# Advanced Resources Reservation in Mobile Cellular Networks: Static vs. Dynamic Approaches under Vehicular Mobility Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Extension of MRSVP protocol with additional features inherited by NISIS, in order to dynamically manage NSIS-MIP and NSIS-MDP classes also during on-going calls;
- (2)
- Proposal of a utility-based rate adaptation scheme with the application of utility functions for the management of Best Effort (BE) associated to NSIS-MDP class and video traffic associated to NSIS-MIP class;
- (3)
- Proposal of a Hand-off Direction and CST based reservation schemes in order to meet adaptive QoS requirements during users’ movements. In-advance bandwidth reservations is proposed in order to reduce the QoS degradation and call dropping probability;
- (4)
- Static and Dynamic (threshold-based) reservation prediction schemes proposal considering real mobility traces;
- (5)
- Validation of the considered scheme through realistic mobility patterns.

## 2. Related Work

#### 2.1. Reservation Schemes and Prediction in Literature

#### 2.2. Mobility Applications in Literature

## 3. The Considered Architecture

#### 3.1. Protocols and Service Classes

- (a)
- NSIS Mobility Independent Guaranteed (NSIS-MIG, which provides intolerant applications, with very stringent guarantees on packet delays and jitter);
- (b)
- NSIS Mobility Independent Predictive (NSIS-MIP, dedicated to elastic real-time applications, able to work with some resource bounds);
- (c)
- NSIS Mobility Dependent Predictive (NSIS-MDP, which can be compared with the best-effort class, subject to continuous QoS degradations and/or droppings).

#### 3.2. Advanced Resource Reservations with NSIS

- (a)
- local proxy agents, generally identified as the active cell in which a mobile host is making the service request (hence, the active reservation); NSIS-MDP users make use of local proxy agents only (they request the service only on the current cells);
- (b)
- remote proxy agents, generally identified as the passive cells which will be probably visited by mobile hosts (hence, dealing with passive reservations); NSIS-MIP make use of remote proxy agents in order to manage their passive requests remotely.

## 4. CityMob and C4R-GUI for Generating Real Mobility Traces

_{1}and F

_{2}describe the reaction of the driver to the in-front situation. In fact, more recent studies [43] consider:

## 5. Traffic Models and Utility Functions

#### 5.1. Real Time Video Traffic for Mobility Independent Predictive Services

_{s}is the received rate level, a

_{s}

_{,k}, b

_{s}

_{,k}, c

_{s}

_{,k}, d

_{s}

_{,k}are normalization factors and ${c}_{s,k}-{\alpha}_{s,k}\le {x}_{s}<{c}_{s,k+1}-{\alpha}_{s,k+1}$, for k = 1, …, n, ${\alpha}_{s,1}={c}_{s,1}$, ${\alpha}_{s,k}=\frac{{c}_{s,k}-{c}_{s,k-1}}{2}>0$ for k = 2, …, n. Figure 2a shows a multi-step utility function for the considered traffic, with the same values used in [4], except for: a

_{s}

_{,1}= 1, a

_{s}

_{,2}= 1.7, a

_{s}

_{,3}= 0.9, a

_{s}

_{,4}= 1, c

_{s}

_{,1}= 512, c

_{s}

_{,2}= 640, c

_{s}

_{,3}= 768, c

_{s}

_{,4}= 896.

#### 5.2. Best Effort Traffic for Mobility Dependent Predictive Services

_{BE}must be a monotonically increasing function of r

_{s}; a is the maximum desired utility value and when r

_{s}approaches to infinity, U

_{BE}(r

_{s}) approaches to a; from [45], generally a = 5. Figure 2b illustrates the trend of U

_{BE}for different values of q with a = 5 and b = −9.

