Many dynamic networks coming from real-world contexts are link streams, i.e. a finite collection of triplets @math where @math and @math are two nodes having a link between them at time @math . A very large number of studies on these objects start by aggregating the data in disjoint time windows of length @math in order to obtain a series of graphs on which are made all subsequent analyses. Here we are concerned with the impact of the chosen @math on the obtained graph series. We address the fundamental question of knowing whether a series of graphs formed using a given @math faithfully describes the original link stream. We answer the question by showing that such dynamic networks exhibit a threshold for @math , which we call the , beyond which the properties of propagation of the link stream are altered, while they are mostly preserved before. We design an automatic method to determine the saturation scale of any link stream, which we apply and validate on several real-world datasets.
Contrastingly, the goal of @cite_2 is precisely to determine an ideal aggregation period. In their method, this period is obtained as a trade-off between two metrics that vary monotonically and oppositely with regard to aggregation: one describing the loss of information (increasing with aggregation) and one describing the noise contained in the series of snapshots (decreasing with aggregation). Compared to them, here, we are concerned only with the loss of information. This allows us to avoid some drawbacks and limitations inherent to the approaches based on a trade-off: i) the value selected for the aggregation period strongly depends on the importance given to each metrics and ii) the selected value does not reveal any particular behavior of the properties of the network used in the trade-off, as each of them varies smoothly and monotonically from one extremal value to another one. On the contrary, our method does not depend on any arbitrary choice of ponderation and reveals a natural change in the way the network responds to aggregation at a certain aggregation scale that we determine.
@cite_2
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Frame aggregation is one of the several enhancements proposed by IEEE 802.11 Task Group n to improve channel utilization. In frame aggregation, more than one data frame is encapsulated to form an aggregate, and once an aggregate is formed, a station contends to access the medium to transmit the entire aggregate. We refer to the number of data frames encapsulated within an aggregated frame as aggregate size. We claim that a static assignment of aggregate size leads to the following performance trade-off: a small value might be insufficient to mitigate the transmission overheads, thereby nullifying the whole purpose of frame aggregation; whereas, a large value might affect the quality of service experienced by higher layers due to the extra wait time to build an aggregate. In this paper, we characterize this trade-off by studying the impact of aggregate size on metrics like frame latency and channel utilization. To estimate these metrics, we model the transmission queue of an 802.11n station as a bulk service queuing system. We study the impact of aggregate size over a wide range of operating conditions covering several traffic arrival rates from higher layers, service distribution and data frame sizes. Apart from validating the existence of above-mentioned performance trade-off, our results indicate that the choice of aggregate size not only depends on the traffic arrival rate, but also (more interestingly) on data frame sizes. This calls for a dynamic assignment of aggregate size.