Stochastic Performance Analysis Of A Tree Topology Network

Wireless networks are stochastic by nature, i.e., the wireless channelcapacity is variant over time due to channel impairment and contention,and e?cient approaches are needed so as to conduct performance analysisof such networks. Stochastic network calculus is a newly developedtheory for queueing systems that provides stochastic service guarantees.Particularly, this thesis focuses on developing wireless channel models forQo S analysis taking into account the underlying statistical properties andproviding stochastic service guarantees of tree topology networks withstochastic network calculus.Future wireless communication calls for exploration of more e?cientuse of wireless channel capacity to meet the increasing demand on higherdata rate and less latency. In order to explore the ultimate capacity thatthe wireless channel can provide and to guarantee pluralistic quality ofservice, cumulative capacity is proposed with focus on the finite timeregime. Specifically, based on the cumulative distribution function ofcumulative capacity, moment generating function, stochastic service curve,and Mellin transform are investigated as further properties of wirelesschannel capacity. These further properties of wireless channel capacityare essential building blocks for Qo S analysis with stochastic networkcalculus.A reference analysis loop is proposed in the process of performanceanalysis, i.e., the performance metrics are derived based on a generic net-work specification, then the network parameters are calculated satisfyinga given performance requirement in a reverse style. The analysis loopis then used to analyze the topology control boundary conditions underperformance constraints in a wireless mesh network and to investigatethe quantitative impact of duty cycle on the end-to-end network perfor-mance. Specifically, properties of logarithm functions and Taylor seriesare utilized to derive closed-form expressions of network diameter subjectto end-to-end performance metrics and / or duty cycle.The basic properties of stochastic network calculus are further in-vestigated under the combination of leaky-bucket-type stochastic arrivalcurve with negative exponential bounding function and latency-rate-typestochastic service curve with negative exponential bounding function. It isshown that all the further results are bounded with a negative exponentialbounding function. These results are applied to a tree topology wirelesssensor network that provides stochastic service guarantees. It is worthnoting that the tree topology is a generalization of the line topology,in other words, line topology network is an end-to-end path of a treetopology network. When analyzing end-to-end performance of a treetopology network, it is transformed to a line topology network, takingadvantage of the properties of stochastic network calculus, a network ser-vice curve is derived for an end-to-end path of the tree topology network,together with the stochastic arrival curve for the input, per-hop backlogand end-to-end delay are easily obtained.