#### 5.3. Utility-Based Bandwidth Management

_{outage}(that is the probability associated to the event that instant perceived utility of any served user falls below its lower threshold). As described in [3,31,46], the wireless link among a user and its current active AP can be modeled by a k-state Markov chain: the average state-permanence time associated to each state m is indicated with t

_{m}, the degradation ratio of the m-th state is D

_{m}(with 0 ≤ D

_{m}< 1, $\forall $ 1 ≤ m ≤ k). If r

_{i}is the amount of bandwidth allocated by the network to user i, the received instant utility is defined on the basis of the belonging service class:

_{i}= U

_{i}− (1 − D

_{i},m)∗r

_{i})

_{i}

_{,m}is associated to every chain state when the FSMC for uIer i is defined, so it is a fixed value. For more details about the FSMC, to see [3,31,46]. The implementation of the wireless channel has been carried out according with the standard IEEE 802.11 [46]. In order to guarantee the intra-class fairness level, a normalized gap of the average received utility can be defined for user i as:

_{i}

_{,avg}is the average received utility by user i and u

_{CLASSi}

_{,min}is the minimum allowed utility level foI user i that belongs to the CLASS service class (NSIS-MIP or NSIS-MDP). The proposed algorithm follows an intra-class fairness criterion, so each value of G

_{i}will be compared only with G

_{j}, where users i,j belong to the same service class. Figure 3 represents the main phases of the proposed reallocation algorithm.

_{CLASS i,min}when its link degrades and to avoid the outage event, the scheme searches for CLASS-benefactor(s) (able to give-up some bandwidth), starting from the user with the largest normalized gap. A deep and complete description of the upgrade/degrade effects on bandwidth reallocations can be found in [31].

_{j}will give up an amount of bandwidth equal to $\mathrm{min}(\mathrm{max}(0,{r}_{j}-\frac{{r}_{j,\mathrm{min}}}{1-{D}_{j,q}}),r)$, where q is j’s link state. The procedure is carried-on until r has been reached (or all the current users have been searched). If r is not reached, a second collection round is started but, this time, each chosen user will be dropped out from the network. A user with a totally degraded communication link has to give up a part of its reserved bandwidth in order to maximize the perceived utility of system users (for details, see [31]). As will be seen in next section, an NSIS-MDP user can use free available bandwidth in the current AP (active-NSIS-MDP) or a certain amount of passive bandwidth that is reserved for NSIS-MIP flows that will come in the current AP (passive-NSIS-MDP).

_{outage-NSIS-MIP}is the outage probability of the wireless system. As regards NSIS-MDP users, the condition in Equation (10) is verified only for the current cell. When a new user makes a service request, the CAC calculates p

_{0,c}and verifies if it is less or equal p

_{outage}for each cell: in this way the new request can be admitted or rejected (if it is not satisfied). The outage probability p

_{0}for user i belonging to the CLASS service class at any time is:

_{i}is user i’s link state, p

_{mi}is the probability of the user i’s link to being in state m, n is the total number users (with the new one) belonging to CLASS and R

_{CLASS}represents the bandwidth dedicated to CLASS services. For a deeper analysis of the proposed CAC and channel model with degradation states to see [30].

## 6. Resource Reservation Schemes: Static vs. Dynamic

_{e}visited by the mobile host during its CHT, the CST of mobile hosts has been obtained by a preliminary set of simulations: it follows a Gaussian distribution under the CityMob generator, with different values of maximum acceleration and maximum speed [29,31]. C

_{e}can be evaluated as in [31], but without any information about user mobility pattern (directional preferences), C

_{e}can be used only to make circular reservations (Figure 4), around the active cell. In this way, following the same approach of [48,49], the number of required passive reservations C

_{r}for NSIS-MIP services increases with polynomial trend, as indicated in Equation (12). Table 1 shows the numerical values for Equation (12) and for the directional reservation policy P, shown later:

_{r}= 3 × C

_{e}× (C

_{e}− 1).

_{e}= 2, 3 or 4 a higher number of C

_{r}passive reservations must be made, through a fixed circular cluster of C

_{r}= 6, 18 or 36 cells with a radius of C

_{e}cells (including the active one). This introduces huge resource wastages, due to the enormous amount of passive pre-reserved bandwidth over C

_{r}cells, which increases for longer calls or for higher values of v

_{max}, for fixed values of CHT and v

_{max}, respectively.

