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(ω) 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(ω) and f(x). The resulting P(ω) is a monotone function of |ω|, 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(ω) 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(ω) 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