  Robust estimates for the performance of complicated queueing networks can be
obtained by showing that the number of jobs in the network is stochastically
comparable to a simpler, analytically tractable reference network. Classical
coupling results on stochastic ordering of network populations require strong
monotonicity assumptions which are often violated in practice. However, in most
real-world applications we care more about what goes through a network than
what sits inside it. This paper describes a new approach for ordering flows
instead of populations by augmenting network states with their associated flow
counting processes and deriving Markov couplings of the augmented state-flow
processes.
