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We generalize previous studies on critical phenomena in communicationnetworks by adding computational capabilities to the nodes to better describereal-world situations such as cloud computing. A set of tasks with randomorigin and destination with a multi-tier computational structure is distributedon a network modeled as a graph. The execution time (or latency) of each taskis statically computed and the sum is used as the energy in a Montecarlosimulation in which the temperature parameter controls the resource allocationoptimality. We study the transition to congestion by varying temperature andsystem load. A method to approximately recover the time-evolution of the systemby interpolating the latency probability distributions is presented. Thisallows us to study the standard transition to the congested phase by varyingthe task production rate. We are able to reproduce the main known results onnetwork congestion and to gain a deeper insight over the maximum theoreticalperformance of a system and its sensitivity to routing and load balancingerrors.

Transition to congestion in communication/computation networks: from ideal to realistic resource allocation via Montecarlo simulations