دانلود رایگان مقاله انگلیسی مدل های صف بندی برای ارزیابی عملکرد شبکه کامپیوتری: تحلیل حالت گذرا - اشپرینگر 2015

Abstract

Queueing theory is a useful tool in design of computer networks and their performance evaluation. The literature concerning this subject is abundant. However, it is in general limited to the analysis of steady states. It means that flows of customers considered in models are constant and obtained solutions do not depend on time. It is in glaring contrast with the flows observed in real networks where the perpetual changes of traffic intensities are due to the nature of users, sending variable quantities of data, cf. multimedia traffic, and also due to the performance of traffic control algorithms which are trying to avoid congestion in networks, e.g. the algorithm of congestion window used in TCP protocol which is adapting the rate of the sent traffic to the observed losses or transmission delays. We discuss here the means used to analyse transient states in queueing models. In computer applications a mathematical model is useful only when it furnishes quantitative results. Therefore practical issues related to numerical side of models are of importance and are here discussed. We present three approaches—Markov models solved numerically, fluid flow approximation and diffusion approximation. A particular importance is given to the latter as the author has here over 20 year experience in development and application of this method. He is also convinced of the qualities of this approach— its flexibility to treat various variants of queueing models. Traffic intensity observed in computer networks have a complex stochastic nature that influences the network performances. We discuss also this side of implemented queueing models.

5 Conclusions

The size and complexity of models which may be analysed by diffusion and fluid flow approximations are much larger than in case of traditional Markovian models. Diffusion and fluid approximations are useful approaches that are complementary to Markov models if we do not need a detailed description including all events concerning singular packets and occurring in a real system. We investigated the limitations of the use of both approximations in the transient analysis of IP router queues in presence of input flow originating from TCP congestion window algorithm. Fluid flow approximation generates much larger errors but is very fast and may be applied to larger networks. Diffusion approximation is more accurate and may furnish not only the mean values of queues but also their distributions, therefore it is better adapted to estimate the packet losses. However, the calculations are more complex. An alternative to analytical models is discrete event simulation—also used here to evaluate results of diffusion and fluid flow approximations. We have developed an extension of OMNET++ (a popular simulation tool written in C++, [59]) allowing simulation of transient state models. In this case a simulation run should be repeated a sufficient number of times (e.g. 500 thousands in our examples) and the results for a fixed time should be averaged. It makes transient simulation models time-consuming.