Analyzing distributed Join-Idle-Queue: A fluid limit approach

In the context of load balancing, Lu et al. [2] introduced the distributed Join-Idle-Queue algorithm, where a group of dispatchers distribute jobs to a cluster of parallel servers. Each dispatcher maintains a queue of recently idle servers; when a job arrives to a dispatcher, it sends it to a server on its queue, or to a random server if the queue is empty. In turn, when a server becomes idle, it requests to be placed on the queue of a randomly chosen dispatcher.