The development of Multi-access edge computing (MEC) has resulted from the requirement for supporting next generation mobile services, which need high capacity, high reliability and low latency. The key issue in such MEC architectures is to decide which edge nodes will be employed for serving the needs of the different end users. Here, we take a fresh look into this problem by focusing on the minimization of migration events rather than focusing on maximizing usage of resources. This is important because service migrations can create significant service downtime to applications that need low latency and high reliability, in addition to increasing traffic congestion in the underlying network. This paper introduces a priority induced service migration minimization (PrISMM) algorithm, which aims at minimizing service migration for both high and low priority services, through the use of Markov decision process, learning automata and combinatorial optimization. We carry out extensive simulations and produce results showing its effectiveness in reducing the mean service downtime of lower priority services and the mean admission time of the higher priority services.