2015/12/14 by Pascal Moyal, Moyal, Pascal
Mathematics · #35B35 #60K25 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:35B35 #msc:60K25
paper · pdf · doi:10.48550/arxiv.1512.04596
arxiv created 2015/12/14 · arxiv updated 2015/12/16
We investigate, under general stationary ergodic assumptions, the stability of systems of S parallel queues in which any incoming customer joins the queue of the server having the p+1-th shortest workload (p < S), or a free server if any. This change in the allocation policy makes the analysis much more challenging with respect to the classical FCFS model with S servers, as it leads to the non-monotonicity of the underlying stochastic recursion. We provide sufficient conditions of existence of a stationary workload, which indicate a "splitting" of the system in heavy traffic, into a loss system of p servers plus a FCFS system of S-p servers. To prove this result, we show \em en route an original sufficient condition for existence and uniqueness of a stationary workload for a multiple-server loss system.