## 1 Introduction  
With the arrival of the era of the Internet of things (IoT), there is an emerging demand for various types of portable smart devices and IoT services. In modern society, IoT technology has greatly facilitated the development of healthcare, autonomous driving, social entertainment, etc. and has become a necessity in people's lives, which has gradually transformed traditional cities into smart cities [1; 2; 3]. Federated learning (FL) has received attention recently for its cutting-edge uses in industries like health, finance, and Industry 4.0. FL makes it possible for numerous mobile devices to work together in training machine learning models without transferring raw data, safeguarding the privacy of users. FL is limited, though, because it must rely on mobile devices having the appropriate CPU power to solve the challenges faced by the millions of parameters in machine learning models in real applications [4]. FL has a substantial number of client nodes--possibly millions--each with a significantly varied data distribution. High communication latency and instability between the client and the central server are present at the same time [5]. Currently, mobile devices produce a lot of data every day, and the available local computation and storage resources are scarce. There are numerous IoT applications that simultaneously have strong criteria for high accuracy and low latency. Utilizing remote clouds with high-speed processing and abundant storage resources to offload activitiesand data from compute-intensive applications, the potential of mobile devices can be more fully exploited [6]. Data storage and compute demands are growing rapidly as a result of people's growing reliance on IoT. The conventional approach of directly offloading to the cloud may result in network congestion, accompanied by unavoidable response delays, and a lower overall quality of service (QoS) [7]. In addition, these resource-intensive computing and storage tasks come at a significant cost. Distributed edge computing makes full use of distributed resources at the edge of the network, including routers, network gateways, and base stations, to provide real-time and context-aware services, which perform better when processing tasks with low latency or complex computation. The application of edge computing can effectively alleviate the problem of network delays, share the load of local devices, and improve the overall performance. However, it is important to point out that edge computing has some limitations in terms of resource and functional scalability compared to cloud computing [8]. Therefore, edge cloud computing was introduced to solve latency-sensitive computing tasks, in place of cloud computing [9]. Edge cloud computing shows a better balance between overcoming the limited computational speed of mobile devices on the one hand and reducing the too-long computational latency when offloading to remote clouds on the other hand [10; 11]. However, determining which tasks are suitable for running locally or offloading to a node is a very challenging NP-hard dilemma [12]. To solve this problem, [PERSON] and [PERSON] [13] used a subgradient-based non-cooperative game model to solve the transmission power allocation problem and the MO-NSGA algorithm to solve the joint request offloading and computational resource scheduling problems. However, the non-cooperative game model usually lacks global coordination, and each device only focuses on maximizing its own interests, resulting in insufficient overall system performance. Meanwhile, the system involves the edge system cost when considering the JRORS problem, but does not take into account the cost of cloud servers, which affects the overall cost of the system operation. In this study, when we study the task scheduling of a federated mobile edge computing (MEC) three-layer computing model, we not only consider the decisions regarding request offloading and computational resource scheduling, but also incorporate the budget constraints of the users, to improve the QoS.