# An Analytical Framework in OFDM Wireless Networks Servicing Random or Quasi-Random Traffic
## 5 Performance Evaluation  
In this section, we consider a cell that accommodates \(KL\) service-classes and provide simulation and analytical congestion probabilities results for the P-S, the P-S/res, and the qr-P-S models. In addition, we provide simulation and analytical SU and PU results for the P-S and the P-S/res models. The required input for these models is: \(B=20\) MHz, \(M=256\), \(P=25\) Watt, \(R=329.6\) kbps, \(L=64\), \(b_{l}=l\), \(l=1\), \(\ldots\), \(64\), while we assume that \(b_{l}\) is uniformly distributed. Due to this assumption, a new call has an average subcarrier requirement \(\hat{g}=32.5\). In addition, let \(K=3\), which means that the cell accommodates \(KL=192\) service-classes. In the case of the qr-P-S model, we assume that \(N_{kl}=20\) sources for all service-classes. Let the integer representations of \(p_{k}\) (\(k=1\), \(2\), \(3\)) and \(P\) be: \(p_{1}^{\prime}=6\), \(p_{2}^{\prime}=10\), \(p_{3}^{\prime}=16,P=2500\). The values of \(p_{1}^{\prime}\) require that: \(p_{1}\approx 0.06\), \(p_{2}\approx 0.01\), \(p_{3}\approx 0.16\) achieved via the following values of the average channel gain \(\gamma_{k}\) (\(k=1\), \(2\), \(3\)): \(\gamma_{1}=24.679\) dB, \(\gamma_{2}=22.460\) dB, \(\gamma_{3}=20.419\) dB. In addition, an arriving call has an average channel gain \(\gamma_{k}\) with a probability that is determined via: (1) set 1: \(r_{k}=1/3\) (\(k=1\), \(2\), \(3\)) and (2) set 2: \(r_{1}=1/4\), \(r_{2}=1/4\), \(r_{3}=1/2\). Furthermore, let \(\lambda_{kl}=\Lambda r_{k}/L\), where \(\Lambda\) is the total arrival rate given by \(\Lambda=\alpha M\mu/\hat{g}\), \(\alpha\) is the cell's traffic intensity and \(\mu\) is the service rate of calls with \(\mu=0.00625\). In the case of the P-S/res model, we assume that \(pb_{k,l}(j_{1})=0\) when \(j_{1}\leq M-b_{l}-t_{l}\) and \(pb_{k,l}(j_{1})=1\) when \(j_{1}>M-b_{l}-t_{l}\). Due to this assumption, we have the P-S/BR model. The values of \(t_{l}\) are \(t_{l}=64-l\), \(l=1\), \(\ldots\), \(64\), and they are chosen in such a way so that \(b_{1}+t_{1}=\ldots=b_{64}+t_{64}\). Regarding the simulation results, they are based on Simscript III [60]. Each simulation run is based on 10 million generated calls while the results presented herein are mean values of 7 runs. Furthermore, the blocking events of the first 3% of these calls are not taken into account in the results, in order to account for a warm-up period. In all figures of this section, the analytical and simulation results are quite close. Note that in the x-axis of Figures 1-5 the value of \(\alpha\) increases from 0.2 to 1.0 in steps of 0.1, while in the x-axis of Figures 6 and 7 the value of \(\alpha\) increases from 0.05 to 0.2 in steps of 0.025. In Figures 1 and 2, we consider the P-S and the P-S/BR models and present the simulation and analytical CBP of service-classes (3, 64), (2, 64), (1, 64) (Figure 1) and service-classes (3, 48), (2, 48), (1, 48) (Figure 2). Note that service-classes (3, 64), (2, 64) and (1, 64) have the highest requirement in terms of subcarriers (\(l=64\)). Regarding the average channel gain we consider set 1 (\(r_{k}=1/3\) (\(k=1\), 2, 3)). In Figure 1, it is obvious that the BR policy decreases the CBP values of service-classes (3, 64), (2, 64) and (1, 64) compared to the corresponding CBP values of the P-S model. In Figure 2, the BR policy increases (in most of the cases) the CBP values of service-classes (3, 48), (2, 48), (1, 48) compared to the corresponding CBP values of the P-S model. A similar behavior appears in most of the service-classes whose calls have a requirement of less than 64 subcarriers. In addition, the same behavior (in terms of CBP) appears when we consider set 2 for the average channel gain. Figure 1: CBP–Service-classes (3, 64), (2, 64), and (1, 64). Figure 2: CBP–Service-classes (3, 48), (2, 48), and (1, 48). In Figures 6 and 7, we consider the PS and the qr-P-S models for both sets of \(r_{k}\). Figures 6 and 7 show the simulation and analytical TC probabilities of service-classes (3, 16) and (3, 64), respectively.