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We consider a two-stage queueing system where the first (upstream) queue serves many flows, of which a fixed set of flows arrive to the second (downstream) queue. We show that as the capacity and the number of flows aggregated at the upstream queue increases, the overflow probability at the downstream queue converges to that of a simplified single queue obtained by removing the upstream queue from...
We consider the following stochastic bandwidth packing process: the requests for communication bandwidth of different sizes arrive at times t=0,1,2,... and are allocated to a communication link using “largest first” rule. Each request takes a unit time to complete. The unallocated requests form queues. Coffman and Stolyar [6] introduced this system and posed the following question: under which conditions...
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