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Analysis of an ATM Buffer with Self-Similar ("Fractal") Input Traffic
Abstract
As ATM high-speed, cell-relay networks will most likely first make their impact as backbones interconnecting enterprise networks consisting of Ethernet and other LANs, their proper design and control is crucial. Recent studies of high quality, high resolution traffic measurements in Bellcore Ethernets have revealed that this aggregate Ethernet traffic is self-similar ("fractal ") in nature, quite different in "burstiness" features from traffic considered and studied up to now. This paper presents an analytical study of an ATM buffer driven with self-similar traffic. The probability of buffer occupancy is obtained. It is shown that this probability decreases with the buffer size not exponentially, as in traditionally Markovian traffic models, but algebraically . 1 Introduction Recent studies of high-quality, high resolution traffic measurements have revealed a new phenomenon with potentially important ramifications to the modeling, design and control of broadband networks. These includ...
... An important theoretical result is the one obtained by Likhanov et. al. 19 . It is described here in a rather informal way. ...
... Most of this information is from Likhanov et. al. 19 . ...
... We are using the approach in Likhanov et. al. 19 . The following relation gives the loss probability in a nite capacity queue: ...
... Therefore, Integrated scheduling algorithm is more conducive to guaranteeing QoS of heterogeneous traffic For another thing, different traffic always has different burst level, the stronger the burst, the larger the buffer increment. To be specific, Many high-quality measurement studies have proved that the traffic of real-world multimedia applications exhibits heterogeneous characteristics and can be divided into two distinct categories, namely SRD and LRD traffic, respectively [17], [18]. Meanwhile, there are significant differences in buffer size requirements for heterogeneous traffic. ...
Buffer sizing of switching and routing devices is of significance to guarantee QoS of critical services in Internet of Things (IoT), continuously evolving scheduling mechanism and complex traffic characteristics pose new challenges to the traditional method of static buffer sizing based on the rule-of-thumb. In this paper, the scope of buffer sizing is extended from simple scheduling system under single traffic to integrated scheduling system under heterogeneous traffic input which is more ubiquitous. Voices, videos and other heterogeneous data in IoT are categorized into Short-Range Dependent (SRD) and Long-Range Dependent (LRD) traffic, and the integrated scheduling system is decomposed into Single-Server Single-Queue (SSSQ) systems, not only decoupling the complex dependence between heterogeneous traffic, but also taking into account the impact of SRD and LRD traffic burstiness on buffer size. On this basis, the expressions of relation between the minimum buffer size and overflow probability are derived in detail are presented. The numerical results show that the average rate, burst level and scheduling priority are positively correlated with the required buffer size, and when the overflow probability is set, the minimum buffer size is determined respectively. The achievements of this paper will provide a theoretical guidance for IoT manufacturers and technicians to set the optimal IoT devices buffer size.
... En[15] y[16] se demuestra el carácter autosimilar del tráfico en redes WAN, mientras que en[17] se coloca de manifiesto la naturaleza fractal del flujo de los datos de los protocolos componentes del sistema de señalización número 7 (SS7) en redes de señalización de canal común, en[18] se demuestra la naturaleza autosimilar del tráfico debida al WWW, y en[19] y[20], en el tráfico de video de tasa variable (VBR).En[21] se demuestra que la distribución de probabilidad que sigue el tamaño de la cola de un multiplexor, exhibe una caída asintótica del tipo Weibull al utilizar como tráfico de entrada cierto tipo de procesos autosimilares, y en[22] que esta caída puede ser aún más lenta y de tipo hiperbólico utilizando otros procesos autosimilares.En[23] se demuestra que el ancho de banda efectivo calculado sobre la base de modelos de Markov en los cuales la distribución del tamaño de la cola presenta una caída exponencial, subestima con creces la tasa de pérdida de celdas en varios órdenes de magnitud.En el análisis de un multiplexor de voz y datos, expuesto en[24] se demuestra una excepcional correlación positiva de largo alcance en el tráfico agregado, obteniendo retardos muy superiores a los predichos con modelos de Poisson.Finalmente, en[25] se demuestra que el número de llegadas en intervalos de tiempo adyacentes, que resultan de la superposición de múltiples fuentes de voz independientes, homogéneas tratadas mediante modelos de procesos de renovación, es un proceso con fuertes correlaciones, que posee un impacto significativo sobre las prestaciones del sistema de comunicaciones bajo estudio.Lo interesante de estos y otros muchos estudios es que colocan sobre relieve el impacto que la dependencia temporal de largo alcance, intrínseca a los más diversos tipos de tráfico, tiene sobre las prestaciones de las redes de comunicaciones frente a los modelos que no presentan correlación temporal por simplicidad analítica (como los procesos de renovación), o exhiben una estructura de correlación más complicada analíticamente (como los modelos de Markov o auto-regresivos habituales), que pueden ser denominados como modelos de corto alcance. Además, el principal inconveniente que presentan la totalidad de los modelos tradicionales, es que requieren un número muy elevado de parámetros para modelar las fuertes correlaciones existentes entre los diferentes tipos de tráficos en una red. ...
The foundation of a research project about a model of computer networks with media access control mechanism based on the IEEE standard 802.3-2005 is presented. The model draws from the theory of self-similar sets for establishing the impact level that the long-range-dependent temporary correlations have on the performance of such networks. A new method for the estimation of self-similar levels based on a variation of the Whittle estimator is postulated.
... esta sea, puede ser magnificada para reproducir exactamente una porción mayor. Esta propiedad se conoce con el nombre de "autosimilaridad exacta" [26]. No se pretende observar en un proceso altamente aleatorio como el de las llegada de paquetes a una red de datos, características autosimilares exactas, pero si se considera el tráfico observado como trazas de muestras pertenecientes a un proceso estocástico y se restringe la similitud solo a ciertas estadísticas específicas de las series temporales pero ajustadas en escala, se descubre autosimilaridad exacta en objetos matemáticos abstractos y autosimilaridad aproximada para cada realización específica que se considere. ...
