Sensitivity analysis for output performance measures in long-range dependent queueing system

In our previous work, we proposed the TNPOSS (To Next-hop Port Sequence Switch) network which can achieve scalable fast forwarding and is suitable for delivering multimedia flows. However, TNPOSS network has no Quality of Service (QoS) tools to provide better QoS guarantee for multimedia flows which often have long-range dependence (LRD) property. To enhance the QoS ability of TNPOSS network, this paper proposes a QoS-enhanced TNPOSS (QTNPOSS) network model by introducing Fractal Leak Bucket (FLB) shaper and Weighted Fair Queuing (WFQ) scheduler into the original TNPOSS network. In the new QTNPOSS network, each packet of multimedia flows is shaped by the FLB when arriving at a node and is scheduled by the WFQ before being outputted. Based on study above, we further analyze the end-to-end (E2E) delay bound of QTNPOSS network by means of the network calculus theory which is an effective mathematical tool on analyzing the worst-case QoS performances of networks. The service curve and the formulation of E2E delay bound of QTNPOSS network are presented and proved. Extensive numerical experiments show that both the LRD property of multimedia flows and the WFQ weight have influences on the E2E delay bound, and the WFQ weight influences the E2E delay bound more greatly than the LRD property does.

On the origins of long-range dependence in TCP traffic

Time series modeling and analysis provides means of predicting the future and has been widely used in a variety of fields ranging from seismology for predicting earthquake and volcanic eruption, to finance for risk assessment, and to quantum information processing. The conventional integer order models can only capture short-range dependence; for example, Poisson processes, Markov processes, autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) processes. In time series analysis, one of the conventional assumptions is that the coupling between values at different time instants decreases rapidly as the time difference or distance increases. However, there are situations where strong coupling between values at different times exhibit properties of long range dependence which cannot be processed by the conventional time series analysis. Typical examples of long range dependence signals include financial time series, underwater noise, electroencephalography (EEG) signal, etc. ARFIMA, a fractional order signal processing technique, is the generalization of the conventional integer order techniques, namely, ARIMA and ARMA methods. Hence, it is capable of capturing both short-range dependence and long-range dependence in signals. Compared to conventional integer order models, the ARFIMA model gives a better fit and result when dealing with the data which possess the long range dependence property. In this paper, we investigate the application of the ARFIMA as well as AR methods to model EEG signals obtained from different brain channels. We analyze the resulting correlations for comparison the benefits of ARFIMA over AR on the EEG data exhibiting the long range dependency property. The results showed that the prediction results have a better performance compared to the conventional ARMA models.

The Shape of the Loss Curve and the Impact of Long-Range Dependence on Network Performance

We analyze 20 large sets of actual variable-bit-rate (VBR) video data, generated by a variety of different codecs and representing a wide range of different scenes. Performing extensive statistical and graphical tests, our main conclusion is that long-range dependence is an inherent feature of VBR video traffic, i.e., a feature that is independent of scene (e.g., video phone, video conference, motion picture video) and codec. In particular, we show that the long-range dependence property allows us to clearly distinguish between our measured data and traffic generated by VBR source models currently used in the literature. These findings give rise to novel and challenging problems in traffic engineering for high-speed networks and open up new areas of research in queueing and performance analysis involving long-range dependent traffic models. A small number of analytic queueing results already exist, and we discuss their implications for network design and network control strategies in the presence of long-range dependent traffic. >

Long-range dependent (LRD) phenomena were first exhibited by Hurst for hydrology purposes. This phenomenon occurs from the superposition of independent sources, e.g. confluent rivers provide this behaviour (see Fig. 4.2). Such aggregation procedures provide this new phenomenon. Hurst (Trans Am Soc Civ Eng 116:770–799, 1951) originally determined the optimum dam sizing for the Nile river’s volatile rain and drought conditions observed over a long period of time. LRD is characterized by slow decorrelation properties and the behaviour of partial sums’s variances. This phenomenon is discussed above, see Sects. 4.3 and 4.4. Asymptotic properties of instantaneous functions of Gaussian processes are provided in Remark 5.2.4. Infinite moving averages models with LRD properties are provided in Sects. 6.4 and 6.6. We refer the reader to Doukhan et al. (Theory and applications of long-range dependence. Birkhauser, Boston, 2002b) for much more.

