# Utility-Centric Service Provisioning in Multi-Access Edge Computing
## 4 Proposed Nested-Genetic Algorithm
As such, the propagation delay between the MEC nodes ranges from 1 to 10 ms, and between the MEC nodes and the core cloud ranges from 100 to 120 ms. We omit the propagation delay between users and their connected MEC due to the close distance between them. For the sake of simplicity, we set the transmission rate of the network link between any two computing nodes to \(r_{n_{u},n}=1\) Gbps (\(\forall n_{u}\in\mathcal{N},n\in\mathcal{N}\cup\{l\}\)), and the wireless transmission rate between users and their connected MEC to \(r_{u_{u},n_{u}}=100\) Mbps (\(\forall u\in\mathcal{U},n_{u}\in\mathcal{N}\)). In the simulation, each user performs only one request for a service drawn from a set of \(|\mathcal{S}|=20\)  services. The service popularity follows the Zipf distribution with exponent \(\alpha=0.8\). For each service \(s\), the storage demand of service image \(img_{s}\) is set randomly within [10; 100] GB. The required input data size per request \(d_{s}\) and computation intensity per request \(w_{s}\) take value within [50; 300] KB and [10; 200] Megacycles, respectively. In addition, each service \(s\) has different latency requirements including two thresholds: \(T^{min}\), \(T^{max}\). For example, latency-sensitive services such as VR require \(T^{min}=20\) ms and \(T^{max}=100\) ms [29]; some cloud-based interactive games require \(T^{min}=50\) ms and \(T^{max}=150\) ms [28; 30]; for latency-tolerant services such as simple web services, web search, \(T^{min}=100\) ms and \(T^{max}=1000\) ms [50]. In our experiment, we consider services of these categories, and thus (\(T^{min}\), \(T^{max}\)) of each service \(s\) is set randomly within {(20, 100), (50, 150), (100, 1000)} ms.

For each MEC node \(n\), unless otherwise stated, the storage capacity and the computation capacity are set as \(R_{n}=500\) GB and \(F_{n}=20\) GHz, respectively. Yet, during the evaluations, we vary these parameters to show their influence on the system performance. Other simulation settings related to the parameters of the proposed GA are described in Table 1.

To evaluate the performance of the proposed algorithm, we compare the Nested-GA with other baseline methods as follows. * The optimal solution of Equation (7) using BONMIN solver in the COIN-OR toolbox, which is a well-known open-source optimization tool for solving non-linear programming. BONMIN solver uses IPOPT package, which implements an interior point line search filter method to find relaxed solutions for the NLP problems. * Top-R service placement with Nearest-based request scheduling (abbr., Top-R Nearest) algorithm, which first places services at each MEC \(n\in\mathcal{N}\) in descending order of service popularity until reaching the storage capacity \(R_{n}\) (i.e., the Top-R most popular services are placed), and then schedules each user request to the nearest (i.e., smallest network latency) hosting node of the requested service. * Top-R service placement with Genetic-based request scheduling (abbr., Top-R Genetic) algorithm, in which the service placement strategy is similar to the Top-R Nearest, and the request scheduling strategy follows the Inner-GA (Algorithm 2). In other words, the service placement and request scheduling decisions are addressed separately, and only the request scheduling is optimized.