_{r}(near or equal to C

_{e}). This last opportunity is provided by our proposal, and the obtained values of C

_{r}depend on the adopted reservation thresholds and policies. A generic cell can be well approached by an n-edge regular polygon as depicted in Figure 4 (n can be considered as an input control parameter and it is commonly equal to 6).

_{ho}(hand-off directions set) of n possible movement directions (i.e., hand-off directions) can be obtained: S

_{ho}= {d

_{1}... d

_{n}}, with d

_{j}= θ(2j − 1)/2 rad., θ = 2π/n rad., j = 1 … n and |S

_{ho}| = n.

_{ho}after CST amount of time (Gaussian distributed), having handed-in the cell from direction x $\in $ S

_{ho}can be defined as:

_{0}is the time at which the user hands-in the considered cell. Once n and S

_{ho}have been defined, a square nxn HDP matrix M is defined as: M(x,y) = p

_{x}

_{,y}= p

_{CNSIS-MIP}(x,y). To be noticed that CST ~ N (µ

_{CST}, σ

^{2}

_{CST}). The composition of M depends on the adopted mobility model and coverage topology. It has the hand-in and hand-out directions on the rows and columns, respectively; its elements can be obtained through the preliminary campaign of simulations, while acquiring the CST distribution. As for the CST analysis, the Kolmogorov-Smirnov (KS) normality test was carried out on the n

^{2}elements of M. This test is based on the p-value concept: it is a measure of how much evidence there is against the null hypothesis; different p-values were obtained, showing the goodness of the Gaussian distribution hypothesis (for details, to see [50]). Therefore, from different simulation runs, it resulted that the elements of M follow also a Gaussian distribution, and they can be represented by a mean and a standard deviation µ

_{p}

_{(x,y)}and σ

_{p}

_{(x,y)}. In this sense, M(x,y) is a couple of values. An example of M is shown in Figure 5.

#### 6.1. Static Scheme

_{ei}≥ 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, …, n} $\forall $ j.

- (1)
- Non-decreasing: each user i will reserve on an increasing number of cells for the increasing number of hand-over (i.e., C
_{i}_{1}≤ C_{i}_{2}≤ … ≤ C_{iCei}_{−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
_{i}_{1}≥ C_{i}_{2}≥ … ≥ C_{iCei}_{−1}); - (3)
- Constant-trend: each user i will reserve on the same number of cells for every hand-over (C
_{i}_{1}= C_{i}_{2}= … = C_{iCei}_{−1}).

_{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 $y=index\left\{max\left[M\left(x\right)\right]\right\}$, 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

_{i}

_{1}, ..., 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}≥ 2. The algorithm starts the prediction from the active cell, where the call originated.

_{k}until the first hand-out event, the identifier of the most C

_{i1}probable cells that user i will visit following direction d

_{ik}from the current position can be discovered and inserted into the prediction set Pcells. From j = 2 to j = C

_{ei}

_{−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)\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

_{ei}

_{−1})∙n

^{2}). Table 1 shows C

_{r}values are obtained through (12) (they belong to the circular reservation policy as depicted in Figure 4), while C

_{r}(P) values are obtained following the approach previously proposed, for different reservation policies P (non-decreasing, non-increasing or constant). However, it can be seen that there is a resource gain if a directional treatment is introduced. For instance and without loss of generality, C

_{ho-max}has been fixed to 3 (under the assumption that the generic call i is long enough in order to suffer at least 3 hand-over events). The notation P(C

_{1}-C

_{2}-C

_{3}) indicates that the reservation policy P makes passive reservations on C

_{1}, C

_{2}and C

_{3}cells for 1-st, 2-nd and 3-rd hand-off, respectively, that is to say the input vector C is [C

_{1},C

_{2},C

_{3}], as previously illustrated (i is not used for the sake of simplicity).

#### 6.2. Dynamic Scheme

_{ei}is evaluated with the approach of [31]. Let h

_{i}= C

_{ei}− 1 be the number of hand-over events of user i. Let v

_{h}

_{i}be an array, whose elements v

_{hi}[k] (k = 1 … h

_{i}) indicate the information about the k-th future hand-off of user i. Each entry v

_{hi}[k] can be a pointer to, for example, a list of tuples {cell_id, from, to, p

_{cell_id}} for the k-th hand-off event, with:

- (a)
- cell_id is a cell identifier;
- (b)
- from, to $\in $ S
_{ho}are the hand-in and hand-out directions for the cell_id; - (c)
- p
_{cell_id}is the probability that user will be covered by cell_id after the k-th hand-off.

