Buffer Behavior for Mixed Arrivals and Single Server with Random Interruptions

A queueing model with finite buffer size, mixed input traffic (Poisson and burst Poisson arrivals), synchronous transmission and server interruptions through a Bernoulli sequence of independent random variables is studied. Using average burst length, traffic intensity and input traffic mixture ratio as parameters, the relationships among buffer size, overflow probability and expected message queueing delay are obtained. An integrated digital voice-data system with synchronous time division multiplexing (STDM) for a large number of voice sources and mixed arrival process for data messages is considered as an application for this model. The results of this study are portrayed on graphs and may be used as guidelines in buffer design problems in digital voice-data systems. The queueing model developed is quite general in a sense that it covers pure Poisson and burst Poisson arrival processes and the mixture of the two as well.     

Edge node buffer usage in optical burst switching networks

Optical Burst Switching (OBS) combines the benefits of Optical Packet Switching and Optical Circuit Switching technologies to provide an efficient, yet cost effective, method for data transmission in an all-optical, bufferless, core network. While most studies on OBS has concentrated on the core OBS network, we contribute new studies for the buffer requirement of an OBS edge node. The buffer usage for OBS systems only arises in the edge nodes since they contain an array of assemblers which combines electronic data with a common destination into an OBS burst stream for transmission in an all-optical bufferless core network. Specifically, we present two analytical results for buffer usage in an OBS edge node: one for Poisson traffic and the other for self-similar traffic input. The results show that the aggregated traffic from many assemblers inherits the characteristics of the source input traffic. This means that the output traffic approaches Poisson if the input traffic is Poisson, and the output traffic remains self-similar if the input is self-similar. These results lead to the following important design issues when dimensioning buffer requirements in an OBS edge node: if the traffic input is Poisson, the M/G/m model is the model to use for obtaining the upper bound on buffer usage in an OBS edge node; and for the case of self-similar traffic, Brichet’s method can be used to provide the upper and lower bound.     

Book reviews: a summary of multifractal traffic modeling

One of the most important discoveries about Internet traffic is the scaling phenomenon. Different from the traditional traffic pattern, primarily the Poisson model, this type of traffic shows a slowly decaying dependence structure and can be approximately characterized by a self-similar process. Multiscale behavior is a more complex version of self-similarity, indicating that the scaling property of the traffic process isn't uniform across multiple time scales and orders of statistics. It's often modeled with the multifractal process. "Multifractal Based Network Traffic Modeling" provides an accessible but somewhat narrow summary of the research on self-similar and multiscale traffic.     

Traffic equivalence and substitution in a multiplexer withapplications to dynamic available capacity estimation

For a multiplexer fed by a large number of sources, we derive conditions under which a given subset of the sources can be substituted for a single source while preserving the buffer overflow probability and the dominant timescales of buffer overflows. This notion of traffic equivalence is stronger than simple effective bandwidth equality and depends on the multiplexing context. We propose several applications of the above traffic substitution conditions. First, we show that fractional Brownian motion as a single source substitute can effectively model a large number of multiplexed sources using information obtained purely from traffic traces; this has direct application to simple but accurate traffic generation. Second, we focus on dynamic (i.e., on-line) estimation of available capacity and buffer overflow probability. This requires the solution of a double optimization problem expressed in terms of functions whose values are obtained from time averages of the traffic traces over a large range of timescales. We show how to solve this problem on-line by reducing it to the calculation of a fixed-point equation that can be solved iteratively by combining traffic substitution using fractional Brownian motion with dynamic measurements of the actual traffic. We have validated this approach by extensive experimentation with large numbers of real traffic sources that are fed to a high bandwidth link, and comparing our on-line estimation of available capacity and the resulting dynamic call admission control with other existing approaches. The superior accuracy of our approach also suggests that taking the buffer size into account, as does our on-line algorithm, may be vital for achieving approximations of practical interest     

Multihop Virtual Topology Design in WDM Optical Networks for Self-Similar Traffic

