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This article proposes a new model which integrates the service level constraints and considers the uncertainty of customer demands at the same time. The customer orders are classified into three classes based on their average size, each with its unique priority and service rate. The logistics system is then modeled as a network of independent priority M/M/m queues in which facility sites are taken as server groups and customers are considered as demand nodes. We try to locate the facilities and determine their quantity, server numbers and customers simultaneously. The optimization goal is to minimize the total cost and meet the specific constraints of mean waiting time at each facility. In order to find the near-optimal solution, we present two heuristic methods based on tabu search and Lagrangian relaxation. Extensive computational results across a variety of problem structures are reported. This model improves previous works through differentiating orders and introducing the mean waiting times into location problem as service level constraints. It can be used in not only logistics but also other service systems.