A new approximation for analyzing the multiplexing of bursty sources in ATM networks

This paper is concerned with the analysis of an asynchronous transfer mode (ATM) multiplexer serving bursty applications such as voice, image, and high-speed data. The model used is a GI _i /D/1 discrete-time single-server queueing system: the arrival process is a superposition of several random processes, and the departure process is a deterministic with a FCFS discipline. The difficulty in solving such a queueing system depends on the model chosen for the individual traffic sources. For the case in which the cell arrival stream from the individual sources is modeled as a Bernouli process, an exact solution is possible. The problem with such a model is that it does not incorporate the effect of burst length, which has been shown through simulation experiments to have a significant effect on the performance. A more realistic model that takes into consideration the impact of the burst length is considered in this study. In particular, an alternating-state Markov process is chosen to model the individual arrival stream.The solution of a GI _i /D/1 queueing system with the arrival process being a superposition of several renewal processes is in general intractable. This paper obtained a new approximation we refer to as the three-parameters approximation (TPA). This approximation was based on the asymptotic properties of the aggregate traffic and the congestion estimates from the simulation experiments. The TPA solution was found to be dependent on three parameters: number of sources, overall traffic intensity at the queue, and multiplexing factor. The TPA is an improvement of a previous approximation developed in analyzing packet voice system.In addition, the study determined an optimal operating point for the ATM multiplexer and the ATM switch that takes into account the tradeoff between delay and throughput. In particular, an optimal operating point is specified by the traffic loading that maximizes the queueing power. This optimal operating point is used to contrast the performance of ATM with synchronous transfer mode (STM).     

Performance analysis of cellular mobile communication systems fordata transmission

Buffers are used to overcome the data losses due to the interruption of data transmission when a mobile station is handed over in a cellular network. Data traffic from a wireline network to its mobile data terminal, such as access to large commercial databases or data transmission from a main computer to its remote mobile terminal, is studied. Compound Poisson (CP) is used to approximate the arrival process of the data traffic, and a modulated D (MD) distribution is used to approximate the service and handover process. The performance of the queueing model CP/MD/1/N is analyzed. Probability generating functions and characteristic functions are used to evaluate the mean queue length and the mean burst delay for an infinite buffer system and the overflow probabilities versus the buffer size for a finite buffer system. A method is presented to find the probability transition matrix entries by recursively taking derivatives of the probability generating function of the number of the characters arriving during the service-time. The queue length distributions for a finite buffer, both at departure instants and at arbitrary time instants are derived. Comparison with simulation indicates that the model is accurate. The numerical results of the model confirm the effectiveness of the scheme     

Scalable architectures for integrated traffic shaping and linkscheduling in high-speed ATM switches

Emerging broad-band switches must accommodate the diverse traffic parameters and quality-of-service requirements of voice, data, and video applications. End-to-end performance guarantees depend on connections complying with traffic contracts as their cells travel through the network. This paper presents a leaky-bucket shaper architecture that scales to a large number of connections with diverse burstiness and bandwidth parameters. In contrast to existing designs, the proposed architecture arbitrates fairly between connections with conforming cells by carefully integrating leaky-bucket traffic shaping with rate-based scheduling algorithms. Through a careful combination of per-connection queueing and approximate sorting, the shaper performs a small, bounded number of operations in response to each arrival and departure, independent of the number of connections and cells. When the shaper must handle a wide range of rate parameters, a hierarchical arbitration scheme can reduce the implementation overheads and further limit interference between competing connections. Through simulation experiments, we demonstrate that the architecture limits cell-shaping delay and traffic distortions, even in periods of heavy congestion. The efficient combination of traffic shaping and link scheduling results in an effective architecture for managing buffer and bandwidth resources in large, high-speed ATM switches     

Buffer Behavior for Mixed Arrivals and Single Server with Random Interruptions

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

An Approximate Time-Delay Analysis for Packet-Switching Communication Networks

A technique is presented for the derivation of approximate average packet time-delay formulas in a packet-switching store-and-forward network. The approximation technique appropriately incorporates arrival and departure packet interferences with the recent queueing results in a noninterfered communication path. Simulation results, for basic flow configurations, show the approximate timedelay function to constitute a very close lower bound over wide range of traffic intensities. The resulting average time-delay approximation when a Poisson assumption is made, is shown to constitute an upper bound. A procedure for approximate network time-delay analysis is then presented.     

