# Call Blocking Probabilities under a Probabilistic Bandwidth Reservation Policy in Mobile Hotspots
## 4 Performance Evaluation  
In this section, we consider an application example of a vehicle with an AP installed on it and let the capacity of the AP's WLAN be equal to \(C=58\) b.u. During the stop phase, the vehicle remains for an exponentially distributed time in a location with mean \(\theta_{s}^{-1}=3\). We also assume that the duration of the moving phase is exponentially distributed with mean \(\theta_{m}^{-1}=6\). The vehicle accommodates Poisson arriving calls with \(\lambda_{h}=24\) (fixed value) and \(\lambda_{new}=2\) (variable value). Accepted calls remain in the system for an exponentially distributed service time with mean \(\mu_{s}^{-1}=\mu_{m}^{-1}=6\). To facilitate handover users, the probabilistic BR policy is considered whereby \(t_{new}=8\) b.u. are reserved for them. In what follows, the generalized probabilistic BR loss model is considered. To this end, five different sets of \(p_{s,new}\) and \(p_{m,new}\) are considered: (1) \(p_{s,new}=p_{m,new}=0.0\) (this is the cutoff priority scheme studied in [7]); (2) \(p_{s,new}=p_{m,new}=0.25\); (3) \(p_{s,new}=p_{m,new}=0.50\); (4) \(p_{s,new}=p_{m,new}=0.75\); (5) \(p_{s,new}=p_{m,new}=1.0\) (this is the nonpriority scheme studied in [7]). Note that the probabilistic BR loss model refers to the case of \(p_{m,new}=1.0\) (the CS policy is applied to new calls and therefore no reservation occurs) and \(p_{s,new}<1.0\). Since this model leads to similar conclusions with the generalized loss model, we present analytical and simulation results of the generalized probabilistic BR loss model only. The simulation results presented herein are based on Simscript III and are the mean values of eight runs [25]. In each run, the initial 5% of the generated calls (one million generated calls per run) is not taken into account in the CBP results, in order to obtain a warm-up period [26, 27]. Finally, reliability ranges which are less than two orders of magnitude are not presented in the CBP graphs. Table 1 includes the list of simulation parameters used in this application example. \begin{table}
\begin{tabular}{l l} \hline AP’s WLAN capacity & \(C=58\) b.u. \\ \hline Duration of the stop phase (exponentially distributed) & \(\theta_{s}^{-1}=3\) (mean value) \\ \hline Duration of the moving phase (exponentially distributed) & \(\theta_{m}^{-1}=6\) (mean value) \\ \hline Arrival rate of handover calls (Poisson arrivals) & \(\lambda_{h}=24\) (fixed value) \\ \hline Arrival rate of new calls (Poisson arrivals) & \(\lambda_{new}=2\), 4, 6, 8, 10, 12, 14, 16, 18, 20 (variable value) \\ \hline Service time in the stop phase (exponentially distributed) & \(\mu_{s}^{-1}=6\) (mean value) \\ \hline Service time in the moving phase (exponentially distributed) & \(\mu_{m}^{-1}=6\) (mean value) \\ \hline BR parameter (for new calls) & \(t_{new}=8\) b.u. \\ \hline Probabilistic BR parameters (stop phase) & \(p_{s,new}=0.0\), 0.25, 0.50, 0.75, 1.0 \\ \hline Probabilistic BR parameters (moving phase) & \(p_{m,new}=0.0\), 0.25, 0.50, 0.75, 1.0 \\ \hline Number of simulation runs and & Mean values of eight runs with \(10^{6}\) generated calls/run and 5\% of them not taken into account (warm-up period) \\ \hline \end{tabular}
\end{table} 
Table 1: List of simulation parameters. In the x-axis of Figures 3-5, the values of \(\lambda_{new}\) increase in steps of 2. Thus, point 1 (in the x-axis) refers to \(\lambda_{new}=2\) and point 10 refers to \(\lambda_{new}=20\). In the x-axis of Figures 6-8, we consider 10 different values of \(\theta_{s}^{-1}\), assuming that \(\lambda_{h}=24\) (fixed value), \(\lambda_{new}=16\) (fixed value) and \(\theta_{m}^{-1}=6\) (fixed value). More precisely, we consider the values 0.2, 0.25, 0.3333, 0.5, 1.0, 2.0, 3.0, 4.0, 5.0 and 6.0. To increase the readability of all graphs, simulation results are represented with different types of dots, while analytical results are represented with different types of lines. Besides, two different arrows have been included in each graph in order to identify the results obtained via [7].