Wireless Network Design: Optimization Models and Solution ...

Recommendations

Info

10 Integer Programming Models for Power-optimal Trees in Wireless Networks 237 ∑ j:(t, j)∈A xt t j − ∑ j:( j,t)∈A xt jt = � ∑ j:(t, j)∈A qt t j − qs � + � t j − ∑ j:( j,t)∈A qt jt − qs � + jt = � −∑j:( j,t)∈A z jt − qs � + jt = −∑j:(t, j)∈A qs t j = −wt = −1. The equalities follow from applying the definition of xt , the facts that qt t j = 0 and qt jt = z jt, (10.20), (10.18), and (10.19), respectively. Thus, xt ∈ F (G,bst). Furthermore, (10.23) implies (10.8) since xt ≤ qt . Utilizing (10.20) and (10.23), we get ∑ N−1 ℓ=k xt � πi(ℓ),i = ∑N−1 ℓ=k qt πi(ℓ),i − qs � + πi(ℓ),i = ∑ N−1 � ℓ=k −qt (iℓ) + qs � + (iℓ) ≤ ∑ N−1 ℓ=k qs (iℓ) ≤ ∑ N−1 ℓ=k y (iℓ), which implies (10.15). The proof is complete by observing that RAP-F2 and RAP-MT have identical objective functions. The inequality in Proposition 10.6 may be strict. Some instances where this occurs are reported in the next section. 10.6 Experimental Results In this section, we report some experimental results of solving MET and RAP using the models discussed in the previous sections. Networks of sizes 10, 20, 30, and 40 nodes are used in the experiments. They are obtained by following the instance generation procedure in [49] with α = 2 in the power formula (Section 10.2.1). For each network size N, two groups of instances with |D| = N/2 and |D| = N, respectively, are generated. There are hence eight network groups in total. The number of instances in each group is 20. For MET, a node in D is randomly chosen as the source s. We have applied CPLEX [32] (version 10.1) to all the models. Throughout the experiments, the CPLEX network optimizer is switched on, and all other solver parameters follow their default values. All experiments have been conducted on a server with an Opteron processor at 2.4 GHz and 7 GB RAM. For all models, we set a time limit of one hour for solving the LP relaxation, and one additional hour for approaching integer optimum. For making comparisons among the models, solution time will be used as one of the performance indicators. However, the aim of the experiments is not to declare the best model for MET or RAP in terms of solution time. For each of the models, the time can be indeed improved by, for example, pre-processing, tweaking the solver parameters, or implementing methods other than using a standard solver. Instead of focusing on time only, the experiments are intended to also shed light on other aspects such as LP strength, size of the branch and bound (B&B) tree, and scalability.
238 Dag Haugland and Di Yuan Table 10.1 Results of solving the LP relaxations of the MET models. Network MET-Das MET-F1 MET-F2 N/|D| Max/min/ave. Max/min/ave. Max/min/ave. 10/5 Gap (%) 86.9/74.8/80.9 78.8/47.6/66.9 0.0/0.0/0.0 Time
Page 2:
International Series in Operations
Page 5 and 6:
Editors Jeff Kennington Eli Olinick
Page 7 and 8:
vi Preface assistance. The work of
Page 9 and 10:
viii Contents 3.4.1 Experiments to
Page 11 and 12:
x Contents 8.3.2 The Solution Proce
Page 13 and 14:
xii Contents References . . . . . .
Page 16 and 17:
List of Contributors Khaldoun Al Ag
Page 18:
List of Contributors xvii Nitin Sal
Page 22 and 23:
Chapter 1 Introduction to Optimizat
Page 24 and 25:
1 Introduction to Optimization in W
Page 26 and 27:
1 Introduction to Optimization in W
Page 29 and 30:
Part I Background
Page 31 and 32:
10 Dinesh Rajan The goal of this ch
Page 33 and 34:
12 Dinesh Rajan The source encoder
Page 35 and 36:
14 Dinesh Rajan ping (FH) CDMA, and
Page 37 and 38:
16 Dinesh Rajan of SNR is given in
Page 39 and 40:
18 Dinesh Rajan 2.3 Information The
Page 41 and 42:
20 Dinesh Rajan Perror ≤ e −nE
Page 43 and 44:
22 Dinesh Rajan For instance, for t
Page 45 and 46:
24 Dinesh Rajan 2.4.1 Block Codes I
Page 47 and 48:
26 Dinesh Rajan B(z) = 1 � (1 + z
Page 49 and 50:
28 Dinesh Rajan layers. Two of the
Page 51 and 52:
30 Dinesh Rajan nel can support a p
Page 53 and 54:
32 Dinesh Rajan 2.5.2 Physical laye
Page 55 and 56:
34 Dinesh Rajan matched filter for
Page 57 and 58:
36 Dinesh Rajan codes) leads to bet
Page 59 and 60:
38 Dinesh Rajan a length N Inverse
Page 61 and 62:
40 Dinesh Rajan the transmission of
Page 63 and 64:
42 Dinesh Rajan setting, a node may
Page 65 and 66:
44 Dinesh Rajan weighting of the si
Page 67 and 68:
46 Dinesh Rajan 29. Oestges, C., Cl
Page 69 and 70:
