The Benes̆ equation and stochastic calculus of variations

We focus our attention on the Benes̆ equation which describes the behavior of the virtual waiting time in the most general single queue. Using the reflection theory and the stochastic calculus of variations, we derive new results on this equation. In particular, we give a criterion on the input stream under which the solution has an absolutely continuous law with respect to the Lebesgue measure.