LB-networks: A model for dynamic load balancing in queueing networks.

Dynamic load balancing plays an important role in the management of data centres where a fair workload distribution may be hard to achieve. Dynamic load balancing algorithms are usually clustered into two families: receiver-initiated and sender-initiated. In the former approach, an idle node transfers some of the jobs of a highly loaded node to its queue, whereas in the latter it is the overloaded node that decides to send somewhere else some of the jobs that have been assigned to itself. The literature has proved the receiver-initiated strategies to be more effective than the sender-initiated ones under heavy load. In this paper, we give for the first time a closed form expression of the stationary distribution of a class of queueing networks where an arbitrary number of nodes implement a receiver-initiated dynamic load balancing algorithm. The result can be applied to Markovian queueing networks with probabilistic routing and exponentially distributed service times.