The Queueing Analysis Of The Self-Similar Traffic And The Design Of Its Simulation Tools

In recent years,with the growth in the number of network applications,a large amount of audio and video data is transmitted on the network,and the self-similar characteristic of the traffic is becoming more and more significant.According to the previous researchers,the reasons that the network traffic presents self-similar patterns include:the packet sizes fit heavy-tailed distributions,the traffic is regulated under the congestion control algorithms,the increase in the number of the ON/OFF sources,the limited processing ability of the network hardware,and the network users show different operation habits.The rapid increase of the self-similar traffic has caused frequent network congestion and data loss problems,and the stability of network services has declined.There has been an increasing demand for designing the network hardware and the network protocols according to the self-similar traffic patterns to ensure the network service quality.Since the traditional queueing analysis methods and simulation tools are not suitable for analyzing and simulating the self-similar traffic,the research problems of the queueing analysis of the self-similar traffic and the design of its simulation tools require to be solved.To study and analyze the network self-similar traffic,measure the self-similar traffic data transmission behavior,and provide theoretical foundations for the network design and the network protocols design,we conduct buffer queueing analysis of a single node in a network with self-similar traffic,calculate the flow completion time distribution of a self-similar traffic data flow,and design and introduce a fast simulation tool and an approximation function for the self-similar traffic based on the lognormal distribution.The research contents and innovations are summarized as follows:(1)The queueing analysis of the self-similar traffic in a data center network bufferTo model,study and understand self-similar traffic data transmission behavior on a single point level,this thesis derives new modeling and novel queueing analysis of the self-similar traffic in a data center network buffer.The self-similar traffic in the data center network is modeled as martingale processes.The stopping time analysis is performed on the queue,and the buffer empty and overflow probabilities under the condition that the stopping time has happened are calculated.The analysis shows that the martingale process is suitable for analyzing buffer queues with the self-similar traffic.The analyzing method in this thesis is simple and scalable.The results lay foundations for the theoretical design of buffer sizes in data center networks with self-similar traffic.(2)The analysis of the flow completion time distribution of a self-similar traffic data flowTo model,study and understand self-similar traffic data transmission behavior on an end-to-end system service level,this thesis derives an innovative model to analyze the flow completion time distribution of a self-similar traffic data flow.The research is divided in four steps.First,the Transmission Control Protocol(TCP)congestion window size distribution is modeled and calculated.The exact distribution of the sum of weighted independent identically distributed exponential random variables is employed in the analysis of the TCP congestion window size distribution to achieve accurate distribution results.Second,the end-to-end data packet transmission delay distribution under the TCP congestion control is analyzed.By solving a renewal equation,a precise distribution result is derived.Third,the TCP flow completion time distribution of a flow of any length is studied.A parallel queueing system is proposed to analyze the TCP flow transmission based on the evolution of the TCP congestion window size,and the accurate TCP flow completion time distribution is achieved.Fourth,the flow completion time of the self-similar traffic is discussed,and novel derivations of its probability density function and cumulative distribution function are given.The analysis of the flow completion time distribution in this thesis is a contribution to the field because it is simpler compared with other existing flow completion time distribution analyses,while being more accurate.It has avoided the complicated iterative calculations and the state diagrams used in other existing flow completion time distribution analyses.The flow completion time distribution derived in this thesis is suitable for analyzing both short and long data flows,while the other existing flow completion time distribution analyses are only valid for short data flows.(3)The design of the simulation tools for the self-similar traffic based on lognormal distributionsTo improve the simulation efficiency of the self-similar traffic simulations,and to enhance the calculation accuracy of the self-similar traffic analysis,this thesis design and introduce a fast simulation tool for the self-similar traffic based on lognormal distributions dubbed hyperspace replication and a Marcum Q-function approximation for the lognormal sum distribution left tails.The hyperspace replication technique employs the mapping between a lognormal distribution and its corresponding normal distribution and the symmetry of the normal distribution to improve the simulation efficiency of the lognormal sum distribution simulations.The hyperspace replication technique can be used in series with importance sampling to further improve the simulation efficiency.In the Marcum Q-function approximation analysis,it is noticed that the lognormal sum event curves have the same shape for different sum values,and there are only translation relationships among the curves along the line of y=x at their vertices.Finding the largest disk that is inner tangent to the curve at the vertex is deriving the optimum Marcum Q-function approximation for the lognormal sum distribution left tail.The hyperspace replication technique is proven the most efficient in simulating lognormal sum distributions.As the lognormal sum value approaches 0(the left-most end of the sum distribution),the Marcum Q-function approximation(lower bound)is tighter than the semi-infinite rectangle approximation(lower bound)proposed by previous researchers.