Design and Modeling of Self-Adapting MAC (SaMAC) Protocol with Inconstant Contention Loss Probabilities

<div>Probability of (a) Markov chain states and (b) contention loss after an idle timeslot in network of 20 active stations and W = 32, <span class="nowrap"><svg height="11.5695pt" id="M235" style="vertical-align:-3.18152pt" version="1.1" viewbox="-0.0498162 -8.38798 55.9356 11.5695" width="55.9356pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M956 650H736V622C814 613 818 602 804 542C789 471 733 275 691 141H689C628 314 570 476 514 641H485C434 478 377 312 323 142H321C277 284 238 419 199 554C184 605 186 613 259 622V650H16V622C77 615 92 606 117 524C172 346 228 170 281 -11H312C363 151 419 312 475 488H477C528 343 597 150 652 -11H683C765 269 826 458 848 522C878 605 887 613 956 622V650Z" id="g121-85"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.623,3.132)"><path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.212,3.132)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path></g><g transform="matrix(.0091,0,0,-0.0091,22.715,3.132)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.013,0,0,-0.013,31.97,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,43.233,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g><g transform="matrix(.013,0,0,-0.013,49.473,0)"><path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z" id="g113-55"></path></g></svg>,</span> and k = 4.</div>

Wireless Communications and Mobile Computing

fig14

Figure 14

Figure 14: Design and Modeling of Self-Adapting MAC (SaMAC) Protocol with Inconstant Contention Loss Probabilities 