Join-the-Shortest-Queue Model as a Mean Field Approximation to a Local Balancing Network

2018/06/12 by Bu, Qihui, Liu, Liwei, Zhao, Yiqiang Q.
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1806.04691

Abstract

In this paper, we consider a queueing network with N nodes, each of which has a fixed number k of neighboring nodes, referred to as the N node network with local balancing. We assume that to each of the N nodes, an incoming job (or task) chooses the shortest queue from this node and its neighboring nodes. We construct an appropriate Markov process for this network and find a mean field approximation to this network as N→∞, which turns out to be the standard join-the-shortest-queue model.

Related

• Queuing Networks with Varying Topology -- A Mean-Field Approach
• Approximations for a Queueing Game Model with Join-the-Shortest-Queue Strategy
• Stability of Join the Shortest Queue Networks
• The stability of join-the-shortest-queue models with general input and output processes
• Join-the-Shortest Queue with Abandonment: Critically Loaded and Heavily Overloaded Regimes