The Distribution of Queueing Network States at Input and Output Instants
Year: 1979
Type: report
Abstract: Queueing networks are studied at selected points in the steady-state, namely the moments when jobs of a given class arrive into a given node (either from the outside of from other nodes), and the moments when jobs of a given class leave a given node (either for the outside or for other nodes). The processes defined by these points are know to he, in général, non-Poisson, interdependent and serially correlated ; therefore the relation between the distribution of the system state embedded at those moments, and the steady-state (or random point) distribution, is not obvions a priori. For a large class of networks having product form equilibrium distributions we show that (a) if the given job class belongs to an open subchain, the state distributions at input points, output points and random points are identical, and (b) if the job class belongs to a closed subchain, the distribution at input and output points is the same as the steady-state distribution of a network with one less job in that suhchain.
Source: HAL
Authors: KC Sevcik, Israel Mitrani
Institution: Newcastle University
Language: English
Subfield: Management Information Systems
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W1482919361