Simplifications of Jackson Queueing Networks.
MICHIGAN UNIV ANN ARBOR DEPT OF INDUSTRIAL AND OPERATIONS ENGINEERING
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This paper deals with valid simplifications of a class of queueing networks. A valid simplification is a complexity reducing map from queuing networks into queuing networks that preserves or reasonably approximates the stochastic properties of interest. The paper exemplifies such maps for the class of Jackson queuing networks independent Poisson inputs, independent Exponential servers, FIFO queue disciplines and memoryless decomposition switches. To ensure true complexity reduction the authors insist that the lumped network i.e. the result of an attempted simplification also be a Jackson network. It is shown that this is not possible for arbitrary networks. Reasonable conditions under which such simplifications are possible are provided. In the process, the authors expose a number of gaps in the theory of Jackson networks as it now stands and settle one of the, the question of existence and uniqueness of a solution to the so called traffic equilibrium equation.
- Operations Research