# Collaborative Allocation Method of En-Route Network Resources Based on Stackelberg Game Model
## 1 Introduction  
The traditional ground waiting strategies, diversion strategies, air traffic management procedures, and the latest Collaborative Trajectory Options Program (CTOP) are the air traffic flow management strategies which are mainly used, the core of which is the rational allocation of limited slot resources and trajectory resources to achieve the efficient utilization of airspace [1, 2]. Most of the early studies focused on the perspective of ATC and study the process of resource allocation aiming at maximizing the utilization of airspace. Subsequently, the research gradually turned to the study of fairness issues. Various theories, models, and algorithms have been applied to the research of fair resource allocation, including the Collaborative Decision Making (CDM) mechanism [3], the 0-1 integer programming model for collaborative multi-route resource allocation integrating diversion strategies and waiting strategies [4], the flight slot assignment model for airlines under the collaborative decision-making mechanism [5], and the slot exchange model based on cooperative game theorywith the goal of minimizing passenger delays for all parties involved in the exchange [6]. In the above results, the focus considers delay fairness from the perspective of ATC based on the number of passengers to allocate the flight slot resources or/and trajectory resources. The fairness of airlines is mainly reflected through the allocation of per-passenger delays, and the different preferences of different airlines are not taken into account, so the fairness achieved by this still remains under the perspective of a single perspective of ATC. With the widespread implementation of air traffic flow management strategies, especially CTOP strategies, the airlines, as important participants and major beneficiaries of resource allocation, have become increasingly involved in flow management decisions. Therefore, some studies have included airlines in the resource allocation process, changing the original resource allocation problem under the single perspective of ATC to a resource allocation problem under the domination of ATC that considers the preferences of airlines. Some studies have shown that the idea of collaborative route resource allocation considering the competitive behavior of airlines is the main research direction of future traffic management technology [7; 8]. For the implementation process of CTOP, considering the gaming behavior between the two airlines participating in the collaborative en-route technology can effectively reduce flight delays [9]. In order to implement and analyze the CTOP program more effectively, a variety of models and methods are proposed to explore the trajectory preference of airlines, study the route resource allocation issues, and improve airspace operation efficiency and resource allocation fairness, as well as reducing the total delay costs. These include an improved Flow Constrained Area (FCA), which is a Potentially Constrained Area (PCA) model combined with heuristic algorithm [10], the stochastic optimization models to set flow in the new traffic management initiatives of CTOP based on linear optimization-based alternative flight scheduling methods [11], the centralized en-route resource allocation mechanism considering fairness [12], the new calculation method of relative en-route flying costs for the difficulty to calculate the relative en-route flying costs for airlines [13], using fuzzy comprehensive evaluation method to evaluate flight delay time, delay costs and the number of turning points [14], using Gini coefficient to define the fairness performance indicators of en-route collaborative allocation and constructing a dual-objective nonlinear integer programming model that considers both efficiency and fairness [15], the multi-objective nonlinear 0-1 integer programming model with the goal of minimizing the total flight delay costs and the deviation coefficient of delay fairness loss for airlines [16], etc.