Computable Exponential Bounds for llntree Networks with Routing
نویسندگان
چکیده
In this paper, we refine the calculus proposed in [5, 8, 91. The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or autoregressive processes, the stationary queue length at a local node is stochastically bounded above b y the sum of a constant and an Erlang random variable. The decay rate of the Erlang random variable is not greater than ( in some cases equal to) the decay rate of the tail distribution of the stationa y queue length. The number of stages of the Erlang random variable is the number of external arrival processes and routing processes contributing to its queue length. For the single queue case, both the lower and upper bounds are derived.
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