We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload $$a\in (0,1)$$ . The result is...

We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$a\in (0,1)$$</EquationSource> </InlineEquation>. The result is...</equationsource></inlineequation>