Transition to congestion in communication/computation networks for near-optimal and sub-optimal resource management via Monte Carlo simulations

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 origins and destinations characterized by a multi-tier computational structure is distributed on a network modeled as a graph. The distribution of execution times (or latencies) of all tasks is statically computed for several initial workloads and its sum is used as the target function to be optimized by Simulated Annealing. A canonical Monte Carlo simulation allows to analyze the network behavior at different levels of sub-optimality of resource management (achieved by changing the temperature). We first study the static transition to congestion of the whole network by varying temperature and workload. Then, we propose a method to approximately recover the evolution of the system in time, by interpolating the static latency probability distributions. This allows to study the dynamic transition to the congested phase by introducing a variable task-production rate, as usually studied in the literature, without the need of explicit time-consuming simulations. We are able to reproduce the main published results on network congestion and to gain a deeper insight over the maximum theoretical performance of a system and its sensitivity to sub-optimality of routing and load balancing.