Analyzing a two-stage queueing system with many point process arrivals at upstream queue (Q702046)

A two-stage queueing network is considered where 1st (upstream) queue can be treated as one of the core routers with large capacity, and the downstream queues represent the periphery routers with a much smaller capacity. It is assumed that after being served at the upstream queues, the \(N\) different flows are routed to many different downstream queues. It is proved that for the point arrival process the steady-state overflow probability at a given downstream queue is asymptotically the same as for a single stage queue with the corresponding fraction of the original input (instead of corresponding fraction of the output from stage 1). This result (called a network decomposition) has been recently established (by the same authors) for many arrival fluid sources. The main difference between these inputs concerns the value of the large deviation rate function at zero which in turn implies the difference of the behavior of the overflow probability as the number of sources \(N\) goes to infinity.