ABSTRACT: We develop and empirically test a parsimonious model of how specific knowledge and the value of knowledge sharing influence manufacturing plants' incentive design choices. Our results confirm the prediction that increases in the extent of agents' specific knowledge and the value of knowledge sharing are associated with greater (less) reliance on output (input) performance measures. Moreover, consistent with our model's prediction, we find that plants rely more on group-based (as opposed to individual-based) output performance measures when the value of knowledge sharing is higher, or the extent of agents' specific knowledge is lower. Finally, consistent with previous research, we find that as output performance measures become noisier, firms rely less on these measures in incentive contracts.

There is mounting experimental evidence that network traffic processes exhibit ubiquitous properties of self-similarity and long range dependence (LRD), i.e. of correlations over a wide range of time scales. However, there is still considerable debate about how to model such processes and about their impact on network and application performance. In this paper, we argue that much recent modeling work has failed to consider the impact of two important parameters, namely the finite range of time scales of interest in performance evaluation and prediction problems, and the first-order statistics such as the marginal distribution of the process.We introduce and evaluate a model in which these parameters can be easily controlled. Specifically, our model is a modulated fluid traffic model in which the correlation function of the fluid rate is asymptotically second-order self-similar with given Hurst parameter, then drops to zero at a cutoff time lag. We develop a very efficient numerical procedure to evaluate the performance of the single server queue fed with the above fluid input process. We use this procedure to examine the fluid loss rate for a wide range of marginal distributions, Hurst parameters, cutoff lags, and buffer sizes.Our main results are as follows. First, we find that the amount of correlation that needs to be taken into account for performance evaluation depends not only on the correlation structure of the source traffic, but also on time scales specific to the system under study. For example, the time scale associated to a queueing system is a function of the maximum buffer size. Thus for finite buffer queues, we find that the impact on loss of the correlation in the arrival process becomes nil beyond a time scale we refer to as the correlation horizon. Second, we find that loss depends in a crucial way on the marginal distribution of the fluid rate process. Third, our results suggest that reducing loss by buffering is hard. We advocate the use of source traffic control and statistical multiplexing instead.

In this paper, we propose a fractional stochastic volatility jump-diffusion model which extends the Bates(1996) model. Where we model the volatility as a fractional process. Extensive empirical studies show that the distributions of the logarithmic returns of financial asset usually exhibit properties of self-similarity and long-range dependence and since the fractional Brownian motion has these two important properties, it has the ability to capture the behavior of underlying asset price. Further incorporating jumps into the stochastic volatility framework gives further freedom to financial mathematicians to fit both the short and long end of the implied volatility surface. We propose a stochastic model which contains both fractional and jump process. Then we price options using Monte Carlo simulations along with a variance reduction technique(antithetic variates). We use market data from the S&P 500 index and we compare our results with the Heston and Bates model using error measures. The results show our model greatly outperforms previous models in terms of estimation accuracy.

A packet switched network such as the Internet provides only the best-effort service for users. Recent studies of the characteristics of packet arrival on a packet switched network have shown a self-similar property with long-range dependence, and also show a heavy-tailed distribution. This paper investigates end-to-end performance of the Internet empirically. It focuses on the inter-arrival process of packets and the property of packet loss between end-to-end hosts. We show that both the inter-arrival process and loss events are self-similar with a long-range dependence property. The inter-arrival process of packets has a heavy-tailed distribution which sums up the difference of all queues in intermediate routers.

Two different kinds of heavy-traffic limit theorems have been proved for s-server queues. The first kind involves a sequence of queueing systems having a fixed number of servers with an associated sequence of traffic intensities that converges to the critical value of one from below. The second kind, which is often not thought of as heavy traffic, involves a sequence of queueing systems in which the associated sequences of arrival rates and numbers of servers go to infinity while the service time distributions and the traffic intensities remain fixed, with the traffic intensities being less than the critical value of one. In each case the sequence of random variables depicting the steady-state number of customers waiting or being served diverges to infinity but converges to a nondegenerate limit after appropriate normalization. However, in an important respect neither procedure adequately represents a typical queueing system in practice because in the (heavy-traffic) limit an arriving customer is either almost certain to be delayed (first procedure) or almost certain not to be delayed (second procedure). Hence, we consider a sequence of (GI/M/S) systems in which the traffic intensities converge to one from below, the arrival rates and the numbers of servers go to infinity, but the steady-state probabilities that all servers are busy are held fixed. The limits in this case are hybrids of the limits in the other two cases. Numerical comparisons indicate that the resulting approximation is better than the earlier ones for many-server systems operating at typically encountered loads.

