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Register a new userPerformance Analysis of a Heterogeneous Traffic Scheduler using Large Deviation Principle
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Added by
Rukhsana Ruby Dr.
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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In this paper, we study the stability of light traffic achieved by a scheduling algorithm which is suitable for heterogeneous traffic networks. Since analyzing a scheduling algorithm is intractable using the conventional mathematical tool, our goal is to minimize the largest queue-overflow probability achieved by the algorithm. In the large deviation setting, this problem is equivalent to maximizing the asymptotic decay rate of the largest queue-overflow probability. We first derive an upper bound on the decay rate of the queue overflow probability as the queue overflow threshold approaches infinity. Then, we study several structural properties of the minimum-cost-path to overflow of the queue with the largest length, which is basically equivalent to the decay rate of the largest queue-overflow probability. Given these properties, we prove that the queue with the largest length follows a sample path with linear increment. For certain parameter value, the scheduling algorithm is asymptotically optimal in reducing the largest queue length. Through numerical results, we have shown the large deviation properties of the queue length typically used in practice while varying one parameter of the algorithm.
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This paper criticises the notion that long-range dependence is an important contributor to the queuing behaviour of real Internet traffic. The idea is questioned in two different ways. Firstly, a class of models used to simulate Internet traffic is shown to have important theoretical flaws. It is shown that this behaviour is inconsistent with the behaviour of real traffic traces. Secondly, the notion that long-range correlations significantly affects the queuing performance of traffic is investigated by destroying those correlations in real traffic traces (by reordering). It is shown that the longer ranges of correlations are not important except in one case with an extremely high load.
This paper has been withdrawn
The dynamics of User Datagram Protocol (UDP) traffic over Ethernet between two computers are analyzed using nonlinear dynamics which shows that there are two clear regimes in the data flow: free flow and saturated. The two most important variables affecting this are the packet size and packet flow rate. However, this transition is due to a transcritical bifurcation rather than phase transition in models such as in vehicle traffic or theorized large-scale computer network congestion. It is hoped this model will help lay the groundwork for further research on the dynamics of networks, especially computer networks.
The growing use of aerial user equipments (UEs) in various applications requires ubiquitous and reliable connectivity for safe control and data exchange between these devices and ground stations. Key questions that need to be addressed when planning the deployment of aerial UEs are whether the cellular network is a suitable candidate for enabling such connectivity, and how the inclusion of aerial UEs might impact the overall network efficiency. This paper provides an in-depth analysis of user and network level performance of a cellular network that serves both unmanned aerial vehicles (UAVs) and ground users in the downlink. Our results show that the favorable propagation conditions that UAVs enjoy due to their height often backfire on them, as the increased co-channel interference received from neighboring ground BSs is not compensated by the improved signal strength. When compared with a ground user in an urban area, our analysis shows that a UAV flying at 100 meters can experience a throughput decrease of a factor 10 and a coverage drop from 76% to 30%. Motivated by these findings, we develop UAV and network based solutions to enable an adequate integration of UAVs into cellular networks. In particular, we show that an optimal tilting of the UAV antenna can increase their coverage and throughput from 23% to 89% and from 3.5 b/s/Hz to 5.8 b/s/Hz, respectively, outperforming ground UEs. Furthermore, our findings reveal that depending on UAV altitude, the aerial user performance can scale with respect to the network density better than that of a ground user. Finally, our results show that network densification and the use of micro cells limit UAV performance. While UAV usage has the potential to increase area spectral efficiency (ASE) of cellular networks with moderate number of cells, they might hamper the development of future ultra dense networks.
We initiate a study of large deviations for block model random graphs in the dense regime. Following Chatterjee-Varadhan(2011), we establish an LDP for dense block models, viewed as random graphons. As an application of our result, we study upper tail large deviations for homomorphism densities of regular graphs. We identify the existence of a symmetric phase, where the graph, conditioned on the rare event, looks like a block model with the same block sizes as the generating graphon. In specific examples, we also identify the existence of a symmetry breaking regime, where the conditional structure is not a block model with compatible dimensions. This identifies a reentrant phase transition phenomenon for this problem---analogous to one established for Erdos-Renyi random graphs (Chatterjee-Dey(2010), Chatterjee-Varadhan(2011)). Finally, extending the analysis of Lubetzky-Zhao(2015), we identify the precise boundary between the symmetry and symmetry breaking regime for homomorphism densities of regular graphs and the operator norm on Erdos-Renyi bipartite graphs.
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