_{cell_id}values. Let δ be an input threshold: if the knowledge of the first hand-off cell is approached, then the threshold-based predictor illustrated in Figure 6 can be activated, for obtaining the complete set of cells that will be visited by the NSIS-MIP i-th user.

_{j}$\in $ S

_{ho}for user i is discovered and the term first_id = first_Cell_id(current_id, d

_{j}) can be obtained, by the function first_Cell_id, which evaluates the identifier of the cell that user i will visit. Th e error introduced by this approach is negligible (around 3–4%). At this point, a tuple {first_id, _, d

_{j}, 1} can be created and appended in v

_{hi}[1] (the ‘from ‘direction cannot be discovered because user i has started its flow in the current first_id cell and p

_{first_id}= 1, because the probability of handing-out from first_id cell during the first hand-off is 1).

_{hi}[k] contains the hand-in direction, the cell identifier and the probability of user i of being in the cell after the (k−1)-th hand-off. Now, a threshold-based comparison is used to decide what are the cells that user i will visit with higher probability, when handing-out the cell of the l-th tuple of v

_{hi}[k], l = 1 … v

_{hi}[k]. size(), with a well-known hand-in direction. The hand-in direction curr_hand_in_dir belongs to S

_{ho}and it specifies a unique row of M.

_{curr}. If the obtained value is higher than δ

^{f(k)}, then the cell that is adjacent to the current one on direction p must be considered as a possible future cell and a tuple {adjacent_p_cell, from, p, curr_prob} is appended in v

_{hi}[k + 1].

_{i}

_{−1}times, a cleaning routine must be executed after finishing appending elements in v

_{hi}[k] position, because of possible duplications of cell identifiers.

_{ei}−1)∙n

^{2}). The prediction result is the set of cell identifiers of the tuples for each v

_{hi}list. Remembering that the hypothesis of M composed of constant values is not suitable, because of M(x,y) consists of a couple of values, we have M(x,y) = N(µ

_{x,y},σ

_{x,y}).

^{−1}, with α > 0, in order to appreciate the different behavior of the algorithm by varying the δ

^{f}

^{(k)}structure and how δ is weighted for consecutive values of k.

## 7. Performance Evaluation

#### 7.1. General Simulation Setup and Parameters

^{2}area (Figure 7), and users move according to C4R and CityMob; the APs are wired connected, by a switching subnet, to the net-sender. The performances of the rate adaptation and CAC schemes for NSIS-MIP and NSIS-MDP users are also taken into account, in order to evaluate their conformance to QoS parameters (outage probability, minimum received utility values and a high system utilization). All the results have been obtained by following the theory of the confidence intervals as illustrated in [50,53]: the number of runs has been set to N

_{sim}= 15, with a simulation time of T

_{sim}= 400 s. In this way the committed error while considering simulation results has been limited to a maximum value of 5% (confidence of 95%). An exponentially distributed CHT with mean λ = 180 s was considered. Traffic load was fixed to 15 requests/s because it guarantees a good level of system saturation. When a session starts, packets are generated as in [54], based on Poisson and Pareto distributions using a file size distribution heavy-tailed with Pareto parameter fixed to 1.85. Each AP has a total bandwidth of 11 Mbps and users can receive discrete resource levels, from 512 Kbps up to 896 Kpbs (with a gap level of 128 Kbps). The considered utility functions are the same of those illustrated in Section 5. It must be outlined that the current AP dynamically choses the right value of B. In our simulations, traffic load is composed of NSIS-MIP and NSIS-MDP flows in variable percentage. The bandwidth is managed by the policies illustrated in Section 5 and the p

_{outage}value is set to 0.05.

