Burst ratio in a single-server queue

Abstract

In contemporary packet networks, the possibility of packet loss is a negative, but inevitable aspect of the network design. One of the most important characteristics of the packet loss process is the burst ratio-a characteristic describing the tendency of losses to occur in long series, one after another. In this paper, we study the burst ratio in the queueing system with the finite buffer for packets. This is motivated by the fact, that most packet losses in wired networks occur due to queueing of packets in routers, and overflowing routers' buffers. We firstly derive the exact formula for the burst ratio. Then we study its behaviour as the buffer size grows, and obtain a simplified formula for large buffers. Thirdly, we present numerical results for different system parameterizations as well as the comparison with simulation results. Then we show results of measurements of the burst ratio in the networking laboratory. Finally, we draw conclusions on the influence (or lack of it) of several factors on the burst ratio.

Burst ratio for a versatile traffic model

“…We have seen also that the burst ratio depends on the system load in a non-monotonic way, and a maximum can be observed in the curve. For an arrival stream of a simple structure, this maximum is close to ρ = 1, what has been already observed in [ 18 ]. However, the more complex structure of the arrival stream, the more this maximum is shifted towards 0 (herein 0.6 in one of the examples).…”

“…In such approach, the actual mechanism of losses is not modeled, what may have some deficiencies, [17]. Analytical studies of the burst ratio in a queueing model in which the losses are actually modeled by buffer overflows, can be found in [18][19][20], for different arrival processes. However, each of these processes has a far less rich structure and modeling capabilities than BMAP.…”

The Single-Server Queue with the Dropping Function and Infinite Buffer

“…The burst ratio in finite-buffer queueing systems without the dropping function has been studied recently in [31,32]. Among other things, it was shown that the buffering itself is responsible for tendency of losses in networks to cluster in long sequences; in typical queueing scenarios the values of burst ratio were significantly greater than 1.…”

“…Among other things, it was shown that the buffering itself is responsible for tendency of losses in networks to cluster in long sequences; in typical queueing scenarios the values of burst ratio were significantly greater than 1. Moreover, in [31] the system with single-arrival stream was considered, while in [32] the system with bursty traffic was modeled by the batch Poisson process. The bursty traffic in [32] resulted in far worse performance in terms of the average length of the sequence of consecutive packet losses.…”

Impact of the Dropping Function on Clustering of Packet Losses

“…This phenomenon was confirmed by direct measurements in a lab and in a real network, [ 2 , 3 ]. It was also explained theoretically, by the derivation of the burst ratio for tail-drop queueing models with various arrival stream types [ 20 , 21 , 22 ]. It is equally easy to understand why the dropping function mechanism can decrease the burst ratio.…”