The non-ergodic Jackson network
- 1 June 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 21 (04) , 860-869
- https://doi.org/10.1017/s0021900200037554
Abstract
We generalize Jackson's theorem to the non-ergodic case. Here, despite the fact that the entire Jackson network will not achieve steady state, it is still possible to determine the maximal subnetwork that does. We do so by formulating and algorithmically solving a new non-linear throughput equation. These results, together with the ergodic results and the ones for closed networks, completely characterize the large-time behavior of any Jackson network.Keywords
This publication has 5 references indexed in Scilit:
- Comparability and Monotonicity of Markov ProcessesTheory of Probability and Its Applications, 1977
- Monotone matrices and monotone Markov processesStochastic Processes and their Applications, 1977
- Closed Queuing Systems with Exponential ServersOperations Research, 1967
- Networks of Waiting LinesOperations Research, 1957
- The Output of a Queuing SystemOperations Research, 1956