MPEG VBR视频流—统计特性及其模型

该文分析了已有的MPEG VBR视频流模型及其缺点,并在此基础上对VBR视频流的统计特性进行了研究,实验结果表明,通过对整个视频流进行场景划分（聚类）,聚类间用Markov调制链建模,而每一聚类中独立的场景则可以采用TES模型基于GOP（Group Of Picture)而非帧进行建模,则该方法既能避免状态空间过大,又能避免帧间周期性的自相关,因而能够更好地拟合VBR视频流序列的一阶和二阶统计特性,同时,对独立场景的GOP分布函数可以采用Gamma函数进行拟合,自相关函数则可以采用双指数函数更好地拟合。     

A Markovian queue with varying number of servers and applications to the performance comparison of HSDPA user equipment

Inspired by the need for performability models for HSDPA user equipment, a Markovian queue with varying number of servers is conceived. The arrival and the service processes, the number of allocated or active servers of the queue are inherently, and independently (or jointly) Markov modulated. Batch arrivals, batch services, autocorrelation of inter-arrival times, and autocorrelation of batch sizes can be accommodated in the queue, by a suitable use of Markov modulation and generalized exponential distribution. The queue has a provision for negative customers too. Transformations of the balance equations into a computable form are proposed in order to obtain the steady state probabilities with the Spectral Expansion method. This queue is used to model the High Speed Downlink Packet Access (HSDPA) wireless networks. The model is an integrated one with respect to HSDPA, capable of accommodating many of the intricate aspects of HSDPA such as, channel allocation policy, loss of packets due to channel fading, bursty and correlated traffic. Good agreement is observed between the numerical results of the proposed analytical model and those of an independent simulator of real HSDPA and radio channel behaviors. The comparison of the terminal categories specified by the 3rd Generation Partnership Project (3GPP) is also presented.     

CIPP — a versatile analytical model for VBR traffic

Correlated interarrival time Poisson process (CIPP) has been proposed in Proceedings of the Fifth Biennial Conference on Signal Processing and Communications (SPCOM’99), IISc, Bangalore, July 1999, pp. 43–50; J. Indian Inst. Sci. 79 (3) (1999) 233–249] for modeling both the composite arrival process of packets in broadband networks and the individual video source modeling. The CIPP — a generalization of the Poisson process — is a stationary counting process and is parameterized by correlation parameter ‘ρ’, the degree of correlation in adjacent interarrivals and ‘λ’, the intensity of the process. In this paper, we develop the theory for CIPP/M/1 queue and undertake the performance modeling of statistical multiplexer with VBR video traffic in broadband networks using the CIPP/M/1 queue. We first derive the expressions for stationary distributions for queue length and waiting time in a CIPP/M/1 queue. Then, we derive the queuing performance measures of interest. For reasons of feasibility of theoretical performance modeling and realistic compulsions, we propose a deterministic smoothing with random (geometrically distributed) packet sizes. We simulate a queue with (thus smoothed) VBR video trace data as input to compare with the theoretical performance measures derived above. Experimental results show that the CIPP/M/1 queue models well the statistical multiplexer performance with the real-world MPEG-1 VBR video traffic input.     

A discrete-time round-robin queue with bernoulli input and general arithmetic service time distributions

Summary We present a discrete-time round-robin queue with a last-in-first-served rule: a newly arriving job receives a quantum of service immediately and only thereafter joins the tail of the queue. For Bernoulli input and general arithmetic service times we compute steady-state probabilities and mean response times.     

On the time scales in video traffic characterization for queueing behavior

To guarantee quality of service (QoS) in future integrated service networks, traffic sources must be characterized to capture the traffic characteristics relevant to network performance. Recent studies reveal that multimedia traffic shows burstiness over multiple time scales and long range dependence (LRD). While researchers agree on the importance of traffic correlation, there is no agreement on how much correlation should be incorporated into a traffic model for performance estimation and dimensioning of networks.In this article, we present an approach for defining a relevant time scale for the characterization of VBR video traffic in the sense of queueing delay. We first consider the Reich formula and characterize traffic by the Piecewise Linear Arrival Envelope Function (PLAEF). We then define the cutoff interval above which the correlation does not affect the queue buildup. The cutoff interval is the upper bound of the time scale which is required for the estimation of queue size and thus the characterization of VBR video traffic. We also give a procedure to approximate the empirical PLAEF with a concave function; this significantly simplifies the calculation in the estimation of the cutoff interval and delay bound with little estimation loss.We quantify the relationship between the time scale in the correlation of video traffic and the queue buildup using a set of experiments with traces of MPEG/JPEG-compressed video. We show that the critical interval, i.e. the range for the correlation relevant to the queueing delay, depends on the traffic load: as the traffic load increases, the range of the time scale required for estimation for queueing delay also increases. These results offer further insights into the implication of LRD in VBR video traffic.     

