What is Fill intensity?

The fill intensity of a resting quote is the rate at which it is executed, as a function of its depth $\delta$ from the mid. The inventory models assume $\lambda(\delta)=A\,e^{-k\delta}$, the same on both sides, with $A$ and $k$ constant (local symbols: $A$ is not an annuity and $k$ not a log-moneyness here).