|Queueing Models for Performance Evaluation of Computer Networks - Transient State Analysis, invited talk
|2018 International Conference on Sensor Networks and Signal Processing (SNSP 2018)
|Xi'an University of Science Technology, China
|fluid-flow approximation, Internet models, IP transmission control, Performance evaluation
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 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. The quality of Internet transmission services depends on current load of links and not on its average value. Also modelling and understanding the performance of traffic control mechanisms, control stability and its impact on quality of service needs transient state analysis.
We discuss mathematical and computational 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. We present three approaches - Markov models solved numerically, fluid flow approximation and diffusion approximation. A particular importance is given to the latter which is describing the evolution of queues and waiting times in terms of partial differential equations. The author has over 20 year experience in development and application of this method and is also convinced of the qualities of this approach, its flexibility to treat various variants of queueing models.
Fluid flow approximation, due its simplicity is popular and frequently used -- but even it, if applied to large topologies, is time and space consuming. Fluid flow approximation is based on first-order differential equations, and its algorithm needs iterative calculations on large mutually interdependent structures. In consequence, the bottleneck of the method lies not in numerical computations but in storing and selection of data. This is why we use an approach in which a database and its language are used to implement the method. The numerical examples are based on a real topology having over 100 000 nodes. We may investigate and compare this way various TCP control algorithms as Vegas or Reno, as well as the influence of the introduction of energy aware algorithms to routers.
Traffic intensity observed in computer networks have a complex stochastic nature (self-similarity and long-range dependence) that influences the network performances. We discuss also this side of implemented queueing models.