The substability and ergodicity of complicated queueing systems

Abstract

The substability and the ergodicity of various queueing models are discussed. This paper considers the vector-valued queueing processXrn= (xrn,1,xrn,2, · ··) with non-negative components and a constant initial valueXrr= a.For this, the substability is derived under simple conditions by showing the finiteness ofWith respect to the ergodicity, in order to make use of Borovkov's theorem, we additionally assume that the distribution of the interarrival of customers has non-bounded tail for any given past sequence.