48 K. V. S. Hari terrain of operati
Page 71 and 72:
50 K. V. S. Hari fading is calculat
Page 73 and 74:
52 K. V. S. Hari terms have been pr
Page 75 and 76:
54 K. V. S. Hari Fig. 3.1 Normalize
Page 77 and 78:
56 K. V. S. Hari Table 3.3 Impulse
Page 79 and 80:
58 K. V. S. Hari where m antennas a
Page 81 and 82:
60 K. V. S. Hari 3.5.2.4 Dominant R
Page 83 and 84:
62 K. V. S. Hari March, 1984-13 Sep
Page 85 and 86:
64 K. V. S. Hari 47. Van Rees, J.:
Page 87 and 88:
66 J. Cole Smith and Sibel B. Sonuc
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 120:
Part II Optimization Problems for N
Page 123 and 124:
102 Eli Olinick carrying capacity.
Page 125 and 126:
104 Eli Olinick 93 85 160 16 38 21
Page 127 and 128:
106 Eli Olinick Amaldi et al. [7] p
Page 129 and 130:
108 Eli Olinick levels (possibly le
Page 131 and 132:
110 Eli Olinick gmℓ ∑ ∑ m∈M
Page 133 and 134:
112 Eli Olinick Using bk to denote
Page 135 and 136:
114 Eli Olinick 5.3.5 Additional De
Page 137 and 138:
116 Eli Olinick capacity, provide n
Page 139 and 140:
118 Eli Olinick ficult optimization
Page 141 and 142:
120 Eli Olinick and-bound so that t
Page 143 and 144:
122 Eli Olinick solution times. Cai
Page 145 and 146:
124 Eli Olinick 27. Glover, F.: Tab
Page 148 and 149:
Chapter 6 Optimization Based WLAN M
Page 150 and 151:
6 Optimization Based WLAN Modeling
Page 152 and 153:
Page 154 and 155:
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Chapter 7 Spectrum Auctions Karla H
Page 170 and 171:
7 Spectrum Auctions 149 full value.
Page 172 and 173:
7 Spectrum Auctions 151 also decide
Page 174 and 175:
7 Spectrum Auctions 153 disclosed t
Page 176 and 177:
7 Spectrum Auctions 155 focused on
Page 178 and 179:
7 Spectrum Auctions 157 bidders to
Page 180 and 181:
7 Spectrum Auctions 159 in the regi
Page 182 and 183:
7 Spectrum Auctions 161 we suggest
Page 184 and 185:
7 Spectrum Auctions 163 pays, since
Page 186 and 187:
7 Spectrum Auctions 165 prior round
Page 188 and 189:
7 Spectrum Auctions 167 and constra
Page 190 and 191:
7 Spectrum Auctions 169 lem has sup
Page 192 and 193:
7 Spectrum Auctions 171 bidder on a
Page 194 and 195:
7 Spectrum Auctions 173 some discus
Page 196 and 197:
7 Spectrum Auctions 175 21. Dunford
Page 198 and 199:
Chapter 8 The Design of Partially S
Page 200 and 201:
8 The Design of Partially Survivabl
Page 202 and 203:
Page 204 and 205:
Page 206 and 207:
Page 208 and 209: 8 The Design of Partially Survivabl
Page 219 and 220: Part III Optimization Problems in A
Page 221 and 222: 200 Khaldoun Al Agha and Steven Mar
Page 240 and 241: Chapter 10 Compact Integer Programm
Page 242 and 243: 10 Integer Programming Models for P
Page 268 and 269: Chapter 11 Improving Network Connec
Page 270 and 271: 11 Improving Network Connectivity i
Page 288: 11 Improving Network Connectivity i
Page 292 and 293: Chapter 12 Simulation-Based Methods
Page 294 and 295: 12 Simulation-Based Methods for Net
Page 308 and 309:
12 Simulation-Based Methods for Net
Page 310 and 311:
Page 312 and 313:
Page 314:
Page 317 and 318:
296 Hang Jin and Li Guo formance in
Page 319 and 320:
298 Hang Jin and Li Guo (ISI) as lo
Page 321 and 322:
300 Hang Jin and Li Guo ARQ (HARQ)
Page 323 and 324:
302 Hang Jin and Li Guo 13.3 Radio
Page 325 and 326:
304 Hang Jin and Li Guo Table 13.2
Page 327 and 328:
306 Hang Jin and Li Guo is transmit
Page 329 and 330:
308 Hang Jin and Li Guo uplink powe
Page 331 and 332:
310 Hang Jin and Li Guo The link ad
Page 333 and 334:
312 Hang Jin and Li Guo where ρ mi
Page 335 and 336:
314 Hang Jin and Li Guo 13.4.4.3 Ex
Page 337 and 338:
316 Hang Jin and Li Guo Fig. 13.9 P
Page 339 and 340:
318 Hang Jin and Li Guo 1. Guarante
Page 342 and 343:
Chapter 14 Cross Layer Scheduling i
Page 344 and 345:
14 Cross Layer Scheduling in Wirele
Page 346 and 347:
Page 348 and 349:
Page 350 and 351:
Page 352 and 353:
Page 354 and 355:
Page 356 and 357:
Page 358 and 359:
Page 360 and 361:
Page 362 and 363:
Page 364 and 365:
Page 366 and 367:
Page 368 and 369:
Page 370 and 371:
Page 372 and 373:
Page 374 and 375:
Chapter 15 Major Trends in Cellular
Page 376 and 377:
15 Major Trends in Cellular Network
Page 378 and 379:
Page 380 and 381:
Page 382 and 383:
Page 384 and 385:
Page 386 and 387:
Page 388 and 389:
Page 390 and 391:
Page 392 and 393:
Page 394:
show all

Wireless Network Design: Optimization Models and Solution ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?