  We analyse an additive-increase and multiplicative-decrease (aka
growth-collapse) process that grows linearly in time and that experiences
downward jumps at Poisson epochs that are (deterministically) proportional to
its present position. This process is used for example in modelling of
Transmission Control Protocol (TCP) and can be viewed as a particular example
of the so-called shot noise model, a basic tool in modeling earthquakes,
avalanches and neuron firings.
  For this process, and also for its reflected versions, we consider one- and
two-sided exit problems that concern the identification of the laws of exit
times from fixed intervals and half-lines. All proofs are based on a unified
first-step analysis approach at the first jump epoch, which allows us to give
explicit, yet involved, formulas for their Laplace transforms.
  All the eight Laplace transforms can be described in terms of two so-called
scale functions $Z_{\uparrow}$ and $L_{\uparrow}$. Here $Z_{\uparrow}$ is
described in terms of multiple explicit sums, and $L_{\uparrow}$ in terms of an
explicit recursion formula. All other Laplace transforms can be obtained from
$Z_{\uparrow}$ and $L_{\uparrow}$ by taking limits, derivatives, integrals and
combinations of these.
