WiMAX is an advanced broadband wireless access technology that supports multimedia transmission. Here we propose a batch-arrival queueing model for evaluating WiMAX QoS-aware packet scheduling systems and obtaining packet loss rate (PLR), queueing delay (QD), and bandwidth utilization (BU) performance measures. These are used to solve a utilization optimization problem associated with QoS constraints. Specifically, a given traffic statistic and maximum PLR and QD constraints were applied to optimize BU for a classified packet-scheduling buffer. It is the writer's hope that operators can apply the model to dynamically control classified buffer size and to enhance profit tied to QoS constraints.