_{sim}= 400 s, in order to obtain a smoother distribution curve. So, after a statistical analysis of the obtained values with MATLAB tool, the matrix M has been generated such as shown in Figure 5. The static algorithm was tested with the following input parameters:

- (1)
- constant trend: C
_{i}_{1}= C_{i}_{2}= C_{i}_{3}= 1; - (2)
- increasing trend: C
_{i}_{1}= 1, C_{i}_{2}= 2, C_{i}_{3}= 3; - (3)
- decreasing trend: C
_{i}_{1}= 3, C_{i}_{2}= 2, C_{i}_{3}= 1 with C_{ij}= 1 $\forall $j $\in $ {4…C_{ei}_{−1}};

_{ij}are different from those of Section 6 because attention was focused only on the first, the second and the third hand-off events.

^{αk}are considered, because the employing of the αk exponent into the dynamic algorithm leads to better results. After a deep analysis of the possible values of α the value α = 1 was chosen, because it guarantees the optimal performances for the chosen exponent function. As for the monitor simulations, the duration was fixed to T

_{sim}= 400 s for each run. Different campaigns were carried out, also varying the amount of NSIS-MIP and NSIS-MDP traffic percentages; in the following, if 60% is the NSIS-MIP percentage then, obviously, 40% is the percentage of NSIS-MDP traffic.

#### 7.2. Main Reachable Results

_{NSIS-MIP}(ho) is the overall number of NSIS-MIP users who have made at least ho hand-overs from the first cell and n

_{NSIS-MIP}(ho) is the overall number of NSIS-MIP users who did not find a passive reservation after the ho-th hand-off event, then the prediction error on ho-th hand-off event is e(ho) = n

_{NSIS-MIP}(ho)/N

_{NSIS-MIP}(ho). In addition, for a fixed prediction scheme with a fixed set of input parameters the trend is almost constant if the NSIS-MIP traffic percentage is varied; obviously, the prediction algorithm is not affected by the number of admitted flows. Some input combinations must be excluded, because they do not lead to any acceptable result. The best results were obtained for the dynamic case with δ = 0.5 and they are not comparable with those obtained with any other input values of the dynamic scheme or with the static one, which has good performances for the input sequence C

_{i}

_{1}= 1, C

_{i}

_{2}= 2, C

_{i}

_{3}= 3. The minimum and maximum error for δ = 0.5 are 10% and 12.57%.

_{outage}= 0.05. The implemented CAC and bandwidth allocation algorithm ensure the threshold constraint to be respected: in fact, the maximum observed value of outage percentage for NSIS-MDP users is 0.0502%. In particular, as discussed earlier, NSIS-MIP users are privileged when compared to NSIS-MDP ones, because of the guaranteed service continuity and the passive reservation policy.

_{i}

_{1}= 1, C

_{i}

_{2}= 2, C

_{i}

_{3}= 3; this can be explained by considering the increasing in prediction error for higher hand-off events due to the intrinsic error that was committed in the generic previous step. Pre-reserving resources on a higher number of cells for the next hand-off event can balance previous prediction errors. The dynamic scheme offers slightly lower performances in terms of amount of assigned bandwidth and perceived utility, but it outperforms the static one in terms of prediction error. For the first hand-off only the static sequence C

_{i}

_{1}= 3, C

_{i}

_{2}= 2, C

_{i}

_{3}= 1 leads to a negligible value of e(1), because reserving on C

_{i}

_{1}= 3 cells reduces the probability of error near to zero. However, the dynamic threshold-based algorithm performs better in the “long-range” prediction: the maximum value of e(3) is 12.57% for δ = 0.5.

#### 7.3. Performance Comparison

_{i}

_{1}= 1, C

_{i}

_{2}= 2, C

_{i}

_{3}= 3 and δ = 0.5, respectively). We provided to consider the same topology of the previous simulations.

