Network Performance Analysis Model Research Based On Network Calculus

Network calculus is a deterministic queuing theory based on non-linear algebra. Ithas been successfully applied to a number of important issues in the field of computer net-works modeling and performance analysis. It is also an efficiency tool for calculating thedeterministic bounds of end-to-end performance parameters such as delay and backlog.The research of network calculus has made great progress in recent years, and networkcalculus has been a hot research field in compute networks.The research of network calculus can be divided into theory research and applicationresearch. Theory research studies the mathematical model of network calculus, and is thebasis for the extensive applications of network calculus. Each advance in theory researchwill cause a rapid progress in application research. But network calculus is an interdisci-plinary research area, and concerns with many mathematical theories. Thus the progressof theory research is relatively slower in comparison to application research. The theoreti-cal background of the basic concepts in network calculus has not got sufficient study suchas arrival curve and service curve. And the theory of network calculus itself is not rigor-ous. Thus the work of studying network calculus by mathematical method and includingnetwork calculus into a rigorous theoretical system is worth well researching.Aimed at these shortcomings of theory research, and based on the summary of exist-ing research results, we study network calculus theoretically by idempotent mathematicsand DEDS theory.We propose a max-plus network calculus and a second order time varying networkcalculus. Max-plus network calculus has advantages in dealing with variable length pack-ets sequence and computing the bounds for performance parameters with respect to time.Max-plus network calculus makes up for the deficiency of min-plus network calculuseffectively. Second order time varying network calculus guarantees bounds for the dif-ference of cumulative function of network element's output ?ow. It's a more efficiencyanalysis tool for network performance than first order time varying network calculus. Wecan obtain more precise performance bounds when we analyze network by second ordertime varying network calculus.We propose a mathematical model of network calculus based on redsiduation theory. The main results of network calculus can be obtained by residuation theory with sim-ple derivation process, thus the difficulty of network calculus theory research is reducedgreatly. We also solve some difficult problems in network calculus by residuation theorymethods, these problems includes the maximum input ?ow of greedy shaper and the op-timal window size for window ?ow control system. There are many other mappings andfunctions in network performance analysis can be studied by residuation theory, includ-ing Legendre transform and packetizer. These mappings and functions are residuated ordual residuated, thus our results enlarge application range of network calculus in networkperformance analysis.We propose an abstract network calculus theory. Abstract network calculus summa-rizes the common ground among different network calculus and put them into a brand-new theoretical framework, thus gives network calculus a solid theoretical foundation.Abstract network calculus has not endowed any special meaning with the dioid element,and the derivation processes of theorems in abstract network calculus only use the basicproperties of dioid. Thus abstract network calculus is simple and understandable, and pro-vides general methods for different network calculus. Researchers can grasp the essenceof network calculus without investigating every existing network calculus branch. As anapplication of abstract network calculus theory, we propose an interval network calcu-lus. Interval network calculus is based on the interval extension of wide-sense increasingfunctions dioid. By interval network calculus, we can calculate the interval bounds of per-formance parameters, thus interval network calculus can deal with uncertainty in network.Interval network calculus is a new analysis tool for network performance. Its complexitylies between deterministic network calculus and stochastic network calculus.We study arrival curve and service curve by idempotent matrix theory, and we alsodefine the concept of arrival matrix and service matrix, and propose a matrix networkcalculus based on these two notions. We also divide network calculus into four categoriesby order of ?ow's generated matrix. There are many advantages of matrix network calcu-lus: First, in matrix network calculus, min-plus convolution turns into our familiar matrixmultiplication; Second we can use the results in developed idempotent matrix theory toanalyze network calculus; At last matrix network calculus deepens the relationship be-tween network calculus and DEDS theory, thus makes it possible for using DEDS theoryto further study network calculus.