Effective Stochastic Modeling of Energy-Constrained Wireless Sensor Networks

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">Power down </td><td align="center"><svg height="11.425" id="M115" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.025 11.425" width="11.025" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g>
</svg>Sim-Markov </td><td align="center"><svg height="11.425" id="M116" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.025 11.425" width="11.025" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g>
</svg>Sim-Petri net</td><td align="center"><svg height="11.425" id="M117" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 11.025 11.425" width="11.025" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path d="M600 0h-557v24l268 633l28 8l261 -641v-24zM497 50l-194 489l-196 -489h390z" id="x394"></path></g>
</svg>Markov-Petri net</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">Avg.</td><td align="center">7.37 </td><td align="center">7.37</td><td align="center">0.05</td></tr><tr><td align="left">Variance</td><td align="center">11.88</td><td align="center">12.18</td><td align="center">0.00</td></tr><tr><td align="left">STD DEV</td><td align="center">3.45</td><td align="center">3.49</td><td align="center">0.03</td></tr><tr><td align="left">RMSE</td><td align="center">8.07</td><td align="center">8.08</td><td align="center">0.06</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

ΔEnergy (Joules) estimates (<svg height="16.6625" id="M114" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 184.8875 16.6625" width="184.8875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><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(.017,-0,0,-.017,10.874,12.162)"><path d="M445 282q0 -64 -27.5 -125t-80.5 -104q-80 -65 -168 -65q-73 0 -109.5 46.5t-36.5 116.5q0 92 46.5 163t119.5 104q66 30 108 30q67 0 107.5 -43.5t40.5 -122.5zM355 280q0 62 -26.5 94.5t-64.5 32.5q-26 0 -44 -8q-39 -18 -74 -82t-35 -163q0 -57 25.5 -90.5t70.5 -33.5
q22 0 36 6q46 20 79 89t33 155z" id="x1D45C"></path></g><g transform="matrix(.017,-0,0,-.017,18.829,12.162)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path></g><g transform="matrix(.017,-0,0,-.017,30.932,12.162)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g><g transform="matrix(.017,-0,0,-.017,37.97,12.162)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26
q13 -21 0 -43z" id="x1D45F"></path></g><g transform="matrix(.017,-0,0,-.017,45.143,12.162)"><path d="M500 -125h-500v50h500v-50z" id="x5F"></path></g><g transform="matrix(.017,-0,0,-.017,53.643,12.162)"><path d="M751 650l-6 -28q-53 -1 -69 -12.5t-24 -38.5q-23 -85 -43 -192l-13 -69q-34 -181 -130 -262q-79 -65 -185 -65t-171 57q-87 77 -54 258l42 232q12 58 0.5 73t-75.5 19l8 28h263l-6 -28q-63 -5 -78 -18t-26 -74l-41 -226q-25 -135 22 -201t139 -66q99 0 161.5 68t91.5 217
l11 57q28 149 28 193q0 28 -19 38t-79 12l6 28h247z" id="x1D448"></path></g><g transform="matrix(.017,-0,0,-.017,66.613,12.162)"><path d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36
t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" id="x1D45D"></path></g><g transform="matrix(.017,-0,0,-.017,76.693,12.162)"><path d="M500 -125h-500v50h500v-50z" id="x5F"></path></g><g transform="matrix(.017,-0,0,-.017,85.192,12.162)"><path d="M780 372q0 -191 -178 -297q-128 -75 -335 -75h-250l7 27q61 7 77 22t28 76l77 398q11 62 0 76.5t-77 22.5l6 28h292q164 0 258.5 -67.5t94.5 -210.5zM678 375q0 119 -73 180.5t-201 61.5q-62 0 -82 -13q-17 -7 -25 -53l-80 -427q-8 -47 -4 -62t26 -20q24 -6 80 -6
q166 0 262.5 95t96.5 244z" id="x1D437"></path></g><g transform="matrix(.017,-0,0,-.017,98.842,12.162)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g><g transform="matrix(.017,-0,0,-.017,105.88,12.162)"><path d="M238 681l-124 -585q-7 -31 4 -31q10 0 37.5 18.5t49.5 41.5l16 -22q-40 -48 -89.5 -81.5t-76.5 -33.5q-42 0 -16 122l105 488q7 32 0 41t-39 9h-35l5 26q35 3 71 13t58 17.5t26 7.5q14 0 8 -31z" id="x1D459"></path></g><g transform="matrix(.017,-0,0,-.017,110.452,12.162)"><path d="M483 97q-42 -50 -88.5 -79.5t-68.5 -29.5q-37 0 -17 93l22 102h-2q-54 -79 -144 -149q-59 -46 -100 -46q-24 0 -43 29t-19 86q0 78 34.5 153t94.5 120q41 31 94 51.5t98 20.5q29 0 72 -9q26 -6 39 -6l2 -4q-30 -117 -67 -323q-8 -41 2 -41q16 0 79 58zM374 387
q-32 15 -73 15q-52 0 -83 -23q-48 -36 -78 -108.5t-30 -152.5q0 -33 8.5 -50.5t20.5 -17.5q31 0 107 79t99 132q15 40 29 126z" id="x1D44E"></path></g><g transform="matrix(.017,-0,0,-.017,119.054,12.162)"><path d="M556 393q0 -39 -36 -106q-42 -78 -185 -279q-47 -66 -81 -108t-117 -135l-112 -26l-8 22q150 90 251 219q-6 136 -39 340q-8 53 -21 53q-6 0 -27 -19.5t-38 -42.5l-16 26q80 111 127 111q23 0 35 -28t20 -90q18 -137 27 -263h2q142 200 142 279q0 24 -14 48q-4 7 5 26
q13 28 43 28q18 0 30 -15.5t12 -39.5z" id="x1D466"></path></g><g transform="matrix(.017,-0,0,-.017,133.605,12.162)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,148.309,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,156.468,12.162)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,160.344,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,168.503,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,176.663,12.162)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg> second).

Journal of Computer Networks and Communications

tab4

Table 4

Table 4: Effective Stochastic Modeling of Energy-Constrained Wireless Sensor Networks 