Variability Functions for Parametric-Decomposition Approximations of Queueing Networks
改进了排队网络的参数分解近似法，用变异性函数替代单一变异性参数，以刻画非泊松到达过程在不同时间尺度下的变异性，并解决重流量瓶颈和周期性确定性到达等问题。
We propose an enhancement to the parametric-decomposition method for calculating approximate steady-state performance measures of open queueing networks with non-Poisson arrival processes and nonexponential service-time distributions. Instead of using a variability parameter c a 2 for each arrival process, we suggest using a variability function c a 2 ρ, 0 < ρ < 1, for each arrival process i.e, the variability parameter should be regarded as a function of the traffic intensity ρ of a queue to which the arrival process might go. Variability functions provide a convenient representation of different levels of variability in different time scales for arrival processes that are not nearly renewal processes. Variability functions enable the approximations to account for long-range effects in queueing networks that cannot be addressed by variability parameters. For example, the variability functions provide a way to address the heavy-traffic bottleneck phenomenon, in which exceptional variability (either high or low) in the input has little impact in a series of queues with low-to-moderate traffic intensities, and then has a big impact when it reaches a later queue with a relatively high traffic intensity. The variability functions also enable the approximations to characterize irregular periodic deterministic external arrival processes in a reasonable way; i.e., if there are no batches, then c a 2 ρ should be 0 for ρ near 0 or 1, but c a 2 ρ can assume arbitrarily large values for appropriate intermediate ρ. We present a full network algorithm with variability functions, showing that the idea is implementable. We also show how simulations of single queues can be effectively exploited to determine variability functions for difficult external arrival processes.