Mathematical Models of Multiserver Queuing System for Dynamic Performance Evaluation in Port

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="710834.fig.003a" src="https://static.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.003a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b><svg height="15.25" id="M207" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 18.9 15.25" width="18.9" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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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="M594 511q0 -122 -171 -157l1 -2q158 -33 158 -159q0 -52 -34.5 -95t-90.5 -65q-76 -33 -217 -33h-223l8 28q63 5 79.5 19t26.5 72l83 426q9 48 -2.5 60t-77.5 17l6 28h259q195 0 195 -139zM499 509q0 59 -37 83t-91 24q-36 0 -51 -9q-17 -9 -22 -44l-35 -195h62
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</svg> as a function of <svg height="10.3875" id="M208" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 5.9250002 10.3875" width="5.9250002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.125)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="710834.fig.003b" src="https://static.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.003b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="21.875" id="M209" style="vertical-align:-4.1277pt" version="1.1" viewbox="0 0 25.5 21.875" width="25.5" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,16.675)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,21.662)"><path d="M730 650l-8 -28q-52 -4 -72 -18t-64 -77q-79 -113 -321 -539h-33l-119 541q-13 59 -29.5 73t-66.5 20l7 28h245l-8 -28l-28 -5q-33 -6 -40.5 -15.5t-0.5 -38.5l102 -450h2q191 320 246 430q21 42 15.5 56t-43.5 19l-31 4l7 28h240z" id="x1D449"></path></g><g transform="matrix(.012,-0,0,-.012,10.875,8.513)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.012,-0,0,-.012,14.992,8.513)"><use xlink:href="#x31"></use></g><g transform="matrix(.012,-0,0,-.012,20.703,8.513)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg> and <svg height="21.875" id="M210" style="vertical-align:-4.1277pt" version="1.1" viewbox="0 0 25.5 21.875" width="25.5" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,16.675)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,21.662)"><use xlink:href="#x1D449"></use></g><g transform="matrix(.012,-0,0,-.012,10.875,8.513)"><use xlink:href="#x28"></use></g><g transform="matrix(.012,-0,0,-.012,14.992,8.513)"><use xlink:href="#x32"></use></g><g transform="matrix(.012,-0,0,-.012,20.703,8.513)"><use xlink:href="#x29"></use></g>
</svg> as a function of  <svg height="10.3875" id="M211" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 5.9250002 10.3875" width="5.9250002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.125)"><use xlink:href="#x1D461"></use></g>
</svg></td></tr></table></td></tr></table>

<table>Impact of the nonstationary work order on operating parameters’ changes for <svg height="18.7875" id="M206" style="vertical-align:-2.22495pt" version="1.1" viewbox="0 0 90.375 18.7875" width="90.375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,15.95)"><path d="M998 650l-8 -28q-71 -4 -86 -16t-22 -69l-50 -397q-3 -28 -4.5 -44t2 -29t6.5 -18.5t17 -10.5t24.5 -6.5t37.5 -3.5l-8 -28h-271l7 28q63 6 78 22t25 90l60 415h-2l-353 -552h-23l-130 536h-2l-70 -254q-44 -158 -47 -188q-5 -38 9 -51t71 -18l-6 -28h-241l8 28
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<g transform="matrix(.012,-0,0,-.012,17.412,7.8)"><path d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g>
<g transform="matrix(.017,-0,0,-.017,27.462,15.95)"><path d="M368 703l-264 -866h-60l265 866h59z" id="x2F"></path></g><g transform="matrix(.017,-0,0,-.017,34.466,15.95)"><use xlink:href="#x1D440"></use></g><g transform="matrix(.017,-0,0,-.017,51.822,15.95)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,58.825,15.95)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,66.985,15.95)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,73.988,15.95)"><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><g transform="matrix(.017,-0,0,-.017,82.147,15.95)"><use xlink:href="#x32"></use></g>
</svg> queue with different distribution of batch size.</table>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Mathematical Models of Multiserver Queuing System for Dynamic Performance Evaluation in Port 