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ALeZi | Active Lempel-Ziv |

AP | Access Point |

BE | Best Effort |

BER | Bit Error Rate |

BRS | Bandwidth Reallocation Scheme |

BS | Base Station |

C4R | Citymob4Roadmaps |

CAC | Call Admission Control |

CAT | Call Arrival Time |

CDP | Call Dropping Probability |

CHT | Call Holding Time |

CST | Cell Stay Time |

DH | Historical Path Database |

DRSVP | Dynamic resource ReServation Protocol |

FSMC | Finite State Markov Chain |

GIS | Geographic Information System |

HDP | Hand-off Directions Probabilities |

HMM | Hidden Markov Models |

ISPN | Integrated Services Packet Network |

KS | Kolmogorov Smirnov |

MDP | Mobility Dependent Predictive |

MIG | Mobility Independent Guaranteed |

MIP | Mobility Independent Predictive |

MRSVP | Mobile resource ReSerVation Protocol |

NSIS | Next Steps in Signaling |

NSLP | NSIS Signaling Layer Protocol |

NTLP | NSIS Transport Layer Protocol |

ODbL | Open Database License |

OSMF | Open StreetMap Foundation |

PD | Path Database |

PoI | Point of Interest |

PPM | Prediction Partial Matching |

QoS | Quality of Service |

RMM | Random Way Point Mobility Model |

RSVP | ReSerVation Protocol |

RTV | Real Time Video |

SS | Switching Subnet |

TRM | Trace Record Matrix |

UMP | User Mobile Profile |

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**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 μ(4,2) = 0.2798 and σ(4,2) = 0.0464.

Mobility Parameters | P(1-1-1) | P(1-2-3) | P(3-3-3) | |||
---|---|---|---|---|---|---|

Cr(P) | Cr | Cr(P) | Cr | Cr(P) | Cr | |

a_{max} = 1.4 m/s^{2}, a_{min} = −2 m/s^{2}, τ = 0.3 | ||||||

µ = 29.26 s, σ = 0.45729 s | 5 | 60 | 22 | 60 | 52 | 60 |

a_{max} = 1 m/s^{2}, a_{min} = −2.5 m/s^{2}, τ = 0.4 | ||||||

µ = 62.22 s, σ = 5.09547 s | 2 | 6 | 3 | 6 | 4 | 6 |

a_{max} = 1.3 m/s^{2}, a_{min} = −2 m/s^{2}, τ = 0.2 | ||||||

µ = 32.46 s, σ = 8.18356 s | 4 | 36 | 16 | 36 | 21 | 36 |

STATIC | DYNAMIC | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

NSIS-MIP | 111 | 123 | 321 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |

0 | 0.01213 | 0.01275 | 0.01542 | 0.01547 | 0.01551 | 0.01558 | 0.01571 | 0.01583 | 0.0163 | 0.018 |

0.2 | 0.01433 | 0.01455 | 0.01143 | 0.01278 | 0.01358 | 0.01945 | 0.01466 | 0.01448 | 0.01479 | 0.01483 |

0.4 | 0.01913 | 0.01874 | 0.01893 | 0.01932 | 0.01945 | 0.02013 | 0.01957 | 0.01961 | 0.01968 | 0.01973 |

0.6 | 0.0214 | 0.01973 | 0.01995 | 0.0214 | 0.01903 | 0.02988 | 0.02531 | 0.0174 | 0.02243 | 0.02673 |

0.8 | 0.0403 | 0.0413 | 0.042 | 0.0416 | 0.0435 | 0.0448 | 0.04532 | 0.04723 | 0.04831 | 0.04981 |

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Fazio, P.; Tropea, M.
Advanced Resources Reservation in Mobile Cellular Networks: Static vs. Dynamic Approaches under Vehicular Mobility Model. *Telecom* **2021**, *2*, 302-327.
https://doi.org/10.3390/telecom2040020

**AMA Style**

Fazio P, Tropea M.
Advanced Resources Reservation in Mobile Cellular Networks: Static vs. Dynamic Approaches under Vehicular Mobility Model. *Telecom*. 2021; 2(4):302-327.
https://doi.org/10.3390/telecom2040020

**Chicago/Turabian Style**

Fazio, Peppino, and Mauro Tropea.
2021. "Advanced Resources Reservation in Mobile Cellular Networks: Static vs. Dynamic Approaches under Vehicular Mobility Model" *Telecom* 2, no. 4: 302-327.
https://doi.org/10.3390/telecom2040020