Transient analysis of multi-server queues with Markov-modulated Poisson arrivals and overload control

This paper studies the transient behavior of a Markov-molulated Poisson arrival queue under overload control. The queue has finite or infinite buffer capacity with multiple exponential servers. A Markov-modulated Poisson process is used to represent an aggregated voice or video packet arrival process in integrated service networks. By overload control, we mean to properly adapt the arrival process once the buffer contents exceed a designated level. The probability distribution of queue length as a function of time is obtained. The temporal effect of the overload control is measured in two forms. While in overload, we measure the amount of time for the queue to fall into underload. While in underload, we measure the amount of time for the queue to rise to overload. A proper design of the control will not only reduce the fall time but also increase the rise time. We also explore the transient queueing behavior as affected by time stochastic properties of the underlying Markov chain for the arrival process.     

A model for the frequency of extreme river levels based on river dynamics

A new model for predicting the frequency of extreme river levels is proposed which encapsulates physical knowledge about river dynamics. The central idea is the use of continuous time stochastic processes that use hydrological equations and ergodic theory to model extreme events, rather than relying on statistical fits of classical models to local maximum data. A simple example shows how changes in discharge characteristics change the extreme river level frequencies. Solutions are provided for special cases, and directions for more general techniques are provided.     

An efficient solution technique for discrete-time queues fed by heterogeneous traffic

During the past couple of years, a lot of effort has been put into solving all kinds of Markov modulated discrete-time queueing models, which occur, almost in a natural way, in the performance analysis of slotted systems, such as asynchronous transfer mode (ATM) multiplexers and switching elements. However, in most cases, the practical application of such solutions is limited, because of the large state space that is usually involved. In this paper we try to take a first step towards obtaining approximate solutions for a discrete-time multiserver queueing model with a general heterogeneous Markove modulated cell arrival process, which allows accurate predictions concerning the behaviour of the buffer occupancy in such a model and still remains tractable, both from an analytical and a computational point of view. We first introduce a solution technique which leads to a closed-form expression for the joint probability generating function of the buffer occupancy and the state of the arrival process, from which an expression for V(z), the probability generating function of the buffer occupancy is easily derived. On the basis of this result we propose an approximation for the boundary probabilities, which reduces all calculations to an absolute minimum. In addition, we show how accurate data for the distribution of the buffer occupancy can be obtained, by using multiple poles of V(z) in the geometric-tail approximation of the distribution. ©1997 by John Wiley & Sons, Ltd.     

A Quick Simulation Technique for a Fluid Information Storage Problem

In this paper we present an application of Importance Sampling (IS) for quick simulation of buffer overflow probability in a statistical multiplexer loaded with a number of independent Markov modulated fluid sources. Runtime improvement is deducible from N_MCσ²(p) and N_ISσ²(p^*) that characterize the trade-offs between sample size and variance of the estimators of buffer overflow probability experienced in Monte Carlo (MC) and Importance Sampling simulations. By assuming that the same precision is achieved for the two kinds of simulations if σ²(p)=σ²(p*), an approximate closed form expression for the ratio N_IS/N_MC is derived, and it is minimized with respect to the load of the multiplexer. In the final part of the paper some numerical examples are presented to illustrate the benefits of IS in evaluating very low overflow probabilities.     

Computational analysis of a Markovian queueing system with geometric mean-reverting arrival process

In the queueing literature, an arrival process with random arrival rate is usually modeled by a Markov-modulated Poisson process (MMPP). Such a process has discrete states in its intensity and is able to capture the abrupt changes among different regimes of the traffic source. However, it may not be suitable for modeling traffic sources with smoothly (or continuously) changing intensity. Moreover, it is less parsimonious in that many parameters are involved but some are lack of interpretation. To cope with these issues, this paper proposes to model traffic intensity by a geometric mean-reverting (GMR) diffusion process and provides an analysis for the Markovian queueing system fed by this source. In our treatment, the discrete counterpart of the GMR arrival process is used as an approximation such that the matrix geometric method is applicable. A conjecture on the error of this approximation is developed out of a recent theoretical result, and is subsequently validated in our numerical analysis. This enables us to calculate the performance measures with high efficiency and precision. With these numerical techniques, the effects from the GMR parameters on the queueing performance are studied and shown to have significant influences.     

