Efficient Deployment of MultiUAVs in Massively Crowded Events^{ †}
Abstract
:1. Introduction
1.1. Related Works
1.2. Paper Contributions
 The existing ATG path loss model [9] and outdoor to indoor path loss model [21] are used to study the problem of a single UAV placement to provide coverage in crowded events for both outdoor and indoor receivers simultaneously, with the objective to minimize the required UAV transmit power. Due to the intractability of the formulated problem, two algorithms are developed to find an efficient 3D UAV placement using two optimization techniques, namely the PSO and KTS algorithms. The proposed algorithms consider the problem in providing wireless coverage for indoor and outdoor users, in a small area using a single UAV.
 The efficient 3D placements of multiple UAVs that provide maximum wireless coverage and minimize the transmission power are found for each UAV.
 The CPT is utilized to find the number of UAVs needed for providing wireless coverage for outdoor users in a large coverage area having three different shapes of coverage area, namely square, rectangle and circular. The problem is formulated with the objective to maximize the wireless coverage area using multiple UAVs. In each subarea, the UAV altitude is optimized using the algorithm to provide wireless coverage using a single UAV above.
2. Providing Wireless Coverage Using a Single UAV
2.1. System Model
2.1.1. ATG Path Loss Model
2.1.2. OutdoortoIndoor Path Loss Model
2.2. Problem Formulation
2.3. Efficient UAV 3D Placement Algorithms
2.3.1. Particle Swarm Optimization Algorithm (PSO)
2.3.2. KMeans with Ternary Search Algorithms
 Initially, random guesses for cluster centroids are made, as shown in Step 3 of Algorithm 2.
 The nearest centroid is determined for each data point, by calculating the Euclidean distance between each point and the centroid of the cluster, as shown in Step 5 of Algorithm 2.
 In each cluster, the centroid is replaced by a new value. This new value is the means of the points belonging to the cluster, as in Step 6 of Algorithm 2.
 Repeat the process in Items 2 and 3 above, until the solution converges. The convergence happens when the centroids and their locations are no longer changed; more specifically, when the cluster mean is not changed as in Steps 4 to 6 of Algorithm 2.
Algorithm 1 Particle swarm optimization algorithm. 

Algorithm 2 Kmeans with ternary search algorithm. 

3. Providing Wireless Coverage Using Multiple UAVs Equipped with Directional Antennas
3.1. Case of a Square Region
3.1.1. Problem Formulation
 $P1$ : Place n identical nonoverlapping circles in a unit square, with the objective function to maximize the radius of the circles r, such that the coverage area and coverage density are maximized.
3.2. Case of a Rectangle Region
3.2.1. Problem Formulation
 $P2$: Place n identical nonoverlapping circles in a rectangle region $L\times W$, with the Cartesian origin $(0,0)$ as the rectangle center. The objective function is to maximize the radius of the circles r such that the coverage area and density are maximized.
3.2.2. Algorithms for Packing Circles in a Rectangle Region
Algorithm 3 CPAMinOSA algorithm. 

Algorithm 4 Formulation space search pseudocode. 

3.3. Case of a Circular Region
3.3.1. Problem Formulation
 $P3$: Place n identical nonoverlapping circles into a unit circle with radius of $r=1$. The objective function is to maximize the radius of the packed circles, such that the coverage area and density are maximized.
3.3.2. Algorithms for Packing Circles into a Circular Region
4. Simulation Results and Analysis
4.1. Providing Wireless Coverage Using a Single UAV
4.2. Providing Wireless Coverage Using Multiple UAVs
4.2.1. Case of a Square Region
4.2.2. Case of a Rectangle Region
4.2.3. Case of a Circular Region
4.3. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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n  ${\mathit{r}}_{\mathit{n}}$  ${\mathit{d}}_{\mathit{n}}$  Ref.  n  ${\mathit{r}}_{\mathit{n}}$  ${\mathit{d}}_{\mathit{n}}$  Ref. 

2  0.292893  0.539  [32]  13  0.133994  0.733  [27] 
3  0.254333  0.6096  [32]  14  0.128556  0.727  [27] 
4  0.250000  0.785  [32]  15  0.126478  0.754  [27] 
5  0.207107  0.674  [32]  16  0.125000  0.785  [27] 
6  0.187681  0.664  [32]  17  0.117186  0.733  [27] 
7  0.174458  0.669  [33]  18  0.115522  0.755  [27] 
8  0.170541  0.731  [33]  19  0.112265  0.752  [27] 
9  0.166666  0.785  [34]  20  0.111382  0.779  [27] 
10  0.148204  0.690  [27]  21  0.106839  0.753  [27] 
11  0.142399  0.701  [27]  22  0.105665  0.772  [27] 
12  0.139959  0.738  [27] 
Parameter  Value  Parameter  Value 

