  We generalize previous studies on critical phenomena in communication
networks by adding computational capabilities to the nodes to better describe
real-world situations such as cloud computing. A set of tasks with random
origin and destination with a multi-tier computational structure is distributed
on a network modeled as a graph. The execution time (or latency) of each task
is statically computed and the sum is used as the energy in a Montecarlo
simulation in which the temperature parameter controls the resource allocation
optimality. We study the transition to congestion by varying temperature and
system load. A method to approximately recover the time-evolution of the system
by interpolating the latency probability distributions is presented. This
allows us to study the standard transition to the congested phase by varying
the task production rate. We are able to reproduce the main known results on
network congestion and to gain a deeper insight over the maximum theoretical
performance of a system and its sensitivity to routing and load balancing
errors.