Output and delay process analysis for slotted CDMA wirelesscommunication networks with integrated voice/data transmission

This paper presents the output and delay process analysis of integrated voice/data slotted code division multiple access (CDMA) network systems with random access protocol for packet radio communications. The system model consists of a finite number of users, and each user can be a source of both voice traffic and data traffic. The allocation of codes to voice calls is given priority over that to data packets, while an admission control, which restricts the maximum number of codes available to voice sources, is considered for voice traffic so as not to monopolize the resource. Such codes allocated exclusively to voice calls are called voice codes. In addition, the system monitoring can distinguish between silent and talkspurt periods of voice sources, so that users with data packets can use the voice codes for transmission if the voice sources are silent. A discrete-time Markov process is used to model the system operation, and an exact analysis is presented to derive the moment generating functions of the probability distributions for packet departures of both voice and data traffic and for the data packet delay. For some cases with different numbers of voice codes, numerical results display the correlation coefficient of the voice and data packet departures and the coefficient of variation of the data packet delay as well as average performance measures, such as the throughput, the average delay of data packets, and the average blocking probability of voice calls     

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

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

Analysis of a discrete-time queue with integrated bursty inputs in ATM networks

In this paper, we carry out an exact analysis of a discrete-time queue system with a number of independent Markov modulated inputs in ATM networks, using a generating function approach. We assume that the queueing system has an infinite buffer with M servers. The cell arrival process is characterized by a number of independent Markov modulated geometrical batch arrival processes. We first obtain the generating function of the queue-size distribution at steady-state in vector form, then derive an expression for the average queue-size in terms of the unknown boundary probabilities. To obtain those unknown probabilities, we use the technique proposed in Reference 1. This involves decomposing the system characteristic function to evaluate the roots and solving a set of linear equations. One of the contributions of this paper is presented in Lemma 1, which characterizes the property of the underlying eigenvalues. For one special case of at least M-1 cell arrivals during one slot at one Markov state and of at least M arrivals at all other states, the determination of the unknowns is straightforward. If every Markov modulated arrival process can be further decomposed into a number of i.i.d. two-state, or three-state, or even four-state Markov modulated arrival processes, then each root can be obtained separately using an iterative algorithm. Numerical results are presented to validate the proposed traffic models against actual traffic measurements.     

A histogram-based model for video traffic behavior in an ATMmultiplexer

The authors introduce a model based on arrival rate histograms for characterizing the behavior of an ATM buffer when it is carrying variable bit rate video traffic. Traffic smoothing on a frame-by-frame basis allows a quasistatic approximation that accurately predicts results such as buffer occupancy distributions and cell loss rates to be made. Convolving individual source histograms allow prediction of the queueing performance of a multiplexed stream. The approximation is investigated in more detail by modeling video as a Markov modulated Poisson process. It is shown that the multiplexer system is nearly completely decomposable (NCD). NCD systems have a well-known approximate solution, which is identical to the histogram approximation. Error bounds for the NCD approximation are also known and are reasonably tight. Results indicate that while the presence of strong correlations is an important characteristic of video traffic, the actual form of that correlation is not     

The teletraffic analysis of the multi-server loss model with renewal distributions

This paper presents a loss model in which a general renewal arrival stream is served by any number of general renewal servers, i.e., theGI/GI/s/s model. Using linear algebraic queueing theory (LAQT), we provide the exact steady-state solution of the number of customers in theGI/GI/s/s model at general, arrival, and departure times. We show that the steady-state solution at arrival times can be used to approximate those at general times and that the third moment of the arrival process significantly affects this approximation. Finally, we show that a conjectured inequality does not hold.This work was performed while at the University of Missouri-Kansas City.     

