## 8 Conclusions  
In this paper, we investigated a Deficit Round Robin (DRR) and a simple scheduling algorithm (imitating Generalized Processor Sharing or GPS) in the context of IEEE 802.16e Mobile WiMAX Networks. We introduced a modification of DRR by allowing packet fragmentation (DRRF) to take the best features of both DRR (reducing a fragmentation overhead) and GPS (achieving full WiMAX frame utilization).  
To overcome the issue of varying link capacity, we used the slot allocation derived from the queue lengths and MCSs. The results show that all three scheduling algorithms can achieve perfect throughput fairness, but the total utilization of the link and the percentages of overhead are different. DRRF provides the best goodput.  
In addition, we formulated a general definition of fairness, the so-called Generalized Weighted Fairness, or GWF. In Mobile WiMAX, this definition provides a compromise between slot fairness or temporal fairness in which the service provider allocates slots fairly, but throughput of the users varies with their locations, and byte fairness or throughput fairness, in which all users get the same throughput, but the service provider has to allocate extra resources for users in poor channel conditions. The GWF criteria allow the service providers to configure the weight parameter to any values between \(0\) and \(1\), and achieve any levels of compromise between these two extremes. We also used DRRF as the scheduling discipline to show the effect of GWF.  
In general, DRRF can be used as a best effort (BE) scheduler when the fairness is mainly used as the metric. However, to support a non real-time Polling Service (nrtPS) class, a mechanism to derive a proper quantum number was also introduced for DRRF to support users with minimum reserved traffic rate, maximum sustained traffic rate, and traffic priority constraints.  
For a real-time Polling Service (rtPS) class, in this paper, video traffic is used as an example. Common well-known scheduling disciplines, Earliest Deadline First (EDF) and DRRF, were investigated. We demonstrated the effect of EDF and DRRF with the deadline enforced. The results show that DRRF outperforms EDF, and maintains fairness under an overload scenario.  
Notice that although the simulations show the precise effect of each algorithm, more variations of simulation topologies, configurations, different traffic types including large number of mobile stations, and variable packet sizes can be further investigated. Moreover, with Automatic Repeat reQest (ARQ) and Hybrid ARQ features enabled, the scheduler needs to accommodate scheduling of the retransmission/feedback and the boundary of ARQ blocks [19].  
One more requirement for Mobile WiMAX scheduling with Hybrid ARQ disabled is that all downlink allocations being mapped to a rectangular area in the Orthogonal Frequency Division Multiple Access (OFDMA) frame. That restriction can reduce the throughput because some spaces may need to be left unused to make the allocation rectangular [20]. Moreover, the optional packing feature can also be added. These issues need further investigation.  
In our analysis, we assumed that the throughput is always non-zero, _i.e._, the worst case MCS is BPSK. However, it is possible that the channel conditions are so poor that even BPSK will not work. In other words, the base station and/or the mobile station cannot transmit any bits for some time. In this case, the scheduler can simply record the transmitted opportunity of MSs during the unacceptable channel state condition [3]. Then, once the mobile station is in an acceptable channel condition, the MS will receive the transmission opportunity back within some specified thresholds distributed uniformly over some periods to prevent the starvation of other flows.