Stability, queue length, and delay of deterministic and stochasticqueueing networks

We present two types of stability problems: 1) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and 2) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate &thetas;. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and MER with respect to &thetas;. We also develop a set of rules for network operations such as superposition, input-output relation of a single queue, and routing. Specifically, we show that: 1) the MER of a superposition process is less than or equal to the sum of the MER of each process, 2) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, 3) the MER of a departure process from a stable queue is less than or equal to that of the input process, and 4) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to &thetas; under a further assumption of independence. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the first come, first served policy. Moreover, when restricting to the family of two-state Markov modulated arrival processes, the notion of MER with respect to &thetas; is shown to be equivalent to the recently developed notion of effective bandwidth in communication networks     

Traffic specifications for the transmission of stored MPEG video onthe Internet

Guarantees of quality-of-service (QoS) in the real-time transmission of stored video on the Internet is a challenging task for the success of many video on demand (VoD) applications. Two QoS classes have been specified by the IETF Integrated Services (intserv) Working Group: Guaranteed Services and Controlled-Load Services. For both of them, it is necessary to provide traffic sources with the capability of calculating the traffic characteristics to be declared to the network, Tspec, on the basis of a limited set of parameters statistically characterizing the traffic and the required level of QoS. The target of this paper is to develop an algorithm for the evaluation of the Tspec parameters which characterize the video stream when a given QoS is required. To this end an analytical framework modeling an MPEG stored-video server and the access network node is introduced. The video emission process is modeled with a switched batch Bernoulli process (SBBP), and performance in the video-server smoother is analytically evaluated. Then the token bucket at the network access point, loaded by the output traffic of the video-server smoother, is modeled to calculate the probability of marking nonconforming data packets     

Modeling buffer utilization in cell-based networks

Variable bit rate traffic is characteristically bursty and the arrivals are highly correlated. New network technology carries such traffic in cell-based networks where the service is a discrete time, deterministic process with the service rate determined by bandwidth negotiated by the user. Managing such networks is hard, and predicting cell loss at a station with limited buffer capacity K is essential to enable the user to negotiate his quality of service requirements. We present an analysis to determine the queue length distribution and the loss probability in such circumstances. For our analysis, we use an m-phase Markov Modulated Bernoulli Process with binomial distributed batch arrivals and deterministic service and limited capacity K, i.e. a MMBP^[X]_(m)/D/1 − K queuing system. We show that the system can be analyzed using the so-called unfinished work approach. The validity of our evaluation technique is illustrated by comparing our analytical results against those obtained from an event-driven siimulation of the same system.     

Performance analysis of wireless mobile networks with queueing priority and guard channels

The blocking probability of originating calls and forced termination probability of handoff calls are important criteria in performance evaluation of integrated wireless mobile communication networks. In this paper, we model call traffic in a single cell in an integrated voice/data wireless mobile network by a finite buffer queueing system with queueing priority and guard channels. We categorize calls into three types of service classes: originating voice calls, handoff voice calls and data calls. The arrival streams of calls are mutually independent Poisson processes, and channel holding times are exponentially distributed with different means. We describe the behavior of the system by a three‐dimensional continuous‐time Markov process and present the explicit expression for steady‐state distribution of queue lengths using a recursive approach. Furthermore, we calculate the blocking, forced termination probabilities and derive the Laplace–Stieltjes transform of the stationary distribution of actual waiting times and their arbitrary kth moment. Finally, we give some numerical results and discuss the optimization problem for the number of guard channels.     