An hypothesis for the existence of a process with long term memory structure, that represents the independence between the degree of randomness of the traffic generated by the sources and the pattern of traffic stream exhibited by the network is presented, discussed and developed. This methodology is offered as a new and alternative way of approaching the estimation of performance and the design of computer networks ruled by the standard IEEE 802.3-2005.
... El comportamiento autosimilar LRD de los flujos de tráfico en las actuales redes de computadoras de alta velocidad es un hecho ampliamente reportado para topologías de diferentes niveles de coberturas (Leland et al., 1994;Paxson and Floyd, 1995;Crovella and Bestavros, 1997;Arlitt and Jin, 2000); tecnologías y técnicas de transmisión (Ge et al., 2000;Liang, 2002;Huang et al., 2005;Fantacci and Tarchi, 2006;Huang et al., 2007;Maier, 2008); protocolos de control y de señalización (Duffy et al., 1994;Pruthi and Erramilli, 1995); aplicaciones de video, especialmente de tasa de bits variable, (Garrett and Willinger, 1994;Beran et al., 1995;Yellanki, 1999, Narasimha andRao, 2002;Narasimha and Rao, 2003), sistemas de colas en redes ATM (Norros, 1994;Likhanov et al., 1995;Tsybakov and Georganas, 1997;Jin et al., 2002); y en comunicaciones inalámbricas (Yu, 2005;Ridoux et al., 2006, Radev andLokshina, 2009;Yeryomin and Petersons, 2011). ...
Este trabajo presenta, desarrolla y discute la existencia de un proceso con estructura de memoria de largo alcance, representativo de la independencia entre el grado de aleatoriedad del tráfico generado por las fuentes y del patrón de flujo exhibido por la red, en términos de una nueva variante algorítmica del estimador de máxima verosimilitud (MLE) de Whittle para el cálculo del exponente de Hurst (H) de las series temporales autosimilares de segundo orden estacionarias representativas de los flujos tanto de las fuentes individuales como de su agregación. Se discute además la problemática adicional introducida por el fenómeno de la localidad del exponente de Hurst, que se presenta cuando los flujos de tráfico se componen de diversos elementos con diferentes exponentes de Hurst. Se expone esta instancia con el ánimo de ser considerada como una forma nueva y alternativa para abordar el modelado y simulación del tráfico en las actuales redes de computadoras.
... esta sea, puede ser magnificada para reproducir exactamente una porción mayor. Esta propiedad se conoce con el nombre de "autosimilaridad exacta" [26]. No se pretende observar en un proceso altamente aleatorio como el de las llegada de paquetes a una red de datos, características autosimilares exactas, pero si se considera el tráfico observado como trazas de muestras pertenecientes a un proceso estocástico y se restringe la similitud solo a ciertas estadísticas específicas de las series temporales pero ajustadas en escala, se descubre autosimilaridad exacta en objetos matemáticos abstractos y autosimilaridad aproximada para cada realización específica que se considere. ...
An hypothesis for the existence of a process with long term memory structure, that represents the independence between the degree of randomness of the traffic generated by the sources and the pattern of traffic stream exhibited by the network is presented, discussed and developed. This methodology is offered as a new and alternative way of approaching the estimation of performance and the design of computer networks ruled by the standard IEEE 802.3-2005.
... But traffic then changed and it was necessary to understand how and why. This model started to be seriously questioned from 1993 onwards, results from the work of Leland, Taqqui, Willinger and Wilson [43], on traffic in Ethernet LAN and followed by other works related to packet traffic [26], [27], [28], namely: Ethernet Local Network [44], Wide Area Network (WAN) [19], [57], Variable bit rate video (VBR) over Asynchronous Transmission Mode (ATM) [13], [33], [45], [62]; CCSN/SS7 [25], multiplexers [54], cellular networks [29], storage models [51], and Integrated Services Digital Network (ISDN) [28]. These works and others [7], [18], [72] showed that, contrary to the Poisson traffic model, the actual traffic of these networks, when observed on multiple timescales, does not smoothinstead, it displays peaks across multiple scales of observation time, when compared to traffic with SRD characteristics. ...
The knowledge about the true nature of the traffic in computer networking is a key requirement in the design of such networks. The phenomenon of self-similarity is a characteristic of the traffic of current client/server packet networks in LAN/WAN environments dominated by network technologies such as Ether- net and the TCP/IP protocol stack. The development of networks traffic simulators, which take into account this attribute, is necessary for a more realistic description the traffic on these networks and their use in the design of resources (contention elements) and protocols of flow control and network congestion. In this scenario it is recommended do not adopt standard traffic models of the Poisson type.
... The work of [10] demonstrated that the network traffic shows self-similar pattern. We verified their results specifically for live streaming multimedia. ...
This paper studies the statistical nature of TV channels streaming variable bit rate distribution and allocation. The goal of the paper is to derive the best-fit rate distribution to describe TV streaming bandwidth allocation, which can reveal traffic demands of users. Our analysis uses multiplexers channel bandwidth allocation (PID) data of 13 TV live channels. We apply 17 continuous and 3 discrete distributions to determine the best-fit distribution function for each individual channel and for the whole set of channels. We found that the generalized extreme distribution fitting most of our channels most precisely according to the Bayesian information criterion. By the same criterion tlocationscale distribution matches best for the whole system. We use these results to propose parameters for streaming server queuing model. Results are useful for streaming servers scheduling policy design process targeting to improve limited infrastructural resources, traffic engineering through dynamic routing at CDN, SDN.
... The work of [10] demonstrated that the network traffic shows self-similar pattern. We verified their results specifically for live streaming multimedia. ...
