Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">  Arrival process</td><td align="center"> Analytical results </td><td align="center"> Simulation results </td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"><span style="width: 52.912498px;"><svg height="15.5125" id="M231" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 52.912498 15.5125" width="52.912498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,46.525,15.45)"><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></span></td><td align="center">0.087475</td><td align="center">0.087430</td></tr><tr><td align="left"><span style="width: 52.912498px;"><svg height="15.5125" id="M232" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 52.912498 15.5125" width="52.912498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q-13 -8 -13 -50v-196zM213 328v-203q0 -54 17 -72.5t66 -18.5q67 1 110.5 37t43.5 110q0 147 -192 147h-45z" id="x42"></path></g><g transform="matrix(.017,-0,0,-.017,10.058,11.363)"><path d="M861 0h-263v28q61 5 73 22t12 97l-4 408h-4l-244 -548h-20l-224 534h-2l-15 -285q-5 -98 -3 -166q1 -34 19.5 -45t72.5 -17v-28h-233v28q45 5 62.5 17t22.5 43q11 65 19 183l14 208q3 36 3.5 55t-2.5 37.5t-6.5 25t-16.5 13t-25.5 8t-39.5 4.5v28h164l228 -501l232 501
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</svg></span></td><td align="center">0.173523</td><td align="center">0.173378</td></tr><tr><td align="left"><span style="width: 52.912498px;"><svg height="15.65" id="M233" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 52.912498 15.65" width="52.912498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td><td align="center">0.324134</td><td align="center">0.324022</td></tr><tr><td align="left"><svg height="15.5125" id="M234" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 52.912498 15.5125" width="52.912498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>(1)</td><td align="center">0.060252</td><td align="center">0.060328</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The loss ratios obtained from analysis and simulations. 

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Transient and Stationary Losses in a Finite-Buffer Queue with Batch Arrivals 