## 6 Resource Reservation Schemes: Static vs. Dynamic
### Static Scheme  
The first proposed policy consists of a static prediction scheme that selects the cells for being involved by passive reservations, according to some parameters (maximum speed, average speed, \(CST\) and HDP). When, for a mobile host \(i\), \(C_{ei}\geq 2\) (at least one predicted hand-off event), let \(j=1\),..., (\(C_{ei}-1\)) be the index associated to the \(j\)-th hand-off event, where \(C_{ei}\) is derived as in [31]; let indicate the number of desired predicted cells for \(j\)-th hand-off of user \(i\) with \(C_{ij}\), where \(C_{ij}\in\{1,\,\ldots,\,n\}\ \forall\,j\). We propose three reservation schemes for the static case:  
1. Non-decreasing: each user \(i\) will reserve on an increasing number of cells for the increasing number of hand-over (i.e., \(C_{i1}\leq C_{i2}\leq\ldots\leq C_{iC{i-1}}\));
2. Non-increasing: each user \(i\) will reserve on a decreasing number of cells for the increasing number of hand-over (i.e., \(C_{i1}\geq C_{i2}\geq\ldots\geq C_{iC{i-1}}\));
3. Constant-trend: each user \(i\) will reserve on the same number of cells for every hand-over (\(C_{i1}=C_{i2}=\ldots=C_{iC{i-1}}\)). Figure 5: The obtained M matrix for the mobility parameters of [42]; for example \(M(4,2)=p4,2=pcNSIS-MIP(4,2)=N(0.2798,0.0464)\), where \(\mu(4,2)=0.2798\) and \(\sigma(4,2)=0.0464\). When \(M\) shows that there are no preferential mobility directions in the analyzed traces, the pre-reservation over only one cell for every hand-over (\(C_{ij}=1\)\(\forall j\)) may lead to a high Call Dropping Probability (CDP), as illustrated in the next section. This issue can be solved by pre-reserving over multiple hand-out directions: this implies that the values of \(C_{ij}\) must be chosen adequately. Once the \(C_{ij}\) values are chosen, the proposed scheme uses \(M\) to predict the next cell directions \(y\) for every \(j\)-th hand-off event of user \(i\). If the current hand-in direction is \(x\), then \(y=index\{max[M(x)]\}\), where \(M(x)\) is the \(x\)-th row of \(M\) and \(x,y\in S_{ho}\); this is repeated \(C_{ij}\) times for every \(j\)-th hand-off. For every iteration, previous chosen values are not considered yet when picking up the current maximum. The pseudo-code illustrated in Figure 6 resumes the main steps of the algorithm. It receives \(n\) and \(C_{i}=[C_{i1}\),..., \(C_{ho\_max}]\) as input control parameters: since \(C_{ei}\) cannot be known a-priori because it depends on the \(CHT\) (which is assumed to be exponentially distributed) a maximum number of hand-off events \(C_{ho\_max}\) for every call must be considered, under the assumption of \(C_{ei}\geq 2\). The algorithm starts the prediction from the active cell, where the call originated. Given the unavailability of \(M\) at the moment of the service request, the first future cell is evaluated by one of the approaches of [51, 52]. Assuming that user \(i\) will probably follow direction \(d_{k}\) until the first hand-out event, the identifier of the most \(C_{i1}\) probable cells that user \(i\) will visit following direction \(d_{jk}\) from the current position can be discovered  
Figure 6: Pseudo-code of the proposed algorithms. and inserted into the prediction set _Pcells_. From \(j=2\) to \(j=C_{i-1}\), the algorithm creates a temporary set called _current_Pcells_ with the predicted cells belonging to \(j\)-th hand-off event. For each of them, it determines the hand-in direction called _current_x_, then it evaluates the maximum value in the vector \(M(current\_x)\backslash current\_max\_set\). The last discovered maximum value is appended into the \"_current_max_set_\" vector, that is subtracted from \(M(current\_x)\) in the next iteration (in this way the new maximum value is always calculated, without considering the previous ones). The algorithm has a time complexity of \(O((C_{i-1})\cdot n^{2})\).