Stability of Jackson-type queueing networks, I

This paper gives a pathwise construction of Jackson-type queuing networks allowing the derivation of stability and convergence theorems under general statistical assumptions on the driving sequences, namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers and basic theorems on monotone stochastic recursive sequences. the techniques which are proposed here apply to other and more general classes of dsicrete event systems, like Petri nets or GSMP's. The paper also provides new results on the Jackson-type networks with i.i.d. driving sequences which were studied in the past.

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