... Information-theoretic approaches and compression methodologies have already been proven successful in capturing entropy in other domains such as email [29], or comment [30] spam filtering, or estimating neural discharges [31]. The study of traffic patterns and the design of models is an evergreen topic of high relevance in the networking literature, and examples where measurement studies spurred much research into traffic modeling dates back to the 1990s [32,33,34]. Since then, a large number of methodologies have been developed [35,36,37], based on temporal statistics [38,39,40], spatial statistics [41,42], and physical [43] and information-theoretic [44,45] models. ...
This paper studies the structure of several real-world traces (including Facebook, High-Performance Computing, Machine Learning, and simulation generated traces) and presents a systematic approach to quantify and compare the structure of packet traces based on the entropy contained in the trace file. Insights into the structure of packet traces can lead to improved network algorithms that are optimized toward specific traffic patterns. We then present a methodology to quantify the temporal and non-temporal components of entropy contained in a packet trace, called the trace complexity, using randomization and compression. We show that trace complexity provides unique insights into the characteristics of various applications and argue that there is a need for traffic generation models that preserve the intrinsic structure of empirically measured application traces. We then propose a traffic generator model that is able to produce a synthetic trace that matches the complexity level of its corresponding real-world trace.
... Both properties were discovered in Beran et al. [3] for variable-bit-rate (VBR) video traffic, in Paxson et al. [23] for traffic in wide area networks, in the landmark papers Leland et al. [14] and Willinger et al. [32] for Ethernet networks, and in Crovella et al. [6] for Web traffic, all these classical studies today. The finding of self-similarity and LRD, in turn, spurred the research on queueing models with "fractal" input traffic Norros [21] and Likhanov et al. [16], and the assessment of their impact on network performance Conti et al. [4] and Erramilli et al [9] as well. As these works demonstrate, the effect of LRD on packet loss and delay may be drastic, leading to subexponential decay of the buffer overflow probability and, consequently, buffer sizes much larger than those predicted by memoryless or short-memory processes. ...
Simulations with long-memory input processes are hindered both by the slowness of convergence displayed by the output data and by the high computational complexity of the on-line methods for generating the input process. We present an optimized algorithm for simulating efficiently the occupancy process of the M/G/∞ system, which can be used as a sequential pseudo-random number generator of a broad class of long-memory sample paths. Our previous approach is the decomposition of the service time distribution as a linear combination of memoryless random variables, plus a residual term. Then, the original M/G/∞ system is replaced by a number of parallel, independent, virtual and easier to simulate M/G/∞ subsystems, the dynamics of which can be replicated sequentially or in parallel too. In this work we improve our previous algorithm, taking into account the generation time of the random variables.
... The literature [17] proved that M/Pareto model can be seen as a large number of independent ON/OFF model with heavy-tailed distribution, and the ON/OFF model with the following characteristics can be convenient to describe the real network traffic. Firstly, a single traffic contains random data packet bursts, and the length of the bursts follows the heavytailed distribution, decay rate obeys the Pareto distribution, after the completion of the burst generated, a silent period of random time is maintained. ...
Modelling WiMAX network traffic based on the self-similarity character is better than the traditional model based on the Poisson process, because the former can provide more accurate calculation for effective bandwidth. In this paper we propose a WiMAX network traffic model based on M/Pareto model to describe its self-similarity character. Then we deduce the average transmission rate and the variance coefficient for the FBM traffic model by the M/Pareto model, and get the Hurst parameter of the FBM traffic model by statistical analysis method. By the FBM traffic model we get a formula for calculating the effective bandwidth. Accordingly, we propose a modified self-similar call admission control algorithm (SS-CAC). SS-CAC can avoid measuring the parameter values of FBM traffic flow to do call admission control. Simulation results show that SS-CAC greatly reduces the call blocking rate and improves the bandwidth utilization.
... In the simulation model Poisson traffic was generated by exponential distribution. Multiplexed ON-OFF model [9] was used in order to generate self-similar traffic. In this model many ON-OFF traffic sources are multiplexed. ...
Providing a Quality of Services (QoS) into current telecommunication networks based on packet technology is a big challenge nowadays. Network operators have to support a number of new services like voice or video which generate new type of traffic. This traffic serviced with QoS in consequence requires access to appropriate network resources. Additionally, new traffic type is mixed with older one, like best-effort. Analysis of these new and mixed traffic types shows that this traffic is self-similar. Network mechanisms used for delivery of quality of services may depend on traffic type especially from the performance point of view. This paper presents a feasibility study done into the effect of traffic type influence on performance of routing algorithm while the routing algorithm is treated as one of the mechanisms to support QoS in the network.
... EEG and reduce packet loss rate [10, 11]. On this basis, some papers put forward the relationship between cache size and lower bound of limited bandwidth within the constraints of packet loss rate [12]. ...
In the body sensor networks (BSN), sensor nodes transmit data to remote receiving terminal via sink node. During the process of data aggregation, interference and self-similar character of wireless business have significant influence on traffic queue performance of sink node. To balance traffic quality of service (QoS) requirement and system present available resource and decide optimum resource distribution project. Hence, a complex function of sink node cache length, distributed channel rate and packet loss probability, and queue delay is built in this paper. Based on the function, by combining multiple target optimizing method and considering joint constraint of queue delay and packet loss probability, we proposed an admission control method based on traffic aggregation QoS constraint. In a BSN consisting of a large amount of sensor nodes, by admission control of sink node, reasonable acceptance of new nodes, and distribution sink node resource, the method we proposed can meet needs of important parameters in WSN design.
... On state time is determined through Pareto distribution, Off state time is determined through exponential distribution. This model is described in detail in [8]. ...
Feasibility studies with QoS routing proved that the network traffic type has influence on routing performance. In this work influence of self-similar traffic for network with DiffServ architecture and OSPF QoS routing has been verified. Analysis has been done for three traffic classes. Multiplexed On-Off model was used for self-similar traffic generation. Comparison of simulation results was presented using both relative and non-relative measures for three traffic classes. Results were commented and analyzed. The basic conclusion is that performance for streaming and best-effort class for self-similar traffic is higher than performance for the same class with exponential traffic (Poisson). The other important conclusion is relation between performance differences and offered traffic amount.
