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.