is set that ETT-towed flights have lower priority than conventional self-taxiing flights.

3. (3) Aircraft are divided into three categories according to their weight [Reference Salihu, Lloyd and Akgunduz5]: small aircraft below 7t, medium aircraft between 7t and 150t and large aircraft above 150t. The aircraft lengths of the three types of aircraft are set as 30m for small, 50m for medium and 70m for large.

4. (4) The model discretisation step is set to 1s, and the real-time position of the aircraft is updated every second based on the real-time speed of the aircraft.

2.1.2 Apron model

The apron model simulates the activities of departing aircraft being pushed back from gates and arriving aircraft taxiing into parking positions. The model records the actual pushback and taxi-in time of flights. Traditional CA models have not accounted for aircraft activities on the apron [Reference Mori13]. Florian was the first to consider the pushback time of aircraft on the apron [Reference Mazur and Schreckenberg15]. Suwan used aggregated time functions to simulate aircraft dwell time on the apron [Reference Yin, Han, Ochieng and Sanchez16]. However, neither of these approaches addressed the determination of the sequence in which neighboring aircraft are pushed back or taxi into the apron. In this section, the actual sequence of aircraft pushback and taxi-in at the airport is considered, and the apron model is established as follows.

1. (1) Figure 1 depicts a schematic representation of different areas within the airport. The purple colour represents the terminal area, the green colour signifies the aircraft parking area (apron), the grey colour represents the runway, the pink shade illustrates the queueing area for aircraft awaiting takeoff at the runway threshold, the yellow area indicates the ETT docking zone, blue circles denote connective cells and the lines represent taxiways. Notably, the green area (apron zone) is divided into 42 blocks based on the principle of grouping adjacent aircraft stands. When there are two or more flights departing or arriving in the same block, due to the proximity of the stands, there is significant mutual influence among the flights, leading to potential operational obstructions. Consequently, aircraft priorities are assigned as outlined in Table 1.

   

   Figure 1. Illustration of aircraft stand area.

As shown in Table 1, landing flights have higher priority than take-off flights. Large aircraft have higher priority than small aircraft. In special cases, the flight priority is raised to the highest level.

1. (2) To avoid airport surface congestion, the number of aircraft operating on the surface is controlled by limiting [Reference Li and Wang19]. The indicator is used to measure the degree of airport surface congestion. When the airport surface operation is highly congested, all flights with priority lower than III are not allowed to push out. The planned push-out time of the delayed flights is set as follows: if

   (1) \begin{align}Q\!\left( {{P^t}} \right) \gt {n_{{{max}}}},{t_{i,plan}} = {t_{i,plan}} + 1\end{align}

2. (3) Considering that the long waiting time ( $wai{t_t}$ ) at the stand will affect the aircraft arrival at the airport and the passenger status, a waiting threshold ( ${t^{gate}}$ ) is set: if

   (2) \begin{align}wai{t_i} \gt {t^{gate}}{\rm{\;}}priorit{y_i} = III\end{align}

Aircraft with priority III are not affected by the degree of surface congestion and can be arranged to push out first.

Table 1. The amount of fuel saved by airports

2.1.3 Taxiway model

The taxiway model is a model that simulates the acceleration, deceleration and waiting activities of aircraft on the taxiway, which is divided into two parts: position change and conflict resolution.

Conflict resolution

Although we try to avoid aircraft taxiing paths crossing at the same time, such conflicts cannot be completely avoided at large airports. In actual airport operations, to resolve conflicts, the controller will order one of the aircraft to decelerate and wait. Mori [Reference Mori13] set the order of aircraft passing through the intersection in advance in the CA model to avoid conflicts. Suwan Yin [Reference Yin, Han, Ochieng and Sanchez16] set the aircraft priority to determine the order of aircraft passing through the intersection. However, he did not consider the use of ETT priority rules for aircraft. Based on Suwan Yin’s [Reference Yin, Han, Ochieng and Sanchez16] priority rule, this paper considers the impact of ETV introduction on the priority rule, and establishes a taxiway conflict resolution model as follows.

Within the model, taxiway intersections are designated as a distinct type of cell referred to as ‘connective cells’. These connective cells store various information about aircraft approaching the intersection, allowing the model to determine the sequence in which aircraft are given priority to pass through. This prioritisation enables aircraft to undertake appropriate actions for conflict resolution when approaching intersections, as illustrated in Fig. 2.

Figure 2. Lict resolution rules.

If ${d_i} \lt 360{\rm{m}},{d_j} \lt 360{\rm{m}}$ , the specific conflict resolution rules are as follows.

1. 1. When aircraft i and j arrive at the connective cell at the same time, the aircraft with higher priority passes through the intersection first, and the aircraft with lower priority decelerates to avoid collision.

2. 2. When aircraft i and j pass through the connective cell one after another, to avoid rear-end collision, the first-come first-served principle is implemented. The subsequent aircraft decelerates until it maintains a safe distance ( ${d_s}$ ) from the aircraft ahead.

2.1.4 Runway model

The runway model is a model that simulates the take-off and landing activities of aircraft on the runway. Although the runway model records the real-time landing and take-off time of flights, which have no direct impact on the number of ETTs, the runway model simulates the runway usage situation, which indirectly affects the pushback and taxiing speed of flights on the taxiway.

