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The explosive growth of mobile devices promotes the prosperity of novel mobile applications, which can be realized by service offloading with the assistance of edge computing servers. However, due to limited computation and storage capabilities of a single server, long service latency hinders the continuous development of service offloading in mobile networks. By supporting multi-server cooperation, Pervasive Edge Computing (PEC) is promising to enable service migration in highly dynamic mobile networks. With the objective of maximizing the system utility, we formulate the optimization problem by jointly considering the constraints of server storage capability and service execution latency. To enable dynamic service placement, we first utilize Lyapunov optimization method to decompose the long-term optimization problem into a series of instant optimization problems. Then, a sample average approximation-based stochastic algorithm is proposed to approximate the future expected system utility. Afterwards, a distributed Markov approximation algorithm is utilized to determine the service placement configurations. Through theoretical analysis, the time complexity of our proposed algorithm is linear to the number of users, and the backlog queue of PEC servers is stable. Performance evaluations are conducted based on both synthetic and real trace-driven scenarios, with numerical results demonstrating the effectiveness of our proposed algorithm from various aspects. [ABSTRACT FROM AUTHOR]