Approximate performance analysis of heavily loaded slotted downlink channel in a wireless CDMA system supporting integrated voice/data services

This paper is concerned with the performance analysis of a slotted downlink channel in a wireless code division multiple access (CDMA) communication system with integrated packet voice/data transmission. The system model consists of a base station (BS) and mobile terminals (MT), each of which is able to receive voice and/or data packets. Packets of accepted voice calls are transmitted immediately while accepted multipacket data messages are initially buffered in first in, first out (FIFO) queues created separately for each destination. The BS distinguishes between silence and talkspurt periods of voice sources, so that packets of accepted data messages can use their own codes for transmission during silent time slots. To fulfill QoS requirements for both traffic types, the number of simultaneous packet transmissions over the downlink channel must be limited. To perform this task, a fair, single-priority multiqueueing scheduling scheme is employed. Discrete-time Markov processes are used to model the system operation. Statistical dependence between queues is the main difficulty which arises during the analysis. This dependence leads to serious computational complexity. The aim of this paper is to present an approximate analytical method which enables one to evaluate system performance despite the dependence. Therefore, it is assumed that the system is heavily loaded with data traffic, and a heuristic assumption is made that makes the queueing analysis computationally tractable. Typical system performance measures (i.e., the data message blocking probability, the average data throughput and delay) are evaluated, however, due to the accepted heuristic assumption, the analysis is approximate and that is why computer simulation is used to validate it.     

Queue Size and Delay Analysis for a Communication System Subject to Traffic Activity Mode Changes

We consider a discrete single-server queueing/communication system, in which the arrival distribution is changing stochastically with time. The distribution of the number of messages to arrive within a time slot depends on a traffic activity process of modes. This process of modes is a two-state Markov chain: mode 0 and mode 1, which represent light and heavy traffic conditions, respectively. The transition probabilities of this Markov chain [herein called mode duration parameters (MDP's)] determine the distribution of the duration of time the process stays in each mode. Expressions for thez-transform, expectation, and variance are obtained for the steady-state queue size and delay. A special consideration is given to the effect of the MDP's on the system performance, and the limiting cases (where the MDP's approach zero) are studied.     

Modeling multiple IP traffic streams with rate limits

We start with the premise, and provide evidence that it is valid, that a Markov-modulated Poisson process (MMPP) is a good model for Internet traffic at the packet/byte level. We present an algorithm to estimate the parameters and size of a discrete MMPP (D-MMPP) from a data trace. This algorithm requires only two passes through the data. In tandem-network queueing models, the input to a downstream queue is the output from an upstream queue, so the arrival rate is limited by the rate of the upstream queue. We show how to modify the MMPP describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that are not tandem, we show how to approximate the superposition of MMPPs without encountering the state-space explosion that occurs in exact computations. Numerical examples that demonstrate the accuracy of these methods are given. We also present a method to convert our estimated D-MMPP to a continuous-time MMPP, which is used as the arrival process in a matrix-analytic queueing model.     

Models for Analysis of Packet Voice Communications Systems

In a packet voice communication system, packets are fed to a common queue by a number of independent voice sources and are removed from this queue on a first-come-first-serve basis for transmission over a communication link of finite capacity. Each voice source alternates between active periods, during which packets are generated at regular intervals, and inactive periods, during which no packets are generated. In this paper, we discuss three models, a semi-Markov process model, a continuous-time Markov chain model, and a uniform arrival and service model, to assess the queueing behavior of such systems. Numerical results obtained from each of the three models are compared to each other, to results obtained from a discrete event simulation program, and to results obtained from anM/D/1analysis. Parameters of the model are the average duration of active and inactive periods, the packet generation rate, the communication link capacity, and the total number of voice sources. Conclusions are drawn regarding which models appear to be most appropriate in the parameter ranges investigated.     