Carrier frequency $({f}_{c})$  2 GHz  (Vmin, Vmax, Vsize)  (0, 1000, 3) 
Noise power $(Np)$  −120 dBm  Population size ($N\_pop$)  50 
Total available  50 MHz  Max number of iterations  50 
bandwidth  ($N\_it$)  
UAV transmit power  ${P}_{t}$ = 5 watt  ($\kappa $, ${\varphi}_{1}$, ${\varphi}_{2}$)  (1, 2.05, 2.05) 
Data rate $(r)$  0.5 Mbps  Tolerance ($\u03f5$)  0.1 
Environment Parameter  Value  Environment Parameter  Value 
a  9.6  ${\eta}_{LSO}$  1 
b  0.28  ${\eta}_{NLSO}$  20 
Algorithm  (Outdoor) Subarea Dimensions  (Indoor) Building Dimensions  Number of Outdoor Users  Number of Active Indoor Users  Efficient UAV Placement (${\mathit{x}}_{\mathit{UAV}}$, ${\mathit{y}}_{\mathit{UAV}}$, ${\mathit{z}}_{\mathit{UAV}}$)  UAV Transmit Power (watt)  Enhanced PSO than KTS 

PSO  300 m × 150 m  $(35,30,60)$  2750  One Building, 12 floors → 600  (117.49, 58.78, 60.89)  0.42  5.7× 
KTS  (129.53, 60.26, 49.1)  2.39  
PSO  300 m × 150 m  $(35,30,60)$  2750  One Building, 12 floors → 750  (151.95, 58.3, 61.5)  0.86  5.4× 
KTS  (158, 60.76, 46.5)  4.639  
PSO  300 m × 150 m  $(35,30,60)$  2750  Two Buildings, 12 floors →960  (161.66, 62.79, 62.12)  3.255  5.1× 
KTS  (162.64, 63.23, 41.11)  16.594 
n  Circle Radius r  Number of Active Receivers 35%  Optimal 3D UAV Placement  UAV Transmit (Power) watt  Density  Antenna Half Beamwidth θ/2 

8  341.1 m  5076  (${x}_{i}$, ${y}_{i}$, 213)  5095 Very High  0.731  58.01 
9  333.3 m  4925  (${x}_{i}$, ${y}_{i}$, 208)  2068 Very High  0.785  58.03 
10  296.4 m  3819  (${x}_{i}$, ${y}_{i}$, 185)  16.5  0.690  58.03 
11  284.8 m  3565  (${x}_{i}$, ${y}_{i}$, 178)  3.39  0.701  58.0 
12  279.9 m  3445  (${x}_{i}$, ${y}_{i}$, 175)  1.61  0.738  57.9 
13  267.9 m  3200  (${x}_{i}$, ${y}_{i}$, 167)  0.373  0.733  58.06 
14  257.1 m  2973  (${x}_{i}$, ${y}_{i}$, 160)  0.091  0.727  58.1 
15  252.9 m  2860  (${x}_{i}$, ${y}_{i}$, 158)  0.043  0.754  58.0 
16  250.0 m  2745  (${x}_{i}$, ${y}_{i}$, 156)  0.020  0.785  58.03 
17  234.4 m  2422  (${x}_{i}$, ${y}_{i}$, 147)  2.60 $\times {10}^{3}$  0.733  57.91 
18  231.0 m  2328  (${x}_{i}$, ${y}_{i}$, 144)  1.40 $\times {10}^{3}$  0.755  58.06 
19  224.5 m  2226  (${x}_{i}$, ${y}_{i}$, 140)  7.34 $\times {10}^{4}$  0.752  58.05 
20  222.8 m  2136  (${x}_{i}$, ${y}_{i}$, 139)  3.87 $\times {10}^{4}$  0.779  58.04 
21  213.7 m  2025  (${x}_{i}$, ${y}_{i}$, 133)  2.03 $\times {10}^{4}$  0.753  58.10 
22  211.3 m  1953  (${x}_{i}$, ${y}_{i}$, 132)  1.24 $\times {10}^{4}$  0.772  58.0 
n  Circle Radius r  Number of Active Receivers 35%  Optimal 3D UAV Placement  UAV Transmit (Power) watt  Density  Antenna Half Beamwidth θ/2 