In this paper, we consider the problem of designing virtual topologies for multihop optical WDM networks when the traffic is self-similar in nature. Studies over the last few years suggest that the network traffic is bursty and can be much better modeled using self similar process instead of Poisson process. We examine buffer sizes of a network and observe that, even with reasonably low buffer overflow probability, the maximum buffer size requirement for self-similar traffic can be very large. Therefore, a self-similar traffic model has an impact on the queuing delay which is usually much higher than that obtained with the Poisson model. We investigate the problem of constructing the virtual topology with these two types of traffic and solve it with two algorithmic approaches: Greedy (Heuristic) algorithm and Evolutionary algorithm. While the greedy algorithm performs a least-cost search on the total delay along paths for routing traffic in a multihop fashion, the evolutionary algorithm uses genetic methods to optimize the average delay in a network. We analyze and compare our proposed algorithms with an existing algorithm via different performance parameters. Interestingly, with both the proposed algorithms the difference in the queuing delays, caused by self-similar and Poisson traffic, results in different multihop virtual topologies.     

A new approach to long‐range dependence in variable bit rate video traffic

Recently it has been observed that variable bit rate (VBR) video traffic displays long‐range dependence, which suggests that traditional Markovian models may not be suitable for performance evaluation of telecommunications networks carrying this traffic. Inspection of the bit rate profile of VBR video traffic suggests that shifting level processes might be more appropriate for this task. In this paper we show that a particular class of these processes matches the autocorrelation and bit rate distribution of real VBR video traffic, including exhibiting long‐range dependent behaviour. This revised version was published online in June 2006 with corrections to the Cover Date.     

Buffer Behavior for Mixed Input Traffic and Single Constant Output Rate

A queueing model with limited waiting room (buffer), mixed input traffic (Poisson and compound Poisson arrivals), and constant service rate is studied. Using average burst length, traffic intensity, and input-traffic mixture rate as parameters, we obtain relationships among buffer size, overflow probabilities, and expected message-queueing delay due to buffering. These relationships are portrayed on graphs that can be used as a guide in buffer design. Although this study arose in the design of statistical multiplexors, the queueing model developed is quite general and may be useful for other industrial applications.     

基于FBNDP自相似业务源建模

基于分形二项噪音驱动泊松过程（FBNDP）动态原理,我们构建了其仿真模型并进行多次仿真实验,提示了FBNDP模型采样数据轨迹的表面现象,并用R/S法和时间方差法对其自相似强度进行分析计算;另外,自相似过程的非退化自相关结构特性得到图形化验证.     

Diffusion approximation modeling for Markov modulated burstytraffic and its applications to bandwidth allocation in ATMnetworks

We consider a statistical multiplexer model, in which each of the K sources is a Markov modulated rate process (MMRP). This formulation allows a more general source model than the well studied “on-off” source model in characterizing variable bit rate (VBR) sources such as compressed video. In our model we allow an arbitrary distribution for the duration of each of the M states (or levels) that the source can take on. We formulate Markov modulated sources as a closed queueing network with M infinite-server nodes. By extending our earlier results we introduce an M-dimensional diffusion process to approximate the aggregate traffic of such Markov modulated sources. Under a set of reasonable assumptions we then show that this diffusion process can be expressed as an M-dimensional Ornstein-Uhlenbeck (O-U) process. The queueing behavior of the buffer content is analyzed by applying a diffusion process approximation to the aggregate arrival process. We show some numerical examples which illustrate typical sample paths, and autocorrelation functions of the aggregate traffic and its diffusion process representation. Simulation results validate our proposed approximation model, showing good fits for distributions and autocorrelation functions of the aggregate rate process and the asymptotic queueing behavior. We also discuss how the analytical formulas derived from the diffusion approximation can be applied to compute the equivalent bandwidth for real-time call admission control, and how the model can be modified to characterize traffic sources with long-range dependence     

Modeling and analysis of self-similar traffic source based on fractal-binomial-noise-driven Poisson process

~~Modeling and analysis of self-similar traffic source based on fractal-binomial-noise-driven Poisson process1. Will E L, Murad S T, Walter W, et al. On the self-similarity nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking…     

