The total time a patient spends in an outpatient facility, called the patient cycle time, is a major contributor to overall patient satisfaction. A frequently recommended strategy to reduce the total time is to perform some activities in parallel thereby shortening patient cycle time. To analyze patient cycle time this paper extends and improves upon existing multi-class open queueing network model (MOQN) so that the patient flow in an urgent care center can be modeled. Results of the model are analyzed using data from an urgent care center contemplating greater parallelization of patient care activities. The results indicate that parallelization can reduce the cycle time for those patient classes which require more than one diagnostic and/ or treatment intervention. However, for many patient classes there would be little if any improvement, indicating the importance of tools to analyze business process reengineering rules. The paper makes contributions by implementing an approximation for fork/join queues in the network and by improving the approximation for multiple server queues in both low traffic and high traffic conditions. We demonstrate the accuracy of the MOQN results through comparisons to simulation results.