Queueing analysis of imbalance between multiple server pools with an application to 3-phase EV charging.

We consider systems where multiple servers operate in parallel, with a particular feature: servers are classified into d classes, and we wish to keep approximate balance between the load allocated to each class. We introduce a relevant imbalance metric, and study its behavior under stochastic demands with different task routing policies. For random routing, we analyze two cases of interest, depending on whether capacity constraints are operative: we obtain expressions for the stationary distribution and analyze the scaling behavior of our metric as a function of system size. Subsequently, we analyze active routing to the least loaded class, obtaining sharp bounds for the imbalance metric. As a practical application, we study the problem of imbalance between d = 3 phases, for the service of electrical vehicle charging. We show the engineering relevance of our imbalance metric in this context, and validate the theoretical results with simulations and real traces from EV charging data.