Effective bandwidths for multiclass Markov fluids and other ATMsources

The authors show the existence of effective bandwidths for multiclass Markov fluids and other types of sources that are used to model ATM traffic. More precisely, it is shown that when such sources share a buffer with deterministic service rate, a constraint on the tail of the buffer occupancy distribution is a linear constraint on the number of sources. That is, for a small loss probability one can assume that each source transmits at a fixed rate called its effective bandwidth. When traffic parameters are known, effective bandwidths can be calculated and may be used to obtain a circuit-switched style call acceptance and routing algorithm for ATM networks. The important feature of the effective bandwidth of a source is that it is a characteristic of that source and the acceptable loss probability only. Thus, the effective bandwidth of a source does not depend on the number of sources sharing the buffer or the model parameters of other types of sources sharing the buffer     

Economies of scale for long‐range dependent traffic in short buffers

Consider the problem of predicting loss ratios for traffic streams sharing a buffer. Approximations based on the temporal statistical properties of single sources do not account for the economies of scale which can arise when there is statistical multiplexing gain across sources. These can occur whether the sources have long or short range dependence; in either case the economies may be positive or negative. In this paper we investigate this matter for sources described by fractional ARIMA processes, and show that their short‐range structure can mean that a simple power‐law tail based on the Hurst parameter alone can be over‐optimistic when the buffer space allocated per source is not large. This revised version was published online in June 2006 with corrections to the Cover Date.     

Finite Buffer Behavior with Poisson Arrivals and Random Server Interruptions

A queueing model with finite buffer size, Poisson arrival process, synchronous transmission and server interruptions is studied through a Bernoulli sequence of independent random variables. An integrated digital voice-data system with Synchronous Time-Division Multiplexing (STDM) for voice sources and Poisson arrival process for data messages is considered as an application for this model. The relationships among overflow probabilities, buffer size and expected queueing delay due to buffering for various traffic intensities are obtained. The results of this study are portrayed on graphs and may be used as guide lines for the buffer design in digital voice-data systems. Although this study arose in the design of a buffer for digital voice-data systems, the queueing model developed is quite general and may be useful for other industrial applications.     

Improved loss calculations at an ATM multiplexer

In this paper we develop a simple and accurate analytical technique to determine the loss probability at an access node to an asynchronous transfer mode (ATM) network. This is an important problem from the point of view of admission control and network design. The arrival processes we analyze are the Markov-modulated Poisson process (MMPP) and the Markov-modulated fluid (MMF) process. These arrival processes have been shown to model various traffic types, such as voice, video, and still images, that are expected to be transmitted by ATM networks. Our hybrid analytical technique combines results from large buffer theories and quasi-stationary approaches to analyze the loss probability of a finite-buffer queue being fed by Markov-modulated sources such as the MMPP and MMF. Our technique is shown to be valid for both heterogeneous and homogeneous sources. We also show that capacity allocation based on the popular effective-bandwidth scheme can lead to considerable under-utilization of the network and that allocating bandwidth based on our model can improve the utilization significantly. We provide numerical results for different types of traffic and validate our model via simulations     

A traffic control method for service quality assurance in an ATMnetwork

The authors describe an ATM traffic control method to avoid both long-term and short-term congestion. Call admission control and policing based on user-specified traffic parameters have mainly been studied as ways to avoid long-term congestion. However, these control methods are not practical since it is difficult for users to specify accurate values of traffic parameters that include the effects of cell collision controllers and multiplexers in the customer premises network. In order to solve the problem, they propose an intelligent call admission control method. This method consists of a function to determine user's traffic parameters by monitoring the cell traffic flow of each service and a function to statistically predict long-term congestion by using Gaussian and Poisson distributions. They show that congestion can be predicted by deriving the peak, average, and variation. They also describe how to derive traffic parameters and determine their values. To avoid short-term congestion, we propose reactive control, which drops cells with lower cell loss priority when congestion occurs, and we show the buffer construction and buffer control algorithm used to achieve this. Computer simulations prove that their control strategy is effective for cell toss sensitive services such as VBR (variable bit rate) video service     

Cell loss analysis and design trade-offs of nonblocking ATMswitches with nonuniform traffic

