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.     

Loss performance analysis of an ATM multiplexer loaded withhigh-speed on-off sources

The performance of an asynchronous transfer mode (ATM) multiplexer whose input consists of the superposition of a multiplicity of homogeneous on-off sources modeled by a two-state Markovian process is studied. The approach is based on the approximation of the actual input process by means of a suitably chosen two-state Markov modulated Poisson process (MMPP), as a simple and effective choice for the representation of superposition arrival streams. To evaluate the cell loss performance, a new matching procedure that leads to accurate results compared to simulation is developed. The application limits of the proposed method are also discussed. The outstanding physical meaning of this procedure permits a deep insight into the multiplexer performance behavior as the source parameters and the multiplexer buffer size are varied     

与多媒体信源模型弱相关的ATM复接器监管方案

本文提出一种与信源模型弱相关的复接器监管方案－－采用模糊漏桶控制方法改变令牌产生速率,对多媒体信源接入实施动态带宽分配。用ＭＭＢＰ模型及其合成讨论了该方案的可能性给出了模糊控制方案和规则,计算机仿真表明,在多个不同速率不同特性的语音、图像、数据信源接入时延该方法能很好地满足低时延低丢失的要求,提高带宽利用率,傅诉异步和编者复用特性被有效、充分地利用。     

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.     

Analysing the interdeparture process in an ATM multiplexer

This paper studies the interdeparture process in a mathematical model of an ATM multiplexer. The technique is based on a discrete-time queueing model of k input queues feeding one output queue, a situation commonly arising in ATM switches. The process between input queues and output queue is analysed in detail. For a service rate of one cell per time slot (s = 1) the exact solution of the interdeparture process is given based on the binomial distribution. For a service rate greater than one cell per time slot (s > 1) a solution is derived using the state probabilities of the input queues. The probability density function of the interdeparture process is then obtained by summing a combination of the multinomial joint distribution function of s random variables. If the state probabilities are referred to as the distribution of buffer contents after arrival, the formula returns exact results. © 1998 John Wiley & Sons, Ltd.     

A Bernoulli process approximation with buffer size adjustment forthe analysis of an ATM multiplexer

The heterogeneity and the burstiness of input source traffic together with large size of the shared buffer make it difficult to analyze the performance of an asynchronous transfer mode (ATM) multiplexer. Based on the asymptotic decay rate of queue length distribution at the shared buffer, we propose a Bernoulli process approximation for the individual on-off input source with buffer size adjustment, which gives a good upper bound of the cell loss probability     

Traffic studies of a multiplexer in an ATM network and applications to the future broadband ISDN

In the first part of this paper the influence of the arrival process on these three performance parameters is discussed. The values of these three performance parameters depend strongly on the utilization distribution over the input trunks of the multiplexer while the total utilization on the input trunks is fixed. If there is the same utilization on all input trunks, the values of these three performance paramters reach a maximum. This result is also valid for an ATM switching matrix with a separate FIFO buffer at each output trunk. In the second part of this paper some examples are provided of how to apply the results of these studies to the future broadband ISDN which is intended to transmit services with very high bit rates (e.g. 135 Mb/s) as well as services with very low bit rates (e.g. 64 kb/s).     

A discrete-time queueing model of the shared buffer ATM switch with bursty arrivals

We model the shared buffer ATM switch as a discrete-time queueing system. The arrival process to each port of the ATM switch is assumed to be bursty and it is modelled by an interrupted Bernoulli process. The discrete-time queueing system is analyzed approximately. It is first decomposed into subsystems, and then each subsystem is analyzed separately. The results from the subsystems are combined together through an iterative scheme. The analysis of each subsystem involves the construction of the superposition of all the arrival processes to the switch. Comparisons with simulation data showed that the approximate results have a good accuracy.Supported in part by DARPA under Grant No. DAEA18-90-C-0039.Work done while on a sabbatical leave of absence at the Computer Science Department of North Carolina State University.     

A control-ahead ATM switch architecture and its performance

An asynchronous transfer mode (ATM) switch architecture that uses the broadcasting transmission medium for transmission of cells from input ports to output ports is introduced. Cell transmission and its control are separated completely, and cell transmission control, i.e. header operation, is executed before cell transmission (control ahead). With this operation, cell transmission and its control can be executed in a pipeline style, allowing high-speed cell exchange and making transmission control easier. One of the essential problems for ATM switches which use the broadcasting transmission medium is high-speed operation of the transmission medium. The switch fabric performance is analyzed according to its switching speed. Numerical results show that the ATM switch proposed shows good cell loss performance even when its switching speed is restricted, provided that switch utilization is below 1. Extensions to the switch that lead to robustness against bursty traffic are shown     

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.     

