Large deviations for a simple closed queueing model
The author considers a simple queueing model with one service station. The arrival and service processes have intensities \(a(N-Q_ t)\) and \(Nf(N^{-1}Q_ t)\), respectively, where \(Q_ t\) is the queue length, \(N\) is a large integer, \(a>0\) and \(f(x)\) is a positive continuous function. He establishes the large deviation principle for the sequence of the normalized queue length process \(q^ N_ t=N^{-1}Q_ t\), \(N\geq 1\), for both light \((a<f(0))\) and heavy \((a\geq f(0))\) traffic and uses this result for an investigation of ergodic properties of \(q^ N_ t\), \(N\geq 1\).
scientific article; zbMATH DE number 438290
scientific article