On the Optimization of the IEEE 802.11 DCF: A Cross-Layer Perspective

<table>Markov chain for the contention model accounting for unsaturated traffic conditions. The model considers <svg height="7.9499998" id="M28" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 13.5375 7.9499998" width="13.5375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6
q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" id="x1D45A"></path></g>
</svg> backoff stages. <svg height="18.112499" id="M29" style="vertical-align:-5.56921pt" version="1.1" viewbox="0 0 22.75 18.112499" width="22.75" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5
t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" id="x1D443"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><path d="M380 106l15 -22q-42 -52 -87 -74t-76 -22q-89 0 -142 62t-53 151q0 103 66 175q67 73 146 73h1q61 0 105.5 -46.5t44.5 -105.5q0 -16 -4.5 -22.5t-18.5 -9.5q-54 -10 -262 -17q1 -95 46 -143.5t104 -48.5q61 0 115 50zM225 412q-35 0 -64.5 -32.5t-40.5 -90.5q83 0 170 3
q14 0 19 4.5t5 15.5q1 41 -23.5 70.5t-65.5 29.5z" id="x65"></path></g><g transform="matrix(.012,-0,0,-.012,15.98,15.187)"><path d="M515 -240h-241v27q59 4 72 17t13 66v160l-106 -42q-101 0 -158 64.5t-57 144.5q0 106 81 179.5t187 72.5q48 -5 69 -14q18 -5 27 -4q13 0 35 11l4 -3q-3 -63 -3 -107v-464q0 -52 12 -64t65 -17v-27zM359 60v306q-17 19 -44.5 30.5t-52.5 11.5q-55 0 -94.5 -47t-39.5 -131
q0 -85 48 -135.5t109 -50.5q40 0 74 16z" id="x71"></path></g>
</svg> is the probability of failed transmission, accounting for both collisions and channel errors affecting the transmitted packets.</table>

International Journal of Digital Multimedia Broadcasting

fig1

Figure 1

Figure 1: On the Optimization of the IEEE 802.11 DCF: A Cross-Layer Perspective 