  We provide a large deviations analysis of deadlock phenomena occurring in
distributed systems sharing common resources. In our model transition
probabilities of resource allocation and deallocation are time and space
dependent. The process is driven by an ergodic Markov chain and is reflected on
the boundary of the d-dimensional cube. In the large resource limit, we prove
Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and
we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi
equation with a Neumann boundary condition. We give a complete analysis of the
colliding 2-stacks problem and show an example where the system has a stable
attractor which is a limit cycle.
