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We consider BMAP/SM/1 type queueing system with finite buffer of size N. The system has two operation modes, which are characterized by the matrix generating function of BMAP-input, the kernel of the semi-Markovian service process, and utilization cost. An algorithm for determining the optimal hysteresis strategy is presented

mathematical problems in engineering

Optimal hysteretic control for a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$BMAP/SM/1/N$" id="E1"><mml:mi>B</mml:mi><mml:mi>M</mml:mi><mml:mi>A</mml:mi><mml:mi>P</mml:mi><mml:mo>/</mml:mo><mml:mi>S</mml:mi><mml:mi>M</mml:mi><mml:mo>/</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>N</mml:mi></mml:math>queue with two operation modes

Optimal hysteretic control for aBMAP/SM/1/Nqueue with two operation modes