Conditioned asymptotics for tail probabilities in large multiplexers

Consider a buffer whose input is a superposition of L independent identical sources, and which is served at rate sL. Recent work has shown that, under very general circumstances, the stationary tail probabilities for the queue of unfinished work Q in the buffer have the asymptotics P[Q > Lb] ≈ e^−LI(b) for large L. Here the shape function, I, is obtained from a variational expression involving the transient log cumulant generating function of the arrival process.

In this paper, we extend this analysis to cover time-dependent asymptotics for Markov arrival processes subject to conditioning at some instant. In applications we envisage that such conditioning would arise due to knowledge of the queue at a coarse-grained level, for example of the number of current active sources. We show how such partial knowledge can be used to predict future tail probabilities by use of a time dependent, conditioned shape function. We develop some heuristics to describe the time-dependent shape function in terms of a reduced set of quantities associated with the underlying arrivals process and show how to calculate them for renewal arrivals and a class of ON-OFF arrivals. This bypasses the full variational calculation of the shape function for such models.     

Analysis of a multi-server queue with two priority classes and (M, N)-threshold service schedule I: non-preemptive priority

In this paper, we propose an ( M , N )-threshold non-preemptive priority service schedule for a queueing system consisting of two-parallel queues and a multi-server. The arrival process for each queue is Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.     

Inferring the capacity of the vector Poisson channel with a Bernoulli model

The capacity defines the ultimate fidelity limits of information transmission by any system. We derive the capacity of parallel Poisson process channels to judge the relative effectiveness of neural population structures. Because the Poisson process is equivalent to a Bernoulli process having small event probabilities, we infer the capacity of multi-channel Poisson models from their Bernoulli surrogates. For neural populations wherein each neuron has individual innervation, inter-neuron dependencies increase capacity, the opposite behavior of populations that share a single input. We use Shannon's rate-distortion theory to show that for Gaussian stimuli, the mean-squared error of the decoded stimulus decreases exponentially in both the population size and the maximal discharge rate. Detailed analysis shows that population coding is essential for accurate stimulus reconstruction. By modeling multi-neuron recordings as a sum of a neural population, we show that the resulting capacity is much less than the population's, reducing it to a level that can be less than provided with two separated neural responses. This result suggests that attempting neural control without spike sorting greatly reduces the achievable fidelity. In contrast, single-electrode neural stimulation does not incur any capacity deficit in comparison to stimulating individual neurons.     

MPEG VBR video traffic modeling and classification using fuzzytechnique

We present an approach for MPEG variable bit rate (VBR) video modeling and classification using fuzzy techniques. We demonstrate that a type-2 fuzzy membership function, i.e., a Gaussian MF with uncertain variance, is most appropriate to model the log-value of I/P/B frame sizes in MPEG VBR video. The fuzzy c-means (FCM) method is used to obtain the mean and standard deviation (std) of T/P/B frame sizes when the frame category is unknown. We propose to use type-2 fuzzy logic classifiers (FLCs) to classify video traffic using compressed data. Five fuzzy classifiers and a Bayesian classifier are designed for video traffic classification, and the fuzzy classifiers are compared against the Bayesian classifier. Simulation results show that a type-2 fuzzy classifier in which the input is modeled as a type-2 fuzzy set and antecedent membership functions are modeled as type-2 fuzzy sets performs the best of the five classifiers when the testing video product is not included in the training products and a steepest descent algorithm is used to tune its parameters     

Performance evaluation and service rate provisioning for a queue with fractional Brownian input

The Fractional Brownian motion (fBm) traffic model is important because it captures the self-similar characteristics of Internet traffic, accurately represents traffic generated as an aggregate of many sources, which is a prevalent characteristic of many Internet traffic streams, and, as we show in this paper, it is amenable to analysis. This paper introduces a new, simple, closed-form approximation for the stationary workload distribution (virtual waiting time) of a single server queue fed by an fBm input. Next, an efficient approach for producing a sequence of simulations with finer and finer detail of the fBm process is introduced and applied to demonstrate good agreement between the new formula and the simulation results. This method is necessary in order to ensure that the discrete-time simulation accurately models the continuous-time fBm queueing process. Then we study the limitations of the fBm process as a traffic model using two benchmark models — the Poisson Pareto Burst Process model and a truncated version of the fBm. We determine by numerical experiments the region where the fBm can serve as an accurate traffic model. These experiments show that when the level of multiplexing is sufficient, fBm is an accurate model for the traffic on links in the core of an internet. Using our result for the workload distribution, we derive a closed-form expression for service rate provisioning when the desired blocking probability as a measure of quality of service is given, and apply this result to a range of examples. Finally, we validate our fBm-based overflow probability and link dimensioning formulae using results based on a queue fed by a real traffic trace as a benchmark and demonstrate an advantage for the range of overflow probability below 1% over traffic modelling based on the Markov modulated Poisson process.     

