Large deviations ordering of point processes in some queueing networks

摘要: Given a stochastic ordering between point processes, say that p.p. N is smooth if it less than the Poisson process with same average intensity for this ordering. In article we investigate whether initially processes retain their smoothness as they cross network of FIFO {\cdot}\,/D/1 queues along fixed routes. For so-called strong variability show remain proceed through tandem quasi-saturated (i.e., loaded to 1) M+{\cdot}\,/D/1 queues. We then introduce Large Deviations ordering, which involves comparison rate functions associated Principles satisfied by processes. retained when feed-forward unsaturated \cdot/D/1 also examine LD characteristics deterministic at output an M+\cdot/D/1 queue.