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.007a" src="https://static.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.007a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b><svg height="15.25" id="M517" 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> versus <svg height="12.4375" id="M518" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.5874996 12.4375" width="8.5874996" 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)"><use xlink:href="#x1D703"></use></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="710834.fig.007b" src="https://static.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.007b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b><svg height="21.875" id="M519" 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="M520" 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> versus<svg height="12.4375" id="M521" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 14.25 12.4375" width="14.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,12.162)"><use xlink:href="#x1D703"></use></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="710834.fig.007c" src="https://static.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.007c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b><svg height="15.4" id="M522" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 24.075001 15.4" width="24.075001" 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="#x1D441"></use></g>
<g transform="matrix(.012,-0,0,-.012,14.925,15.187)"><use xlink:href="#x1D464"></use></g>
</svg>  versus <svg height="12.4375" id="M523" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.5874996 12.4375" width="8.5874996" 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)"><use xlink:href="#x1D703"></use></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="710834.fig.007d" src="https://static.hindawi.com/articles/mpe/volume-2012/710834/figures/710834.fig.007d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b><svg height="14.4125" id="M524" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 15.0125 14.4125" width="15.0125" 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>
<g transform="matrix(.012,-0,0,-.012,5.862,14.2)"><use xlink:href="#x1D464"></use></g>
</svg> versus <svg height="12.4375" id="M525" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.5874996 12.4375" width="8.5874996" 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)"><use xlink:href="#x1D703"></use></g>
</svg></td></tr></table></td></tr></table>

<table>  Impact of the traffic intensity on operating parameters’ changes for <svg height="18.7875" id="M516" 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

fig7

Figure 7

Figure 7: Mathematical Models of Multiserver Queuing System for Dynamic Performance Evaluation in Port 