... Pero en cualquier caso, estos modelos, fundamentalmente markovianos, desprecian la correlación a partir de una determinada separación temporal, aun cuando esta pueda ser arbitrariamente aumentada a costa de complicar el modelo con parámetros adicionales y disminuir con ello la plausibilidad de interpretarlos físicamente. Se informa a continuación un conjunto de resultados relevantes, referentes sin parangón de lo planteado.En[1] se demuestra tras exhaustivas mediciones sobre una red Ethernet, que el tráfico, entendido como el número de tramas en la red por unidad de tiempo, presenta naturaleza autosimilar o fractal, lo cual pone al descubierto la existencia de una acusada correlación de largo alcance.En[15] y[16] se demuestra el carácter autosimilar del tráfico en redes WAN, mientras que en[17] se coloca de manifiesto la naturaleza fractal del flujo de los datos de los protocolos componentes del sistema de señalización número 7 (SS7) en redes de señalización de canal común, en[18] se demuestra la naturaleza autosimilar del tráfico debida al WWW y en[19] y[20], el tráfico de video de tasa variable (VBR).En[21] se demuestra que la distribución de probabilidad que sigue el tamaño de la cola de un multiplexor, exhibe una caída asintótica del tipo Weibull al utilizar como tráfico de entrada cierto tipo de procesos autosimilares y en[22] que esta caída puede ser aún más lenta y de tipo hiperbólico utilizando otros procesos autosimilares.En[23] se demuestra que el ancho de banda efectivo calculado sobre la base de modelos de Markov, en los cuales la distribución del tamaño de la cola presenta una caída exponencial, subestima con creces la tasa de pérdida de celdas en varios órdenes de magnitud.En el análisis de un multiplexor de voz y datos expuesto en[24], se demuestra una excepcional correlación positiva de largo alcance en el tráfico agregado, obteniendo retardos muy superiores a los predichos con modelos de Poisson.Finalmente, en[25] se demuestra que el número de llegadas en intervalos de tiempo adyacentes, resultante de la superposición de múltiples fuentes de voz independientes, homogéneas tratadas mediante modelos de procesos de renovación, es un proceso con fuertes correlaciones, que posee un impacto significativo sobre las prestaciones del sistema de comunicaciones bajo estudio.Lo interesante de estos y otros muchos estudios es que colocan sobre relieve el impacto que la dependencia temporal de largo alcance, intrínseca a los más diversos tipos de tráfico, tiene sobre las prestaciones de las redes de comunicaciones frente a los modelos que no presentan correlación temporal por simplicidad analítica (como los procesos de renovación), o exhiben una estructura de correlación más complicada analíticamente (como los modelos de Markov o autorregresivos habituales), que pueden ser denominados como modelos de corto alcance. Además, el principal inconveniente que presentan la ...
The foundation of a research project about a model of computer networks with media access control mechanism based on the IEEE standard 802.3-2005 is presented. The model draws from the theory of self-similar sets for establishing the impact level that the long-range-dependent temporary correlations have on the performance of such networks. A new method for the estimation of self-similar levels based on a variation of the Whittle estimator is postulated.
... Currently a large body of literatures investigate the loss ratio where the service rate is deterministic and the arrival process has long memory property (e.g., see 4,8,10,13]). These studies focus on how to guarantee the maximum CLR for VBR tra c. ...
In this paper, we give a flow control algorithm which guarantees maximum cell loss ratio for a buffer unit in a switch. The algorithm relies on explicit-rate-based available-bit-rate flow control and will converge to the equilibrium satisfying max-min fairness within finite time interval. We also propose a buffer management scheme bounding the cell loss ratio for the low-loss-ratio traffic when the traffic have two loss-ratio priorities. This buffer management scheme also preserves the cell ordering. The simulation shows that our algorithm bounds the cell loss ratio above by a given constant and converges to a new equilibrium very fast. In addition, the utilization of the link with large link capacity, such as 149.76Mbps, with buffer size to be 2000 cells, is more than 95% when the given upper bound for the cell loss ratio is 1%. Keywords: fractional ARIMA model and prediction, available-bit-rate flow control, queue length distribution approximation. 1 Introduction Transmitting dat...
... There is a rapidly growing literature on this topic at the interface of data analysis and performance evaluation. The interested reader will nd additional material in 3,4,6,9,11,12,14,18,20,27,29,33,34], to only list a few references. ...
The impact of unsmoothed traffic on the performance of a simple queueing system is investigated in this paper. Under the assumption that the input process to the queue is a Cox process we show that the distribution of the buffer occupancy (representing, for instance, the number of packets waiting for transmission in a router in the networking setting) has a heavy tail when burst lengths are themselves heavy-tailed. This result is in sharp contrast to the exponential decay rate of the tail distribution of the buffer occupancy in presence of smoothed traffic (e.g. Poisson-like traffic).
... In [15] the Poisson arrival rate, link rate, and buffer size are scaled as nλ, C ≡ nc, and B ≡ nb, respectively, with n growing large; this regime allows explicit asymptotic analysis as results from large-deviations theory become applicable. Related results are given in Likhanov et al. [27] and Liu et al. [28]. ...
