On Input State Space Reduction and Buuer Noneeective Region

Consider a single-server nite-buuer system. Its stationary random input process is characterized by power spectrum P (!) and input rate steady state distribution f(x). The two functions represent second-order and steady-state input statistics. Here we use the superposition of heterogeneous 2-state Markov chains for construction of P (!) and f(x). The resulting P (!) is a monotone function of j!j, and f(x) is the convolution of heterogeneous binomial functions. The rst part of this paper shows how to eliminate the state space explosion in input modeling. Unlike the existing modeling technique which matches 2-state MCs with each individual source, our 2-state MCs are built to statistically match with functions P (!) and f(x) of the aggregate input. The input state space is then reduced by many orders of magnitude. In the second part of this paper, we examine the maximum throughput of a nite-buuer system to support P (!) and f(x) subject to a desired average loss rate L. Our numerical study explores a fundamental limit of buuer sizing to the maximum throughput improvement. A simple heuristic formula is developed, which tells us quantitatively whether a given nite-buuer system operates in a so-called buuer-noneeective region. The new insight relating link capacity to low frequency input statistics explored in this paper is a fruitful starting point for further research. K µ ω P(), f(x) Figure 1: A network link modeled by a single-server nite-buuer system.