In actual airport operations, aircraft usually need to stop at the runway entrance and wait for the controller’s instructions. The controller decides the order of aircraft using the runway. When there is already an aircraft waiting for take-off, the aircraft needs to maintain a safe distance from the waiting aircraft. Suwan Yin [Reference Mori13] set the runway take-off and landing interval time in the model. This section refers to Suwan Yin’s [Reference Yin, Han, Ochieng and Sanchez16] runway interval time, considering the take-off and landing order of flights using the runway, and establishes the runway take-off and landing model as follows.

In the model, the controller’s instructions are simulated by defining the flight priority. The take-off aircraft queue up in the order of arrival at the runway, and the landing aircraft also queue up in the order of planned landing time. When there is already an aircraft waiting at the runway end, the aircraft needs to maintain a minimum distance (50m) [Reference Yang, Yin, Han, Haddad and Hu14] from the other aircraft in the queue. Due to the influence of aircraft wake and safety issues, an interval time needs to be guaranteed between two consecutive take-offs ( ${t_{take{\rm{\;}}off}}$ ), and the minimum time interval between take-off and landing ( ${t_{interval}}$ ), the time for taxiing out of the fast exit after landing is recorded as ${t_{exit}}$ , and the runway take-off and landing interval time is shown in Table 2.

Table 2. The runway take-off and landing interval time [Reference Mazur and Schreckenberg15, Reference Yin, Han, Ochieng and Sanchez16] 0

That is, at t time, the aircraft using the runway need to satisfy the formula:

(7) \begin{align}t \gt {t_{take{\rm{\;}}off}} + {t_{previous{\rm{\;}}take{\rm{\;}}off}}\end{align}

(8) \begin{align}t \gt {t_{exit}} + {t_{previous{\rm{\;}}land}} + {t_{interval}}\end{align}

In addition, for departing aircraft, engine preheating time needs to be taken into consideration. Assume the engine preheating time is ${t_{prepare}}$ , meaning that aircraft taking off at time t need to satisfy the following formula:

(9) \begin{align}t \gt {{max}}\!\left\{ {{t_{take{\rm{\;}}off}} + {t_{previous{\rm{\;}}take{\rm{\;}}off}},{t_{arrival}} + {t_{prepare}}} \right\}\end{align}

(10) \begin{align}t \gt {t_{exit}} + {t_{previous{\rm{\;}}land}} + {t_{interval}}\end{align}

Where ${t_{arrival}}$ is the time for the departing aircraft to reach the end of the runway.

${t_{prepare}}$ is the engine preheating time. According to the regulations of the Civil Aviation Administration, the engine preheating requires a speed of 60%. This value varies for different engines. The Civil Aviation Administration of China stipulates that the preheating time should not be less than 3min.

For take-off aircraft, since the airport prioritises serving landing aircraft, the take-off aircraft need to additionally satisfy the formula:

(11) \begin{align}t + {t_{interval}} \lt {t_{next{\rm{\;}}land}}\end{align}

2.2.1 ETT service process

ETT scheduling is mainly based on the estimated take-off time of flights, to determine the service path and timetable of vehicles, to meet the demand of aircraft. By considering time constraints, this problem can be abstracted as a vehicle routing optimisation problem with time windows. The ETT service process is shown in Fig. 3.

Figure 3. ETT service process.

Figure 3 shows the ETT service process, different colours indicate different airport areas, [] indicates the different time points of ETT operation, and arrows indicate the direction and path of ETT operation. The service time required by each flight constitutes the time window of the corresponding node to be visited.

At time ${t_0}$ , ETT leaves the parking area and heads to the stand;

At time ${t_1}$ , ETT arrives at the stand and waits for the aircraft to push back. To prevent delays caused by ETT not arriving, it is required that the aircraft arrives at the stand 1min before the planned take-off time. This time can be obtained from the apron operation model in the airport real-time simulation model;

At time ${t_2}$ , ETT actually pushes the aircraft out to the taxiway, which usually takes 2min;

At time ${t_3}$ , ETT pulls the aircraft to the runway end. The aircraft can obtain each node on the taxiway from the taxiway taxiing model in the airport real-time simulation model;

At time ${t_4}$ , ETT detaches from the aircraft. The detachment time is usually 2min;

At time ${t_5}$ , ETT returns to the parking area.

2.2.2 The hard time window model

The hard time window model necessitates that the ETT can fulfil the aircraft requirements at any given moment. The model’s solution process consists of four steps:

1. Step 1: The airport real-time simulation model generates the actual pushback time for each aircraft and, based on the time taken by ETT to reach the corresponding gate, deduces the starting node for each task’s time window. Subsequently, the time windows are sorted in order of their start time.

2. Step 2: Set the aircraft’s ‘zero waiting’ policy for ETT, and set the initial number set of ETT to infinity, to avoid aircraft delays due to insufficient ETT. When ETT receives the tug task issued by the aircraft, the nearest ETT will be assigned. The ETT that completes the tug task will automatically return to the ETT docking area and wait for a new round of task allocation. And compared with the same ETT docking area, the ETT that has not completed the tug task in the current period will be preferentially allocated.

3. Step 3: Loop through each time window and assign ETT to each time window in turn until all time windows are assigned.

4. Step 4: Calculate the ETT occupancy time window for each tug operation on the selected day: The occupancy time includes traveling time, waiting time, towing time, disengaging time and returning time.

Figure 4 shows the visualisation result of the time window model. The horizontal axis represents the time of the day, and the vertical axis represents the tug operations of different flights. Red, blue, green, grey and yellow represent the traveling time, waiting time, towing time, disengaging time and returning time of ETT respectively. This figure can reflect the number of ETTs required in each time period, and find the maximum value of ETT demand for the day.

Figure 4. The hard time window model.