In practical ATM switch design, a proper dimensioning of buffer sizes and a cost effective selection of speed-up factor should be considered to guarantee a specified cell loss requirement for a given traffic. Although a larger speed-up factor provides better throughput for the switch, increasing the speed-up factor involves greater complexity and cost. Hence, it may not be cost effective to increase the speed-up factor for 100% throughput. Moreover, with a given buffer budget, an increase in the speed-up factor beyond a certain value only adds to the cell loss. The paper addresses design trade-offs existing between finite input/output buffer sizes and speed-up factor in a nonblocking ATM switch. Another important issue is the adverse effect on cell loss performance caused by nonuniform traffic (different traffic intensity and unevenly distributed routing). The paper analyzes cell loss performance of ATM switches with nonuniform traffic, and examines the effect of each nonuniform traffic parameter. The authors also provide an algorithm for effective buffer sharing that alleviates the performance degradation caused by traffic nonuniformity     

A new approach for allocating buffers and bandwidth toheterogeneous, regulated traffic in an ATM node

A new approach to determining the admissibility of variable bit rate (VBR) traffic in buffered digital networks is developed. In this approach all traffic presented to the network is assumed to have been subjected to leaky-bucket regulation, and extremal, periodic, on-off regulated traffic is considered; the analysis is based on fluid models. Each regulated traffic stream is allocated bandwidth and buffer resources which are independent of other traffic. Bandwidth and buffer allocations are traded off in a manner optimal for an adversarial situation involving minimal knowledge of other traffic. This leads to a single-resource statistical-multiplexing problem which is solved using techniques previously used for unbuffered traffic. VBR traffic is found to be divisible into two classes, one for which statistical multiplexing is effective and one for which statistical multiplexing is ineffective in the sense that accepting small losses provides no advantage over lossless performance. The boundary of the set of admissible traffic sources is examined, and is found to be sufficiently linear that an effective bandwidth can be meaningfully assigned to each VBR source, so long as only statistically-multiplexable sources are considered, or only nonstatistically-multiplexable sources are considered. If these two types of sources are intermixed, then nonlinear interactions occur and fewer sources can be admitted than a linear theory would predict. A qualitative characterization of the nonlinearities is presented. The complete analysis involves conservative approximations; however, admission decisions based on this work are expected to be less overly conservative than decisions based on alternative approaches     

An approximation for the loss probability in a multiserver queue fed by a shifting level process

A shifting level (SL) process is useful to traffic modeling because it is very easy to match the stationary distribution and autocorrelation function of the SL process with those of measured real traffics. Especially, SL processes have been used to traffic modeling for VBR video traffics reflecting the long range dependence and the scene structure. We give an approximation for the loss probability in a multiserver queue fed by a SL process. Numerical examples show that our approximation is very accurate.     

Statistical multiplexing and buffer sharing in multimediahigh-speed networks: a frequency-domain perspective

We study the effectiveness of statistical multiplexing and buffer sharing under the multimedia high-speed networking environment. We focus on the impact of frequency-domain source characteristics on dynamic resource sharing. By applying a novel statistical matching technique, we can, for the first time, investigate the multiplexing performance of a wide-range of realistic traffic sources using sophisticated traffic models. It has been shown that the effectiveness of statistical multiplexing and buffer sharing highly depends on the frequency-domain characteristics of the traffic as well as the corresponding QoS requirements. For practical “low-frequency” sources; e.g., VBR-video streams and LAN-to-LAN traffic, we show that significant savings in bandwidth and buffer-space can be achieved via resource sharing under practical loss and delay constraints. These findings re-illustrate the important role of traffic characteristics in the design/selection of network control strategies. The trade-offs among different design alternatives (e.g., multiplexing versus buffering) and the implications on some control schemes, e.g., traffic shaping/input-rate control, are also discussed     

ATM网络中CBR业务排队性能分析

分析了ATM网络中CBR业务排队性能,给出了一种简单的计算信元丢失率和信元平均时延的表达式.分析结果表明,一方面在较小的缓冲区容量下,即使CBR业务被分配的带宽大于等于其峰值速率,也还存在着较大的信元丢失;另一方面,当复用的CBR业务源数目很大时,只需要分配相对较小的缓冲区容量就可以满足十分低的信元丢失率要求.该结果对于ATM设备中相应的缓冲区设计、带宽分配以及连接允许控制机制的研究具有重要的意义.