We consider a fluid queue fed by the superposition of n homogeneous on-off sources with generally distributed on and off periods. The buffer space B link rate C are scaled by n, so that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n. We specifically examine the scenario where b is also large. We obtain explicit asymptotics for the case where the on periods have a subexponential distribution e.g., Pareto, Lognormal, or Weibull. The results show a sharp dichotomy in the qualitative behavior, depending on the shape of the function v(t) qq -log P(A* > t) for large t, A* representing the residual on period. If v(·) is regularly varying of index 0 (e.g., Pareto, Lognormal), then, during the path to overflow, the input rate will only slightly exceed the link rate. Consequently, the buffer will fill 'slowly', and the typical time to overflow will be 'more than linear' in the buffer size. In contrast, if v(·) is regularly varying of index strictly between 0 and 1 (e.g., Weibull), then the input rate will significantly exceed the link rate, and the time to overflow is roughly to the buffer size. In both cases there is a substantial fraction of the sources that remain in the on state during the entire path to overflow, while the others contribute to their mean rates. These observations lead to approximations for the overflow probability. The approximations may be extended to the case of heterogeneous sources. The results provide further insight into the so-called reduced-load approximation.
... Self-similarity degrades the overall performance of the network by affecting its quality of service and capacity utilization. Quite number of models had been developed to address self-similarity issues on internet network since its discovery, but still situation prevails due to the huge or the varying nature of the input characteristics [10]. Therefore, when we want to study the self-similar nature of traffic of all kinds on internet network usually question of constructing a model of input characteristics (volume of the traffic) arise [4][11]. ...
In this work, four different sets of data traffic have been generated from fractional brownian motion (fBm) to estimate true values of Hurst exponent boundaries in order to determine the degree of self-similarity in terms of long range dependence (LRD). One-dimensional multilevel wavelet decomposition and filtering algorithm is applied to filter fractional Gaussian noise (fGn) in the fBm generated. Autocorrelation function (ACF) and fast Fourier transform (FFT) energy spectrum is used to validate the result of the filtering effect. The result of the filtering process revealed that fGn in the fBm is de-noised successfully as the coefficient of ACF grow above zero and energy rate in the FFT-spectrum increases tremendously Keywords—fBm, ACF, FFT, LRD Hurst exponent and self-similarity.
... Both properties were discovered in Beran et al (1995) for variable-bit-rate (VBR) video traffic, in Paxson and Floyd (1995) for traffic in wide area networks, in Leland et al (1994) and Willinger et al (1997) for Ethernet networks and in Crovella and Bestavros (1997) for Web traffic. The finding of self-similarity and LRD, in turn, spurred the research on queueing models with 'fractal' input traffic (Likhanov et al, 1995;Norros, 1995), and the assessment of their impact on network performance (Conti et al, 1996;Erramilli et al, 1996;Jiang et al, 2001) as well. As these works demonstrate, the effect of LRD on packet loss and delay may be drastic, leading to subexponential decay of the buffer overflow probability and, consequently, buffer sizes much larger than those predicted by memoryless or short-memory (ie, Markov) processes. ...
Detailed observations of communications networks have revealed singular statistical properties of the measurements, such as self-similarity, long-range dependence and heavy tails, which cannot be overlooked in modelling Internet traffic. The use of stochastic processes consistent with these properties has opened new research fields in network performance analysis and particularly in simulation studies, where the efficient synthetic generation of samples is one of the main topics. In this paper, we describe an efficient and online generator of the correlation structure of the fractional Gaussian noise process.
... (e.g., see [21]). The Hurst parameter is designed to capture the degree of long-range-dependence. ...
This paper studies the impact of long-range-dependent (LRD) traffic on the performance of a network multiplexer. The network multiplexer is characterized by a multiplexing queue with a finite buffer and an M/G/∞ input process. Our analysis expresses the loss probability bounds using a simple relationship between loss probability and buffer full probability. Our analysis also derives an exact expression for the buffer full probability and consequently calculates the loss probability bounds with excellent precision. Through numerical calculations and simulation examples, we show that existing asymptotic analyses lack the precision for calculating the loss probability over realistic ranges of buffer capacity values. We also show that existing asymptotic analyses may significantly overestimate the loss probability and that designing networks using our analysis achieves efficient resource utilization.
Possible applications of the developed method with assignment of preemptive priorities determined by infinite markings of the service time semiaxis are analyzed. In queueing systems without priority the stationary average queue length is infinite when the service time has infinite variance even if the utilization is less than one. In case of Poisson arrival flow and Pareto distributed service times with finite mean and infinite variance, the stationary distribution of the queue length is shown to be asymptotically power-law with the exponent less than one; consequently, the stationary average queue length is infinite. But if we use the preemptive priorities in accordance with infinite markings method, the average waiting time in the queue and, hence, its average length become finite. For the case when the request length is proportional to its service time, we introduce an indicator defined as the sum of request lengths in the queue. Generalized Little’s formula for calculating and estimating of average value of the indicator in systems with finite and infinite stationary average queue length is derived. We consider the case when actual service time of arriving requests is unknown. For this situation it is proposed to employ a version of infinite markings method based on dynamically configurable preemptive priorities. In this case, it is found that the infinite markings method provides finite average waiting time.
The foundation of a research project about a model of computer networks with media access control mechanism based on the IEEE standard 802.3-2005 is presented. The model draws from the theory of self-similar sets for establishing the impact level that the long range temporary correlations have on the performance of such networks. A new method for the estimation of self-similar levels based on a variation of the Whittle estimator is postulated-
Los flujos de tráfico tanto de las fuentes como agregados presentan con frecuencia propiedades de dependencia de largo alcance (LRD). En este trabajo se modela el comportamiento del tráfico de una red de computadoras de alta velocidad desde la perspectiva autosimilar y se analiza y discute su validez restringiendo su ámbito de aplicabilidad al nivel de red. Se demuestra que las propiedades más relevantes de los procesos autosimilares son consistentes para su empleo en el modelado de tráfico cuando se realiza esta distinción. Se demuestra que desde esta perspectiva los modelos de tráfico que consideran la dependencia de largo alcance son descriptores bien definidos para condiciones de tráfico en ráfagas y facilitan su formulación. Finalmente, se demuestra que los modelos restringidos son capaces de representar eficientemente a los procesos de tráfico reales y que poseen mayor plausibilidad de interpretación física que los basados en sistemas de colas tradicionales.
