On the Maximum Queue Length of the Hyper Scalable Load Balancing Push Strategy

In this paper we derive explicit and structural results for the steady state probabilities of a structured finite state Markov chain. The study of these steady state probabilities is motivated by the analysis of the hyper scalable load balancing push strategy when using the queue-at-the-cavity approach. More specifically, these probabilities can be used to determine the largest possible arrival rate that can be supported by this strategy without exceeding some predefined maximum queue length. Contrary to prior work, we study the push strategy when the queue length information updates occur according to a phase-type renewal process with non-exponential inter-renewal times.