An Efficient Biobjective Heuristic for Scheduling Workflows on Heterogeneous DVS-Enabled Processors

<table class="table-group" id="tab4"><tr><td><table class="table"><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr class="thead"><td align="left"><span style="width: 12.525px;"><svg height="11.9625" id="M164" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 12.525 11.9625" width="12.525" 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="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" id="x1D45B"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.6,11.762)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
q16 0 76 48z" id="x1D456"></path></g>
</svg></span></td><td align="center">0</td><td align="center">1</td><td align="center">2</td><td align="center">3</td><td align="center">4</td><td align="center">5</td><td align="center">6</td><td align="center">7</td></tr><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr><td align="left"><i>b-level </i></td><td align="center">178.50</td><td align="center">138.87</td><td align="center">127.63</td><td align="center">125.67</td><td align="center">128.00</td><td align="center">87.30</td><td align="center">76.57</td><td align="center">34.67</td></tr><tr class="table-tr"><td colspan="9"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Task priorities of <svg height="11.75" id="M163" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 12.4375 11.75" width="12.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242
q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" id="x1D43A"></path></g>
</svg>.

Journal of Applied Mathematics

tab4

Table 4

Table 4: An Efficient Biobjective Heuristic for Scheduling Workflows on Heterogeneous DVS-Enabled Processors 