Timescale of interest in traffic measurement for link bandwidth allocation design

Consider the link bandwidth allocation for transport of correlated traffic through a queueing system under a maximum allowable delay constraint d_max. We decomposed the traffic into three frequency regions: low-frequency traffic in 0<|ω|⩽ω _L, high-frequency traffic in |ω|⩾ω_H and mid-frequency traffic in ω _L<|ω|<ω_H. The zero-frequency component (DC term) of the traffic provides the average input rate which corresponds to the minimum link bandwidth requirement. Subject to delay constraint d_max, we identify ω_λ=0.01π/d_max and ω_H =2π/d_max. Hence, the transport of low-frequency traffic exceeds the limit of d_max-constrained buffer capacity; its link bandwidth is essentially captured by its peak rate. In contrast, for the transport of high-frequency traffic the d_max -constrained buffering is most effective and no additional link bandwidth is required. Essentially, the solution of ω_L and ω_H plays a role as “sampling theory” in traffic measurement for buffer capacity design and link bandwidth allocation. Equivalently in the time domain, the timescale of the low-frequency traffic is longer than or equal to 200d_max; the timescale of high-frequency traffic is shorter than or equal to d_max. Since the link bandwidth allocation of low- and high-frequency traffic requires no measurement of second-order statistics, the timescale of interest for traffic measurement must be identified in [d_max, 200d_max]