Analyzing a degenerate buffer with general inter-arrival and service times in discrete time

Abstract

In novel switching approaches such as Optical Burst Switching, the involved buffers can only provide a degenerate waiting room, with delays restricted to multiples of a basic value, the granularity. Although the resulting performance loss was already studied analytically, previous work is either limited by the assumption of independent arrivals, or it involves a matrix with size growing fast with buffer size or arrival process complexity.Overcoming this, we developed a generic and accurate loss performance model for a degenerate GI/G/1 buffer in discrete time, that yields results instantly for any constellation of burst sizes, inter-arrival times, granularity, load and buffer size. This paper presents our model and compares its results to simulations, illustrating the impact of different types of correlation in the arrival process on loss performance. Our basic model is general and accurate, it can thus serve as a basic tool for optical switch design.

Heuristic performance model of optical buffers for variable length packets

“…The proposed heuristic unifies two seemingly disparate elements: recent results for systems with quantization of delay [14] on the one hand, and a well-known result for systems with impatience [16] on the other hand. Main advantage is that this approach is "simple", in the sense that it is complex only to the degree needed to model the most characteristic features of the original system, and nothing more.…”

“…In [14] (discrete time) and [15] (continuous time), the effect of quantization was traced in an exact manner, for a degenerate buffer setting with infinite buffer size. The effects of impatience were also taken into account, but only by means of an indirect approximate approach, which was hardly open for intuition, and inaccurate if the number of lines is few (say, smaller than 5).…”

“…For degenerate settings, stability is studied in detail in [14], and yields following stability condition,…”

“…For example, while it is well-known for an M/G/1 classic system in a continuous-time setting that the probability of finding an empty system upon arrival equals 1 − ρ, this is not the case for an optical system: neither (1 − ρ) nor (1 − ρ eq ) provides an answer, and the probability in question can only be determined after full queueing analysis, as available in [14]. In this regard, the definition of ρ eq proposed here is prone to discussion:…”

“…A general expression can be readily obtained from the expression available in [14], valid for discrete time, by applying a limit procedure, similar as is done in [15] for an optical M/G/1 setting.…”