A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns

<table>Effect of reneging <svg height="12.175" id="M261" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 8.6374998 12.175" width="8.6374998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> on the probability that the server is providing service in mode 2 (when <svg height="16.6625" id="M262" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 37.587502 16.6625" width="37.587502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, <svg height="11.075" id="M263" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 37.362499 11.075" width="37.362499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>, <svg height="16.625" id="M264" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 71.724998 16.625" width="71.724998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg>.</table>

Journal of Probability and Statistics

fig3

Figure 3

Figure 3: A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns 

Figure 3 | A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns 