## 7 Performance Evaluation
### Performance Comparison  
In this sub-section, our proposed idea is compared with other two ones: the User Mobile Profile (UMP, as already discussed for [12]) and the Active Lempel-Ziv (ALeZi) algorithm [55], with the aim of showing the advantages introduced by a passive reservation approach and if the proposed idea could be better than other ones. The UMP algorithm evaluates the probabilities of each cell that the user can visit in the future by using three main data structures: the Trace Record Matrix (TRM), the Path Database (PD) and the Historical Path Database (DH). It is also able to perform a multi-step prediction, in the sense that it can predict the probability of visiting cells at the \(k\)-th hand-over event (with \(k=1,\,\ldots,\,n\) where \(n\) is the number of hand-overs that the mobile host will perform). Obviously, given the visiting probabilities determined by UMP, if more cells are considered in the prediction, then a better approximation will be obtained, at the price of a bigger resource wastage (in the figures, UMP-2 and UMP-3 indicate the UMP with 2 or 3 passive reservations for each next cell). The AleZi scheme, instead, represents a single-step predictor (for each prediction step, only the first next cell is predicted), based on the Lempel-Ziv algorithm. Each cell of the system will be represented by a symbol, so the sequence of the previously visited cells will be represented by a string, used to predict the most probable next symbol (i.e., the next cell), by the Prediction by Partial Matching (PPM) approach. For the static and dynamic schemes the best cases have been considered (that is the sequence \(C_{i1}=1\), \(C_{i2}=2\), \(C_{i3}=3\) and \(\delta=0.5\), respectively). We provided to consider the same topology of the previous simulations. Figure 14 shows the trend of the average system utilization offered by the four different algorithms, in function of the number of requests per second (only for MIP traffic). It can be seen that the ALeZi scheme outperforms the other three algorithms, because it is able to reserve passive bandwidth only on the single predicted next cell, so there is a very limited presence of passive reservations into the system, leading to a balanced level of active bandwidth (perceived by mobile hosts while served by a coverage cell). Clearly, the  
Figure 14: Average system utilization for the considered predictive algorithms. absence of a multi-step approach, makes the ALEZi weak in terms of service continuity, given that the mobile hosts could reach a cell in which there are no passive reservations for it. Our dynamic proposal, offers a good trade-off in terms of system utilization: it cannot perform as good as ALEZi, but the possibility to dynamically choose the number of cells over which the passive reservations should be made gives the opportunity to be near ALEZi for higher MIP requests. As regards UMP-2 and UMP-3, their utilization is very low when 2 or 3 cells are considered to be influenced by passive reservation. Figure 15, instead, shows the average prediction error committed during the whole CHT of mobile hosts. It is evident that a single-step predictor (such as ALEZi) is not able to guarantee a good performance for this metric, given that only the next cell is predicted for each hand-over event, so it fails to capture the dynamics of mobile users (no memory effect). Additionally, in this case, our dynamic scheme outperforms the UMP, with a maximum error of 16.8% for higher service request rate. In Figure 16, the average Call Dropping Probability (CDP, the probability of a forced termination of a call after an hand-over event) is clearly unacceptable for the ALEZi algorithm: given that it predicts only one next cell (if enough bandwidth is available), the probability of finding a saturated/congested coverage cell is much higher. For the other schemes, no big differences are visible (their CDP ranges from 0.081, almost constant for the static predictor, to 0.123 for the UMP-2 approach, so for the CDP metric they are quite similar.