## 1 Introduction
The mobile station has an agreed quality of service (QoS) requirement that is negotiated between the base station and the mobile station at the time of the connection setup. The base station grants transmission opportunities to various mobile stations based on their bandwidth requests and QoSs. In IEEE 802.16e Mobile WiMAX Networks, several modulation and coding schemes (MCSs), such as Binary Phase Shift Keying (BPSK) and Quadrature Amplitude Modulation (QAM), are supported. BPSK results in 1 bit per symbol, and is used for channels in poor conditions. QAM results in more bits per symbol, and is used for more reliable channel conditions. Since MCS used for each user depends upon the user location, and varies with time, the slot capacity (number of bits in the slot) is also varied with time and location. In this paper, we use different MCSs to represent a variation of channel interferences. The IEEE 802.16e standard defines five classes of service: 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). Each of these has its own set of QoS parameters, such as minimum throughput, maximum allowable delay, and delay variation (delay jitter). In this paper, our focus is on non real-time traffic, _i.e._, BE and nrtPS classes. The QoS parameters are the throughput and the fairness criteria. However, we also investigate video traffic, an example of a real-time traffic class. The delay constraint (maximum allowable delay) is an additional QoS parameter for this class. For other classes of services, _i.e._, UGS, and ertPS, normally a fixed size allocation mechanism applied in every Mobile WiMAX frame and/or a simple earliest deadline first (EDF) algorithm can be used as a scheduling discipline [3, 5, 7]. To summarize, in this paper, our contributions are as follows: first we investigate two fair scheduling algorithms; namely, Generalized Processor Sharing (GPS) [8] and Deficit Round Robin (DRR) [9] in the context of IEEE 802.16e Mobile WiMAX Networks. Each algorithm has its own pros and cons; for example, both GPS and DRR result in perfect fairness, _i.e._, equal throughput for contending users. Since Mobile WiMAX allows a fragmentation, GPS can utilize full frame resource allocation; however, it creates high overhead because the allocation is usually distributed equally for all MSs in each Mobile WiMAX frame. In contrast, because of the packet-based allocation framework, DRR results in the least overhead, but can leave some unused-space within the Mobile WiMAX frame. Thus, to achieve both full frame utilization and overhead reduction, we introduce a Deficit Round Robin with Fragmentation (DRRF) [10] by taking advantage of both approaches to best suit the scheduling of the best effort traffic, in which the goal is to maintain the fairness among competing flows. Second, in wireless networks, the link capacity keeps changing over time and distance. Especially in wireless broadband networks where a longer distance means lower channel quality. The issue of defining fairness depends upon both service provider's and customers' points of views. As a result, in this paper, we also propose a Generalized Weighted Fairness (GWF) [11] which equalizes the weighted sum of service time units and transmitted bytes. In Mobile WiMAX, again the service time unit is represented as a number of slots allocated to each mobile station. Mobile WiMAX equipment manufacturers can implement the generalized fairness concept. The service providers can then set a weight parameter to any desired values, and achieve either slot fairness or throughput fairness or some combination of the two. We use DRRF to illustrate the effect of GWF. In addition, we extend DRRF to support other QoS parameters for non real-time traffic (nrtPS class) in IEEE 802.16e Mobile WiMAX Networks, _i.e._, minimum reserved traffic rate, maximum sustained traffic rate, and traffic priority [1].