In Worldwide interoperability for Microwave Access (WiMAX) network, QoS(quality of service) is provided for service flows. For this, five classes of services are defined in IEEE 802.16. They are Unsolicited Grant Service (UGS), Extended Real-Time Polling Service (ertPS), Real-Time Polling Service (rtPS), Non Real-Time Polling Service (nrtPS) and Best Effort (BE). For real-time classes, the sent packet has a deadline. As the transmission delay is over the limitation of deadline, the packet becomes useless and will be discarded. Thus, they will be served earlier and have higher probability. Nevertheless, non-real-time packets need also to be served from time to time. The scheduler should assign proper bandwidth for non-real-time flows and send the real-time packets before they are discarded. To deicide the right allocated bandwidth, the arrival rate of each flow is a good parameter for assignment. The average µ and standard deviation σ of arrival rate correspond to the long term need and variation of load for one flow. Thus, we proposed a scheduling algorithm named BAcSOA in which µ+kσ is used as a reference to allocate bandwidth with weighted round robin for one flow [5]. Different classes of flows will be given different values of k which corresponds to the priorities of classes. In this algorithm, flow with higher priority should have larger value of k. The value of k will decide the performance of this class. In this paper, we revise the algorithm to EBAcSOA and propose a mathematical way to decide the value of k for a required performance. Then, a simulation platform is proposed to decide k such that a required performance can be obtained for an operating system. This approach may be different from other researches in which there is no required performance and the performance results are obtained only for several operating points. However, the approach proposed is more practical from the view of an operator and may become an attractive point for other researchers.