10  493 m  7634  (${x}_{i}$, ${y}_{i}$, 307)  Very High  0.707  58.089 
15  402 m  5020  (${x}_{i}$, ${y}_{i}$, 251)  Very High  0.709  58.02 
18  368 m  4181  (${x}_{i}$, ${y}_{i}$, 229)  53.9 High  0.708  58.107 
19  357 m  3953  (${x}_{i}$, ${y}_{i}$, 223)  11.95  0.706  58.009 
20  351 m  3843  (${x}_{i}$, ${y}_{i}$, 219)  6.088  0.719  58.039 
21  345 m  3736  (${x}_{i}$, ${y}_{i}$, 215)  3.306  0.729  58.069 
22  341 m  3626  (${x}_{i}$, ${y}_{i}$, 213)  1.59  0.744  58.010 
23  339 m  3559  (${x}_{i}$, ${y}_{i}$, 211)  1.013  0.768  58.101 
24  334 m  3518  (${x}_{i}$, ${y}_{i}$, 208)  0.847  0.779  58.087 
25  331 m  3418  (${x}_{i}$, ${y}_{i}$, 206)  0.435  0.796  58.104 
26  330 m  3384  (${x}_{i}$, ${y}_{i}$, 20 6)  0.246  0.825  58.026 
27  319 m  3213  (${x}_{i}$, ${y}_{i}$, 199)  0.125  0.798  58.043 
28  308 m  3006  (${x}_{i}$, ${y}_{i}$, 192)  0.036  0.771  58.062 
29  303 m  2890  (${x}_{i}$, ${y}_{i}$, 189)  0.018  0.777  58.046 
30  300 m  2821  (${x}_{i}$, ${y}_{i}$, 187)  0.011  0.785  58.063 
31  289 m  2636  (${x}_{i}$, ${y}_{i}$, 180)  0.0037  0.755  58.084 
32  285 m  2543  (${x}_{i}$, ${y}_{i}$, 178)  0.0020  0.756  58.013 
33  279 m  2459  (${x}_{i}$, ${y}_{i}$, 174)  0.0012  0.748  58.050 
n  Radius (r) (Unit Circle)  Circle Radius (r) (R = 1125 m)  Number of Active Receivers 35%  Optimal 3D UAV Placement  UAV Transmit (Power) watt  Density  Antenna Half Beamwidth θ/2 

8  $0.30259339$  340  5077  (${x}_{i}$, ${z}_{i}$, 212)  53,564 Very High  $0.7325020$  $58.06$ 
9  0.27676865  311  4252  (${x}_{i}$, ${y}_{i}$, 194)  267.1 Very high  0.68940799  $58.04$ 
10  0.26225892  295  3820  (${x}_{i}$, ${y}_{i}$, 184)  17.43  0.68779743  $58.05$ 
11  0.2548547  287  3600  (${x}_{i}$, ${y}_{i}$, 179)  4.29  0.71446011  $58.05$ 
12  0.24816347  279  3445  (${x}_{i}$, ${y}_{i}$, 174)  1.63  0.7390213  $58.05$ 
13  0.23606798  266  3082  (${x}_{i}$, ${y}_{i}$, 166)  0.166  0.72446517  $58.03$ 
14  0.23103073  260  2973  (${x}_{i}$, ${y}_{i}$, 162)  0.0874  0.74725276  $58.07$ 
15  0.22117254  249  2746  (${x}_{i}$, ${y}_{i}$, 155)  0.0199  0.73375938  $58.10$ 
16  0.21666474  244  2634  (${x}_{i}$, ${y}_{i}$, 152)  9.80 $\times {10}^{3}$  0.75109777  $58.08$ 
17  0.20867967  235  2422  (${x}_{i}$, ${y}_{i}$, 147)  2.40 $\times {10}^{3}$  0.74030245  $57.97$ 
18  0.20560465  231  2318  (${x}_{i}$, ${y}_{i}$, 144)  1.30 $\times {10}^{4}$  0.76091887  $58.06$ 
19  0.20560465  231  2318  (${x}_{i}$, ${y}_{i}$, 144)  1.30 $\times {10}^{4}$  0.80319214  $58.06$ 
20  0.19522401  220  2127  (${x}_{i}$, ${y}_{i}$, 137)  3.76 $\times {10}^{4}$  0.76224829  $58.09$ 
21  0.19039215  214  2026  (${x}_{i}$, ${y}_{i}$, 133)  2.01 $\times {10}^{4}$  0.76123256  $58.14$ 
22  0.18383303  207  1851  (${x}_{i}$, ${y}_{i}$, 129)  6.29 $\times {10}^{5}$  0.7434808  $58.07$ 
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Sawalmeh, A.; Othman, N.S.; Shakhatreh, H. Efficient Deployment of MultiUAVs in Massively Crowded Events. Sensors 2018, 18, 3640. https://doi.org/10.3390/s18113640
Sawalmeh A, Othman NS, Shakhatreh H. Efficient Deployment of MultiUAVs in Massively Crowded Events. Sensors. 2018; 18(11):3640. https://doi.org/10.3390/s18113640
Chicago/Turabian StyleSawalmeh, Ahmad, Noor Shamsiah Othman, and Hazim Shakhatreh. 2018. "Efficient Deployment of MultiUAVs in Massively Crowded Events" Sensors 18, no. 11: 3640. https://doi.org/10.3390/s18113640