## 5 Evaluation
### Simulation Model  
To model video communication over WiMAX, the well-known ns-2 simulator [57] was combined with a module from the Chang Gung University, Taiwan [58] that has turned out to be an effective way of modeling IEEE 802.16e's behavior. In the evaluation, transmission over WiMAX was carefully modeled. The IEEE 802.16e TDD frame length was set to 5 ms, as previously remarked, because only this value is supported in the WiMAX Forum simplification of the standard (In fact, a frame size of 20 ms benefits video streaming [59] because there is more time to transfer enough data.). The raw downlink data rate of 10.67 Mbps results from the use of one of the mandatory WiMAX modulation and coding modes [50] for a TDD downlink/uplink sub-frame ratio of 3:1, namely 16-QAM at 12 rate. The WiMAX BS was assigned more bandwidth capacity than the uplink to allow the BS to respond to multiple MSs. All buffers were set to 50 packets and all packets were directed to WiMAX's real-time Polling System (rtPS) class of service. Apart from video streaming to a WiMAX MS, three other MSs received continuous CBR data, Figure 14, with two receiving at 1 kbps, and one at 840 kbps. A typical low bitrate parametric speech codec such as a Linear Prediction Coding (LPC) vocoder operates from 1.2 kbps to 4.8 kbps, close to the lowest rate of these two signals. The G.711 vocoder for high-quality Voice-over-IP (VOIP) has a typical data rate of 87 kbps, implying that the larger of these signals is equivalent to ten such speech signals. Packet size was set at 1 kB, the WiMAX maximum transport unit. It is these streams that inject cross-traffic into the scenario modeled and provide any congestion experienced in the experiments by the video stream. Figure 13: Overview of protection measures and packet handling across the upper and WiMAX protocol stack layers. To model adverse channel conditions across the WiMAX link, \"bursty\" errors (time correlated errors) were modeled by a Gilbert-Elliott two-state hidden Markov model [60]. This channel model was introduced into the ns-2 simulator. The Gilbert-Elliott channel model itself is a two-state Markov chain. It is based on good and bad states, the probabilities of these states, and the probabilities of the transition states between them. In the bad state, losses happen with higher probability, whereas in the good state, losses happen with lower probability. \(P_{GG}\) refers to the probability of being in the good state and \(P_{GB}\) is the probability of a transition from the good state to the bad state. \(P_{BB}\) is likewise the probability of being in the bad state and transitioning back to the same bad state. \(P_{BG}\) refers to the probability of a transition from the bad to good state. \(P_{GG}\) (\(P_{BB}\)) can be interpreted as the probability of remaining in the good (bad) state, given that the previous state was good (bad). Conversely, \(P_{GB}\) represents the probability that, given that the previous state was good, a transition is made from the good to the bad state. By the law of total probability, all probabilities sum to one (certainty). Therefore, we have \(P_{GG}+P_{GB}=1\), resulting in Equation (4). A similar argument for the bad state leads to Equation (6). \[P_{GG} =1-P_{GB} \tag{4}\] \[P_{BB} =1-P_{BG} \tag{5}\]  
For the stochastic process to remain stationary in time,  
\[\pi_{\text{G}}P_{GB}=\pi_{\text{B}}P_{BG} \tag{6}\]  
where \(\pi_{\text{G}}\) and \(\pi_{\text{B}}\) are the steady state probabilities of being in a good or bad state respectively. The law of total probability \(\pi_{\text{B}}=1-\pi_{\text{G}}\) again applies. Substituting this expression for \(\pi_{\text{B}}\) into Equation (6) easily leads to:  
\[\pi_{{}_{G}}=\frac{P_{{}_{BG}}}{P_{{}_{BG}}+P_{GB}} \tag{7}\]  
Figure 14: Scenario for evaluation experiments. Similarly, \(\pi_{G}=1-\pi_{B}\).