Traffic distortion and inter-source cross-correlation in high-speed integrated networks

In this paper we study the changes in individual source characteristics as traffic flows through a network. The effects of inter-source dependence caused by multiplexing at various network nodes are also investigated. Each traffic source is modeled as a 2-state or multiple-state Markov modulated process. Extensive simulations have been performed for homogeneous and heterogeneous traffic environments. Various network configurations have also been considered. We have identified the factors and parameters which have dominant effects on source distortions and inter-source cross-correlations. We also discuss the implications of our findings on the feasibility of decomposing the analysis of an ATM network into a set of separate nodal analyses.     

GOP ARIMA: Modeling the nonstationarity of VBR processes

In this work, we develop a stochastic model, GOP ARIMA (autoregressive integrated moving average for a group of pictures) for VBR processes with a regular GOP pattern. It explicitly incorporates the deterministic time-dependent behavior of frame-level VBR traffic. The GOP ARIMA model elaborately represents the inter- and intra-GOP sample autocorrelation structures and provides a physical explanation of observed stochastic characteristics of the empirical VBR process. We explain stochastic characteristics of the empirical VBR process, e.g., slowly decaying sample autocorrelations and strong correlations at the lags, based on the aspect of nonstationarity of the underlying process. The GOP ARIMA model generates synthetic traffic, which has the same multiplicative periodic sample autocorrelation structure as well as slowly decaying autocorrelations of the empirical VBR process. The simulation results show that the GOP ARIMA process very well captures the behavior of the empirical process in various respects: packet loss, packet delay, and frame corruption. Our work makes a contribution not only toward providing a theoretical explanation of the observed characteristics of the empirical VBR process but also toward the development of an efficient method for generating a more realistic synthetic sequence for various engineering purposes and for predicting future bandwidth requirements.     

MPEG-4 FGS视频流量模型的仿真应用研究

针对MPEG-4 FGS可伸缩的视频流量,采用马尔可夫链调制的一阶自回归方法对其统计特性进行建模,通过与Trace流量的仿真结果对比,证明了该模型的有效性。在此基础上,提出了基于FGS流量模型的层次化速率控制方法,在NS-2中将该方法与三种典型的CBR层次流量模型方法对分层视频组播RLM协议性能的影响进行了仿真实验对比。仿真结果表明：采用CBR模型来模拟MPEG-4 FGS层次流量对RLM协议进行性能仿真评价存在较大的误差,采用所提出的基于FGS流量模型的层次化速率控制方法对自适应视频组播协议的性能进行仿真具有更好的精确性。     

大时间尺度上MPEG4视频流量预测的自适应算法

为了保证用户的服务质量(QoS),宽带分组网络需要进行动态带宽分配,而视频流量预测在动态带宽分配中发挥着重要的作用。本文从自相关性、自相似性的Hurst参数两个方面,阐明图像组(GOP)时间尺度上的流量能够体现原有视频帧序列的流量特性,并在固定步长的LMS自适应算法(FSSA)的基础上提出了一种新的可变步长自适应算法(VSSA),在GOP所表示的大时间尺度上预测MPEG4视频流量。大量的仿真实验结果表明,VSSA算法可以明显地改善预测性能。     

The Geometry of M/D/1 Queues and Large Deviation

Since an M/D/1 queue is represented by a Markov chain, we can consider the set of all the M/D/1 queues as a subset of Markov chains. A geometric structure is induced from the geometric structure of the set of Markov chains, which forms an exponential family. In this paper, we show that in the large deviation of the tail probability of the queue length of an M/D/1, the rate function and a twisted Markov chain, etc., are represented in terms of the geometry. Moreover, in the importance sampling (IS) simulation for the M/D/1 queue, we elucidate the geometric relation between the underlying distribution and a simulation distribution, and evaluate the variance of an IS estimate by geometric quantities.