This paper considers subexponential asymptotics of the tail distributions of waiting times in stationary work-conserving single-server queues with multiple Markovian arrival streams, where all arrival streams are modulated by the underlying Markov chain with finite states and service time distributions may differ for different arrival streams. Under the assumption that the equilibrium distribution of the overall (i.e., customer-average) service time distribution is subexponential, a subexponential asymptotic formula is first shown for the virtual waiting time distribution, using a closed formula recently found by the author. Further when customers are served on a FIFO basis, the actual waiting time and sojourn time distributions of customers from respective arrival streams are shown to have the same asymptotics as the virtual waiting time distribution.

<p>Since the fractional $ G $-Brownian motion (fGBm) generalizes the concepts of the standard Brownian motion, fractional Brownian motion, and $ G $-Brownian motion, while it can exhibit long-range dependence or antipersistence and feature the volatility uncertainty simultaneously, it can be a better alternative stochastic process in the financial applications. Thus, in this paper, some empirical studies for the financial applications of the fGBm were carried out, where the recent high-frequency data for some selected assets in the financial market are from the Oxford-Man Institute of Quantitative Finance Realized Library. There are two main empirical findings. One was that the H-$ G $-normal distributions associated with the fGBm are more suitable in describing the dynamics of daily returns and increments of log-volatility for these assets than the usual distributions, since they not only characterize the properties of skewness, excess kurtosis, and long-range dependence $ \left(\frac{1}{2} < H < 1\right) $ or antipersistence $ \left(0 < H < \frac{1}{2}\right) $, but also feature the volatility uncertainty. The other one was that the daily return and log-volatility both behave essentially as fGBm with different $ \underline{\sigma}^2 $ and $ \overline{\sigma}^2 $, but Hurst parameters $ H < \frac{1}{2} $, at any reasonable time scale. Then a generalized stochastic model for the dynamics of the assets called rough fractional stochastic volatility model driven by fGBm (RFSV-fGBm) was developed. Finally, some parameter estimates and numerical experiments for the RFSV-fGBm model were investigated and carried out.</p>

While in recent years backbone bandwidth has experienced substantial growth, little has changed in the access network. “Last mile” still remains the bottleneck between a high capacity LAN or home network and the backbone. Passive optical network (PON) is a technology viewed by many as an attractive solution to this problem. In this study, we discuss and evaluate design issues for PON access networks. Specifically, to drive the cost of an access network down, it is very important to have an efficient, scalable solution. We believe that a PON based on polling, with data encapsulated in Ethernet frames, possesses the best qualities, such as dynamic bandwidth distribution, use of a single downstream and a single upstream wavelength, ability to provision a fractional wavelength capacity to each user, and ease of adding a new user. To support dynamic bandwidth distribution, we propose an interleaved polling algorithm. We then suggest a scheme for in-band signaling that allows using a single wavelength for both downstream data and control message transmission. To obtain realistic simulation results, we generated synthetic traffic that exhibits the properties of self-similarity and long-range dependence. We then analyzed the network performance and its effect on various types of traffic, e.g., best-effort data traffic, VBR video traffic and CBR streams.

With the rapid development of the network, more and more new kinds of network traffic emerge in the network. These new traffic exhibit the properties of self-similarity and long-range dependence. Connection Admission Control (CAC) is one of the important mechanisms for guarantee the QoS while improving the utilization rate high-efficiently. At first, self-similar traffic service model based on CAC scheme in this paper are studied. And then the formula for effective bandwidth of admitted aggregated traffic sources is got. A CAC algorithm of self-similar traffic based on fairness is proposed. The equality mechanism is introduced in the admitting deterministic process. Simulation has analyzed the factors of effective bandwidth and has proved the validity of the algorithm.