This paper presents a systematic approach to identify and quantify the types of structures featured by packettraces in communication networks. Our approach leverages an information-theoretic methodology, based oniterative randomization and compression of the packet trace, which allows us to systematically remove andmeasure dimensions of structure in the trace. In particular, we introduce the notion oftrace complexitywhichapproximates the entropy rate of a packet trace. Considering several real-world traces, we show that tracecomplexity can provide unique insights into the characteristics of various applications. Based on our approach,we also propose a traffic generator model able to produce a synthetic trace that matches the complexity levelsof its corresponding real-world trace. Using a case study in the context of datacenters, we show that insightsinto the structure of packet traces can lead to improved demand-aware network designs: datacenter topologiesthat are optimized for specific traffic patterns.
The knowledge about the true nature of the traffic in computer networking is a key requirement in the design of such networks. The phenomenon of self-similarity is a characteristic of the traffic of current client/server packet networks in LAN/WAN environments dominated by network technologies such as Ethernet and the TCP/IP protocol stack. The development of networks traffic simulators, which take into account this attribute, is necessary for a more realistic description the traffic on these networks and their use in the design of resources (contention elements) and protocols of flow control and network congestion. In this scenario it is recommended do not adopt standard traffic models of the Poisson type.
Queuing systems with an infinite variance of service time are considered. The average waiting time in such systems is equal to infinity at a stationary regime. We analyze the efficiency of introducing of absolute priorities with infinite number of priority classes determined by the special axis marking on intervals for possible values of service time. It is stated that queues in systems become normalized, i.e. the average queue length become finite, when using regular marking. Furthermore, request loss probabilities radically decrease when buffer size is finite. More efficient marking – exponential marking – is proposed for practical purposes in networks with fractal traffic. The optimization problems of regular and exponential markings are solved.
The problem of reducing loss probability in systems with finite buffer and infinite service time dispersion. Efficient method of loss reduction is developed for system M/Pa/1/m, in which Pareto distribution has infinite dispersion. The method is based on absolute priority discipline with afterservice. At infinite buffer m = \(\infty \) the introduction of absolute priorities into the systems is proven to allow the transformation of waiting time distribution in a way that its average values becomes finite. This underlies the development of the numerical method for optimal requests separation into priority classes with respect to minimal average waiting time in a system with infinite buffer It is demonstrated that the resulting priority assignment decreases the loss probability significantly if the infinite buffer in a system is replaced by a finite one. The method remains highly efficient even when extended to other systems GI/GI/1/m with infinite service time dispersion. The developed priority assignment method has a number of important advantages over other methods for dealing with requests losses. As a result, it can be efficiently used in practice, namely, to lower the messages loss probability in data networks with fractal traffic.
Recent measurement studies of real teletraffic data in modern telecommunication networks have shown that self-similar (or fractal) processes may provide better models of teletraffic in modern telecommunication networks than Poisson processes. If this is not taken into account, it can lead to inaccurate conclusions about performance of telecommunication networks. Thus, an important requirement for conducting simulation studies of telecommunication networks is the ability to generate long synthetic stochastic self-similar sequences. A new generator of pseu-do-random self-similar sequences, based on the fractional Gaussian nois and a wavelet transform, is proposed and analysed in this paper. Specifically, this generator uses Daubechies wavelets. The motivation behind this selection of wavelets is that Daubechies wavelets lead to more accurate results by better matching the self-similar structure of long range dependent processes, than other types of wavelets. The statistical accuracy and time required to produce sequences of a given (long) length are experimentally studied. This generator shows a high level of accuracy of the output data (in the sense of the Hurst parameter) and is fast. Its theoretical algorithmic complexity is 0(n).
We consider a fluid queue fed by the superposition of n homogeneous on-off sources with generally distributed on and off periods. The buffer space B and link rate C are scaled by n , so that we get nb and nc , respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n . We specifically examine the scenario where b is also large. We obtain explicit asymptotics for the case where the on periods have a subexponential distribution, e.g., Pareto, Lognormal, or Weibull.
The results show a sharp dichotomy in the qualitative behavior, depending on the shape of the function v(t) := - logP(A* > t ) for large t , A* representing the residual on period. If v (.) is regularly varying of index 0 (e.g., Pareto, Lognormal), then, during the path to overflow, the input rate will only slightly exceed the link rate. Consequently, the buffer will fill ‘slowly’, and the typical time to overflow will be ‘more than linear’ in the buffer size. In contrast, if v (.) is regularly varying of index strictly between 0 and 1 (e.g., Weibull), then the input rate will significantly exceed the link rate, and the time to overflow is roughly proportional to the buffer size.
In both cases there is a substantial fraction of the sources that remain in the on state during the entire path to overflow, while the others contribute at their mean rates. These observations lead to approximations for the overflow probability. The approximations may be extended to the case of heterogeneous sources. The results provide further insight into the so-called reduced-load approximation.
In this paper we study the asymptotic behavior of the tail of the stationary backlog distribution in a single server queue with constant service capacity c , fed by the so-called M / G /∞ input process or Cox input process . Asymptotic lower bounds are obtained for any distribution G and asymptotic upper bounds are derived when G is a subexponential distribution. We find the bounds to be tight in some instances, e.g. when G corresponds to either the Pareto or lognormal distribution and c − ρ < 1, where ρ is the arrival rate at the buffer.
Providing QoS guarantees in packet switched networks requires the use of traffic scheduling algorithms in switches or in routers. Frame-based Fair Queueing (FFQ), a scheduling algorithm for packet switched networks, has been proposed. The algorithm has O(1) timestamp computation complexity. This makes the algorithm more practical for implementation in both general packet networks with variable packet sizes and in asynchronous transfer mode (ATM) networks with fixed packet sizes. Recent work, on the other hand, has shown that the network traffic may exhibit self-similar behavior even during light loads. In this paper, we analyze FFQ under self-similar traffic source in terms of the delay experienced in FFQ and compare it to the delays in Packet-by-packet Generalized Processor Sharing (PGPS) and Self Clocked Fair Queueing (SCFQ). The delays are measured while all the sessions are transmitting within their reserved rates and also when one of these sessions is misbehaved.
