## 2 Related Work  
As a core technology in the field of edge computing, the technology of computing offloading has attracted widespread attention. Recent research has made significant contributions in this field. A lightweight and efficient offloading method based on genetic algorithms was proposed for single server scenarios, achieving minimum average computation delay for tasks [11]. Researchers proposed a task offloading and power allocation optimization algorithm to minimize task completion time under energy constraints on mobile devices [12]. A fast offloading algorithm based on policy gradient was proposed for queuing tasks with a single terminal and a single edge server [13]. Researchers proposed a resource allocation algorithm based on the Deep Deterministic Policy Gradient for task offloading and resource optimization [14]. The algorithm can quickly find the optimal decision and maximize long-term benefits. Recently, in order to study joint resource allocation and task offloading in an ultra-dense edge computing network, a heuristic task offloading scheme based on binary mixed gray wolf optimization was proposed [15]. A Joint Optimization method based on the Discrete Binary Particle Swarm Optimization Algorithm for system load was proposed for single mobile device to one mobile edge server scenarios, effectively reducing delay and energy consumption [16]. Most current research on task offloading focuses on offloading decisions and resource allocation, primarily addressing implementation details of the offloading process. This often overlooks the huge burden of heterogeneity and environmental configuration on the network, lacking detailed performance analysis of the offloading process. In the mobile edge computing (MEC) system, real-time indicators are very important, such as immediate service probability is related to the timeliness of task processing, and blocking probability reflects the probability of a task being discarded. At present, the performance analysis of the offloading process mainly focuses on the average number of requests, average delay, average energy consumption and other average indicators [17; 18; 19; 20], ignoring the impact of real-time indicators such as immediate service probability and blocking probability. The mean number of requests and mean response time were used for analyzing the performance of multi-access edge computing networks [21]. Researchers used average delay and average energy consumption to performance evaluation on the mobile edge computing [22]. Average delay was used for performance research in a two-tier edge structure [23]. There has been intense interest in MEC, especially in single-server scenarios [24; 25; 26; 27; 28], and, to a lesser extent, in homogeneous multi-server scenarios [29; 30; 31; 32; 33]. In contrast, only a few studies have been conducted to investigate the heterogeneous servers scenarios. In the future, MEC will be applied not only to access points (APs) and base stations (BSs) but also to mobile devices and all computing devices around us. Thus, it is necessary to study how to design a network with various types of MEC servers and analyze network performance. In cases where APs have different resources (such as transmission power), the Heterogeneous Networks have been studied, focusing on communication performance rather than computational performance [34; 35]. Most works apply random geometry to spatial models of distributed users and APs using Poisson point processes (PPP) [36]. For example, uplink network modeling and coverage analysis [37], downlink network modeling and coverage analysis [38], and decoupling of the uplink and downlink [39]. Recently, random geometry has also been applied to performance analysis of randomly distributed MEC servers [40], but delay distribution and heterogeneous MEC servers are not considered in the design of Heterogeneous Mobile Edge Computing Networks (HetMECNets).