The computing and storage resources of an edge node in a mobile edge computing (MEC) system are limited. One edge computing node cannot cache all the services supported by the entire MEC system. A service chain caching and scheduling strategy should be designed to improve the service processing capacities of the edge computing nodes under high computing load conditions. This article combines the open Markov queuing network for the first time to model the process of edge node analysis and processing of computationally intensive tasks as a mixed integer nonlinear programming problem. Moreover, a mathematical model for the service chains is established. We analyze the average service response time during task execution to optimize the performance of service chain caching and scheduling. Experiments show that the outer approximation (OA) algorithm obtains better results than MindtPy and Multistart. The average response time obtained by the OA algorithm is 2.2% and 6.9% lower than those obtained by the MindtPy and Multistart algorithms, respectively. The OA algorithm using this mathematical model can effectively reduce the average service response time and improve the resource utilization of the edge server.