Different models are used to describe different types of traffic. For example, voice traffic is commonly described using the on–off source or the Markov modulated Poisson process (MMPP). Studies suggest that traffic sources such as variable bit rate (VBR) video and Ethernet traffic are better represented by self-similar traffic models [2–7]. The important characteristics of a traffic source are its average data rate, burstiness, and correlation. The average data rate gives an indication of the expected traffic volume for a given period of time. Burstiness describes the tendency of traffic to occur in clusters. A traffic burst affects buffer occupancy and leads to network congestion and data loss. Data burstiness is manifested by the autocorrelation function which describes the relation between packet arrivals at different times. It was recently discovered that network traffic exhibits long-range dependence, i.e. the autocorrelation function approaches zero very slowly in comparison with the exponential decay characterizing short-range dependent traffic [2–7]. Long-range dependent traffic produces a wide range in traffic volume away from the average rate. This great variation in traffic flow also affects buffer occupancy and network congestion. In summary, high burstiness or long-term correlation leads to buffer overflow and network congestion. We begin by discussing the different models describing traffic time arrival statistics.
Analyzing the characterestics of bandwidth management in the architecture of the new generation Internet based on virtualization technologies, we use on/off model to produce self-similar traffics and develop an algorithm for dynamically allocating bandwidth of a virtual network based on traffic linear prediction. Simulation was done by NS2 to investigate the changes in bandwidth utilization and packet loss rate before and after running the algorithm with a predictor embedded. Results show that bandwidth utilization comes up to 97% from 80% and packet loss rate drops to 0.27% from 0.48% using the algorithm proposed.
As to the self-similarity of WiMAX network traffic, M/Pareto model was proposed to model the network traffic. Through the statistical nature between the M/Pareto model and FBM traffic model, the parameters of the M/Pareto were mapped to the ones of FBM traffic model. The effective bandwidth formula was derived for M/Pareto model parameters. Whereby, a self-similar call admission control algorithm (SS-CAC) was designed. It avoided getting the parameter values of FBM traffic flow model with the measurement method and adapted to the self-similarity of WiMAX traffic. Since the calculation of the effective bandwidth was accurate and convenient, simulation results show that SS-CAC greatly reduces the call blocking rate and improves the bandwidth utilization.
Detection of malicious activity in the network still is a challenge. The self-similarity feature of traffic can be used in an anomaly detection method. The influence of traffic generated by intruder who performs access attack is analyzed. In the other hands the simulation of threads is useful in designing and testing processes of a network. For this purpose a multi-layer 'on-off' model of traffic source is developed and a traffic generator is implemented according this model. Finally the real traffic including attacker flow is compared to the traffic generated by generator. This comparison proves that it is possible to simulate traffic similar to malicious one.
Based on fractional Brownian motion (FBM), one calculation of the packet drop probability in the RED algorithm was derived under self-similar flows. Based on the self-similarity and the long-range dependence characteristics of Internet network traffics, a time slot-based RED algorithm on self-similar flows (SFRED) was proposed to the router queue management. The packet drop probability is calculated in every time-slot so that the burden is greatly reduced. It is simulated by NS2 and the experimental results show that the algorithm SFRED outperforms RED. SFRED can control the queue length under adaptive flows with a good throughput.
In this work, a model of the corporate network had been developed, simulated and implemented using an optimized network engineering tool in a simulation area of 1.5 × 1.5 km enterprise topology network to stream video between each other. Total of 14,670 video traffic (traffic load) is streamed from different sources and destinations at random. The video streaming traffic is monitored, analyzed in view of identifying traffic self-similarity in the network. The results of the analysis show that video traffic is highly self-similar in the network using Abry-Veitch and smoothing algorithms method. The effect of self-similarity in the network is reduced with the help of 1D wavelet technique.
Key words: Smoothing algorithms, video, traffic, optimized network engineering tools (OPNET), self-similar.
For the safety applications in road vehicle communication, the existing research did not take it into account that the generation of the safety messages is event driven and the network traffic is self-similar. We propose an ON/OFF Pareto process based safety application self-similar model according to the above features and prove the effectiveness of this model analytically. Then we verify the model on NS2 simulation platform by showing the network traffic generated by our model is self-similar. At last, we use this model to simulate and analyze the performance of safety applications (adopting IEEE 802.11p) by computing the average delay and packet delivery ratio (PDR) with different vehicle densities, speeds and packets generation rates. The simulation results show that IEEE 802.11p can be used for safety applications in road vehicle communication. We also find the optimal working range for safety applications on vehicle density and packets generation rate except vehicle speed, which shows that we must make compromises between short delay and high packet delivery ratio. The conclusion is highly valued for safety applications applied in actual environment.
We create software tools for the generation of sample traces of self-similar traffic as fractional Brownian motion, using Mathcad. These methods have been widely used in simulation studies, but they present the difficulty of generating negative samples. So we also introduce a very efficient technique for the generation of multifractal traffic by means of wavelet synthesis, which posses the property of positiveness.
The paper is a review of some results on the discrete-time finite-buffer queueing system which models a communication network multiplexer fed by a self-similar cell traffic. The review includes also some new results. First, the definitions of second-order self-similar processes are given. Then, a queue model is introduced. It has a finite buffer, a number of servers with unit service time, and an input traffic which is an aggregation of independent source-active periods having Pareto-distributed lengths and arriving as Poisson batches. A source generates a Bernoulli sequence of cells. The asymptotic bounds to the buffer-overflow and cell-loss probabilities are given in some cases. The bounds show a true asymptotic behaviour of the probabilities. The bounds decay polynomially with buffer-size growth and exponentially with excess of channel capacity over traffic rate.
