Performance Bounds for Synchronized Queueing Networks (original) (raw)

A Note on Stochastic Bounds for Queueing Networks

Advances in Applied Probability, 1984

Recently, Massey [1] proved that the vector of queue lengths of some queueing networks is stochastically dominated at any given time by that of a corresponding system of parallel M/M/l queues. This result is interesting, even though the bounds are generally quite conservative, in that the transient behavior of independent parallel M/M/l queues is considerably easier to analyze than that of a network.This note provides an alternative proof of a generalized form of that result.

On the tra c equations for batch routing queueing networks and stochastic Petri nets

1994

Abstract The tra c equations are a set of linear equations, which are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the tra c equations are therefore of great importance. This note provides a necessary and su cient condition on the structure of the network for a solution of the tra c equations to exist.

Throughput upper bounds for Markovian Petri nets: Embedded subnets and queueing networks

1991

Addresses the computation of upper bounds for the steady-state throughput of stochastic Petri nets with immediate and exponentially distributed service times of transitions. The authors try to deeply bridge stochastic Petri net theory to untimed Petri net and queueing network theories. Previous results for general service time distributions are improved for the case of Markovian nets by considering the slowest embedded subnet (generated by the support of left annullers of the incidence matrix of the net). The obtained ...