On input state space reduction and buffer noneffective region

Considers a single-server finite-buffer system. Its stationary random input process as characterized by the power spectrum P(/spl omega/) and the input rate steady state distribution f(x). The two functions represent second-order and steady-state input statistics. The authors use the superposition of heterogeneous 2-state Markov chains (MC) for construction of P(/spl omega/) and f(x). The resulting P(/spl omega/) is a monotone function of |/spl omega/|, and f(x) is the convolution of heterogeneous binomial functions. They show how to eliminate the state space explosion in input modeling. Unlike the existing modeling technique which matches the 2-state MC with each individual source, their 2-state MC are built to statistically match with functions P(/spl omega/) and f(x) of the aggregate input. The input state space is then reduced by many orders of magnitude. They examine the maximum throughput of a finite-buffer system to support P(/spl omega/) and f(x) subject to a desired average loss rate L. The numerical study explores a fundamental limit of buffer sizing to the maximum throughput improvement. A simple heuristic formula is developed, which tells quantitatively whether a given finite-buffer system operates in a so-called buffer-noneffective region. The new insight relating link capacity to low frequency input statistics explored in the paper is a fruitful starting point for further research.<
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