This paper studies the impact of long-range-dependent traf-fic on the performance of a network multiplexer. The network multiplexer is modeled by a finite buffer multiplexing queue driven by a general class of fluid input processes which include a large class of long-range-dependent (LRD) and short-range-dependent (SRD) processes. The loss occur probability and loss probability of the multiplexing queue is derived by extending Bene s's fluid queue analysis. The analysis is, then, applied to study a finite buffer multiplexing queue driven by a M=G=1 process. Through this example, our analysis is validated, and the impact of the LRD traffic on the performance of the multi-plexing queue is investigated. We show that existing analysis assuming an infinite buffer multiplexing queue overestimates the loss probability of the network multiplexer, and designing networks using such analysis will cause inefficient resource uti-lization. We also show that existing analysis fail to completely capture the impact of LRD traffic when the buffer capacity is small.
In this paper, we extend the performance of bidirectional TCP connection over end-to-end network that uses transfer rate-based flow and congestion control. The sharing of a common buffer by TCP packets and acknowledgement has been known to result in an effect called ack compression, where acks of a connection arrive at the source bunched together, resulting in unfairness and degraded throughput. The degradation in throughput due to bidirectional traffic can be significant. Even in the simple case of symmetrical connections with adequate window size, the connection efficiency is improved about 20% for three levels of background traffic 2.5Mbps, 5.0Mbps and 7.5Mbps. Otherwise, the throughput of jitter is reduced about 50% because round trip delay time is smaller between source node and destination node. Also, we show that throughput curve is improved with connection rate algorithm which is proposed for TCP congetion avoidance as a function of aggressiveness threshold for three levels of background traffic 2.5Mbps, 5Mbps and 7.5Mbps. By analyzing the periodic bursty behavior of the source IP queue, we derive estimated for the maximum queue size and arrive at a simple predictor for the degraded throughput, applicable for relatively general situations.
As new communications services evolve, professionals must create better models to predict system performance. The article provides an overview of computer simulation modelling for communication networks, as well as some important related modelling issues. It gives an overview of discrete event simulation and singles out two important modelling issues that are germane to extant and emerging networks: traffic modelling and rare event simulation. Monte Carlo computer simulation is used as a performance prediction tool and Markov models are considered.< >
The purpose of this paper is twofold. From the viewpoint of communications engineering, it presents a model of certain random perturbations that appear to come in clusters, or bursts. This will be achieved by introducing the concept of "self-similar stochastic point process in continuous time." The resulting mechanism presents fascinating peculiarities from the mathematical viewpoint. In order to make them more palatable as well as to help in the search for further developments, the basic concept of "conditional stationarity" will be discussed in greater detail than would be strictly necessary from the viewpoint of the immediate engineering problem of errors of transmission. This work is related to an earlier "new model" due to J. M. Berger and the author; the logical structure of the theory has been further streamlined and a number of fresh consequences have been derived; the empirical fit has been further improved, while recourse to ad hoc corrective terms was made unnecessary.
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
We provide models which are capable of describing the long term
correlations and self similar burstiness structure found in recent
measurements of packet networks and VBR video. Two families of
“fractal” arrival processes are presented which capture
these features extremely compactly. We show the equivalence of one of
these to processes with unsummable auto-correlation functions used by
Leyland, Taqqu, Wilinger and Wilson (1993) to describe long term
correlation and burstiness. Our approach however has advantages. The
other (1 parameter) family generates burstiness on all time scales. It
shows how blocking can occur even for arrival streams with zero arrival
rate. This illustrates how parameters describing scaling of burstiness
and correlation must replace useless long terms averages
"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
In order to study the interactions between LANs and proposed
interconnection networks, a high time-resolution hardware monitor for
Ethernet LANs is presented that avoids the shortcomings of previous
monitoring tools, such as traffic burst clipping and timestamp jitter.
Using data recorded by a monitor for several hundred million Ethernet
packets, an overview of the short-range time correlations in external
LAN traffic is presented. The analysis shows that LAN traffic is
extremely bursty across time domains spanning six orders of magnitude.
This behavior is compared with simple formal traffic models. The results
suggest that the pronounced short-term traffic correlations, together
with the extensive time regime of traffic burstiness, strongly influence
the patterns of loss and delay induced by LAN interconnection
Demonstrates that Ethernet LAN traffic is statistically
self-similar, that none of the commonly used traffic models is able to
capture this fractal-like behavior, that such behavior has serious
implications for the design, control, and analysis of high-speed,
cell-based networks, and that aggregating streams of such traffic
typically intensifies the self-similarity (“burstiness”)
instead of smoothing it. These conclusions are supported by a rigorous
statistical analysis of hundreds of millions of high quality Ethernet
traffic measurements collected between 1989 and 1992, coupled with a
discussion of the underlying mathematical and statistical properties of
self-similarity and their relationship with actual network behavior. The
authors also present traffic models based on self-similar stochastic
processes that provide simple, accurate, and realistic descriptions of
traffic scenarios expected during B-ISDN deployment
The authors examine the phenomenon of congestion to better
understand the congestion management techniques that will be needed in
high-speed, cell-based networks. The first step of this study is to use
high time-resolution local area network (LAN) traffic data to explore
the nature of LAN traffic variability. Then the data are used for a
trace-driven simulation of a connectionless service that provides LAN
interconnection. The simulation allows one to characterize what
congestion might look like in a high-speed, cell-based network. When
realistic data are applied to simple models of LAN interconnection, it
is observed that during periods, congestion persists and losses can be
significant; congestion losses cannot be avoided by modest increases in
buffer capacity; consequences of misengineering can be serious; and,
fortunately, most congested periods are preceded by signs of impending
danger
- L Kleinrock
L.Kleinrock, "Queueing Systems-Vol. I: Theory",
Wiley, N.Y., 1975.