Markov调制服务时间的单服务台排队近似分析

研究一种具有马尔科夫调制服务时间的单服务台排队系统。顾客到达服从参数为λ的泊松过程,服务时间为连续时间马尔科夫链调制,若马尔科夫链处于状态i（i=1,2,...N）,则服务时间服从参数为μi的负指数分布。为优化排队系统采用仿真无线通信中信道衰减导致的信道速率变化问题非常有意义。区别于以往的数值计算方法（如矩阵几何分析）,提出了一种离散时间马尔科夫链模型来分析服务台状态的变化过程,导出一组闭合公式来计算排队系统的各性能指标。此外,还开发出一种递推过程来计算队列长度的任意阶矩。数值计算结果显示出近似分析具有良好的精确性。     

A UNIFYING QUEUEING MODEL FOR ATM AND ITS ANALYSIS

This paper considers a discrete-time single-server queueing system with infinite buffer size and a finite number of independent Markov-modulated Bernoulli processes (MMBPs). A simple analytical approach is presented to analyse the asymptotic behaviour of such a queueing system. An explicit expression for the tail distribution of the buffer contents is given, from which two upper bounds for the tail distribution are derived. These two upper bounds are good and even tight in many cases, as shown by the numerical results. Compared to a previously reported general solution technique, our approximate analytical approach is very easy to use and is not limited by the system size and the traffic parameters. The CPU time required to calculate the upper bounds of the tail distribution is quite acceptable for practical use; especially for a single traffic type, the calculation costs nearly no CPU time on a normal PC. This analytical method is also suitable for more general Markov-modulated arrival processes.     

一类马氏调制风险模型的破产概率

本文研究一类马氏调制风险模型的破产概率,在此模型中索赔到达间隔和索赔额都受一外在马氏过程的影响,保费收入则受该外在的马氏过程和公司的储备金水平的影响.本文不仅考虑了随机环境对保险公司的影响,而且考虑了保险公司为了吸引新的顾客,会根据储备金的水平来调整保费收入.因此所考虑的保险模型更加贴近现实,更加易于应用.通过向后微分讨论,根据外在过程的马氏性,严格推导出破产概率所满足的积分方程.进一步,通过拉普拉斯变换的方法,给出了积分方程的解.最后,给出一个例子来展示所得结果的可行性和有效性.     

FPGEN: A fast, scalable and programmable traffic generator for the performance evaluation of high-speed computer networks

Testing today’s high-speed network equipment requires the generation of network traffic which is similar to the real Internet traffic at Gbps line rates. There are many software-based traffic generators which can generate packets according to different stochastic distributions. However, they are not suitable for high-speed hardware test platforms. This paper describes FPGEN (Fast Packet GENerator), a programmable random traffic generator which is entirely implemented on FPGA (Field Programmable Gate Array). FPGEN can generate variable packet sizes and traffic with Poisson and Markov-modulated on-off statistics at OC-48 rate per interface. Our work that is presented in this paper includes the theoretical design of FPGEN, the hardware design of the FPGA-based traffic generator board (printed circuit board design and construction) and the implementation of FPGEN on FPGA. Our experimental study demonstrates that FPGEN can achieve both the desired rate and statistical properties for the generated traffic.     

需求和退货与供应中断相关环境下库存控制

需求和退货与供应中断相关会引发库存剧烈波动,从而导致库存控制非常困难.在采用Markov调制Lévy过程描述库存水平变化条件下,利用水平穿越法、更新过程和鞅理论确定循环期望时间和费用函数,据此构建系统长程平均费用率模型.在此基础上,通过仿真实验研究需求(退货)与供应中断相关度对最优库存控制策略的影响,并分析不同中断和退...