Computational methods for performance evaluation of a statisticalmultiplexer supporting bursty traffic

A statistical multiplexer supporting a number of bursty sources is modeled as a discrete time, single server queueing system with an infinite buffer. The probability generating function (PGF) method is used to analyze the queueing behavior. The PGF method requires the determination of a large number of boundary values and, hence, the roots of the characteristic equation. An iterative algorithm to evaluate the characteristic roots is proposed. When the arrival process is a superposition of independent processes, a decomposition approach is used to reduce the state space involved in the computational algorithm. Additionally, the computational algorithm is made efficient through the establishment of conditions under which all the roots are either real or nonnegative real numbers. A set of equations to recursively compute the moments of the queue length are established. Sample applications of the computational methods to evaluate the performance of a multiplexer supporting voice and video sources, modeled by two-state Markov and L-state MMPP processes, respectively, demonstrate the viability of the proposed methods     

User behavior modeling of voice communications: an empirical study

In this study, analysis and modeling of arrival and service processes are presented in a comprehensive fashion in order to determine statistical properties of voice traffic from end‐user perspective in accordance with the queueing theory. For the first time in the literature, we introduce a user centric approach and examine these services considering both flow directions of voice traffic, the uplink and the downlink as opposed to existing studies with the network centric approach. In our study, we use experimental data composed of actual phone calls collected from 2G/3G networks. To achieve this, we designed and implemented a data collection system for mobile users and compared the results by using data from an operational cellular network. In order to determine the time correlation of voice calls, Hurst parameter estimation methods are used. On the basis of the outcomes, independency of call arrivals is shown. Additionally, it is shown that calls acquired from user and network centric approaches are both Poisson distributed. Next, looking at the problem from service process perspective, thorough analyses are performed to determine mathematical models that can best characterize call holding times. Maximum likelihood estimation and expectation maximization algorithm are used, and it is shown that the optimum mathematical model for the characterization of call holding times is the lognormal distribution family. Copyright © 2014 John Wiley & Sons, Ltd.     

Cell arrival modeling and related statistical multiplexer performance in ATM networks

A source is assumed to go through independently distributed ON and OFF periods. During an ON period, cells arrive spaced apart in time by a fixed interval. No cells arrive during an OFF period. The probability distribution of the ON and OFF periods are arbitrary. Traffic from a number of such sources is statistically multiplexed. The related statistical multiplexer performance is studied analytically as follows. A statistical multiplexer is modeled as a discrete-time single-server queueing system where the traffic from a new source (conforming to the cell arrival process described above) joins traffic that is already being statistically multiplexed. The aggregated arrival of cells from existing traffic is assumed to follow a two-state Markov modulated cell arrival process. Numerical examples that relate the performance at the statistical multiplexer to the parameters describing the traffic from the new source and the aggregated traffic are presented.This research was supported in part by the National Science Foundation under Grant No. NCR-9016348, and by the Pacific Bell External Technology Program.     

DYNAMIC BANDWIDTH ALLOCATION IN AN ATM MULTIPLEXER WITH MULTICLASS TRAFFIC AND ITS PERFORMANCE ANALYSIS

This paper introduces two source models: MAP(Markovian arrival process) model for the traffic with correlation and burst, e.g., voice, video, etc. and PAP(Poisson arrival process) model for the traffic with non-correlation, such as data, etc. Then a movable boundary bandwidth access policy is chosen.Basing on above model, the performance measures, e.g., mean waiting time and loss probability,especially the queue length time distribution are obtained. Finally, a number of numerical results are provided and shown through simulation.     

Finite Buffer Behavior with Poisson Arrivals and Random Server Interruptions

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

Performance Analysis of Statistical Voice/Data Multiplexing Systems with Voice Storage

In this paper the performances of four statistical voice/data multiplexers are analyzed and compared. The structures of these multiplexers are based on the newly proposed queueing, frame management, and integrated flow control methods. For the queueing purpose, two separate finite voice and data buffers are used to queue voice and data packets independently. For frame management, four versions of master frame management are considered. As for the integrated flow control algorithm, speech coding techniques such as variable rate coding and embedded coding are considered. To evaluate the performances of the multiplexers, analytical formulations are made from the equivalent queueing models of the proposed systems. Then, numerical results on the performance of the multiplexers are obtained by using the Gauss-Seidel iteration method. These results show that there exist tradeoffs between data and voice traffic performances for a given input traffic load and the output channel rate.