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.006a" src="https://static-preview.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.006a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b><svg height="15.25" id="M511" 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">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><use xlink:href="#x1D435"></use></g>
</svg> as a function of <svg height="10.3875" id="M512" 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><tr class="fig-image" id="b"><td><img alt="710834.fig.006b" src="https://static-preview.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.006b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="21.875" id="M513" 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="#x31"></use></g><g transform="matrix(.012,-0,0,-.012,20.703,8.513)"><use xlink:href="#x29"></use></g>
</svg> and <svg height="21.875" id="M514" 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="M515" 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: <svg height="15.25" id="M507" 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">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><use xlink:href="#x1D435"></use></g>
</svg> and <svg height="15.4" id="M508" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 20.387501 15.4" width="20.387501" 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)"><use xlink:href="#x1D443"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.875,15.187)"><use xlink:href="#x1D449"></use></g>
</svg> as a function of <svg height="10.3875" id="M509" 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> for <svg height="18.7875" id="M510" 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)"><use xlink:href="#x1D440"></use></g>
<g transform="matrix(.012,-0,0,-.012,17.412,7.8)"><use xlink:href="#x1D44B"></use></g>
<g transform="matrix(.017,-0,0,-.017,27.462,15.95)"><use xlink:href="#x2F"></use></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)"><use xlink:href="#x33"></use></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)"><use xlink:href="#x33"></use></g><g transform="matrix(.017,-0,0,-.017,82.147,15.95)"><use xlink:href="#x36"></use></g>
</svg> queue with different distribution of batch size.</table>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Mathematical Models of Multiserver Queuing System for Dynamic Performance Evaluation in Port 