An error-controlled approximate analysis of a stochastic fluid flowmodel applied to an ATM multiplexer with heterogeneous on-off sources

The stochastic fluid flow approach is applied to the analysis of the cell loss performance of an ATM multiplexer. The input traffic stream offered to the multiplexer is the superposition of heterogeneous on-off sources with independent and exponentially distributed on and off times. The focus is on the numerical investigation of the steady-state behavior of models involving very large state spaces. To this end, an efficient algorithm for the evaluation of tight upper and lower bounds of the cell loss probability is developed. The algorithm allows a significant reduction of the computational burden, while yielding a guaranteed overestimate of the error implied by the proposed approximation of the cell loss probability. Numerical results are presented both to assess the tightness of the proposed bounds and to gain insight into the behavior of heterogeneous traffic mixes. The main conclusion, from the multiplexer performance evaluation point of view, is that it is not convenient to mix very different traffic streams in a completely shared FIFO buffer, without some kind of control     

DELAY JITTER OF A PERIODIC CELL STREAM THROUGH AN ATM MULTIPLEXER IN A BURSTY TRAFFIC ENVIRONMENT

The periodic cell stream is a very important member among the input traffic sources in ATM networks. In this paper, a finite-buffered ATM multiplexer with traffic sources composed of a periodic cell stream, multiple i.i.d Bernoulli cell streams and bursty two-state Markov Modulated Bernoulli Process (MMBP) cell streams is exactly analyzed. The probability mass function of queuing delay, the autocorrelation and power spectrum of delay jitter for this periodic cell stream are derived. The analysis is used to expose the behavior of delay jitter for a periodic cell stream through an ATM multiplexer in a bursty traffic environment. The simulation results indicate that the analytical results are accurate.     

A discrete-time framework for proximate time-optimal performance of damped servomechanisms

This paper proposes nonlinear control strategies for the discrete-time near time-optimal control of damped servomechanisms. Both the well established Proximate Time Optimal Servomechanism (PTOS) and its dynamically damped version (ddPTOS) are extended for damped systems. Stability results are presented in a general discrete-time framework suitable for both damped and undamped systems. These results allow the reduction of constraints in the traditional PTOS – particularly regarding the acceleration discount factor – while encompassing the nonlinear damping of the ddPTOS. Experimental results demonstrate the efficiency of the proposed controllers.     

Estimation of equivalent bandwidth without modeling arrival processes for connection admission control in an ATM multiplexer

The traffic modeling is a key element in analyzing and simulating communications network. Most of the previously studied approaches to the connection admission control (cac) are based on an assumed arrival process model. However, there are some limits to apply the assumed model to the real environment. In this paper, we study a connection admission control (cac) method without assuming arrival processes in an atm multiplexer when homogeneous traffics are multiplexed. To obtain the equivalent bandwidth (eb) without modeling arrival processes, the concept of equivalent bandwidth convergence (ebc) is proposed and implemented by using the upper bound of the first derivative of cell loss rate (clr) for the load. With the ebc concept, one can avoid modeling of the arrival process and implement the cac simply and effectively. We show by numerical examples the convergence process of the average clr and the eb for voice and video traffics, and the robustness of the ebc concept.     

A review of error performance models for satellite ATM networks

ITU-T Recommendations G.826 and 1.356 set the basis for error performance standardization at the lower layers of B-ISDN networks. The specific performance parameters of these recommendations are directly related to the bit error rate and are strongly dependent on the level of correlation of the error sequence. Bit errors in typical satellite transmissions occur in bursts, and that should be taken into account when designing satellite ATM networks. Error modeling and analysis of G.826 and 1.356 performance criteria and satellite design principles are reviewed     

Analysis of a discrete-time single-server queue with bursty inputsfor traffic control in ATM networks

The performance of an asynchronous transfer mode (ATM) network subject to admission control and traffic smoothing is analyzed. Basically, an ATM switch is modeled as a discrete-time single-server queuing system in which a new call joins existing calls. Cell arrivals from a new call are assumed to follow a general distribution. It is also assumed that aggregated arrivals of cells from existing calls form batch arrivals with a general batch size distribution and a geometric distribution of the interarrival times between batches. Both finite- and infinite-buffer cases are considered. An exact analysis yields the waiting time distribution and cell loss probability for a new call and for existing calls. Numerical examples are given to show how the network performance depends on the statistics of a new call (burstiness, time that a call stays in an active or inactive state, etc.) and to demonstrate the effectiveness of admission control and traffic smoothing     

A performance model for ATM switches with general packet lengthdistributions

The maximum throughput of an ATM switch is investigated in the presence of an offered load of multicell packets. For the case of input queueing coupled with a round-robin policy for transferring cells from inputs to outputs, the system is approximated by a product form queueing network. Under the assumption that packet lengths are described by random variables with discrete Coxian distributions, it is shown that the balance equations describing the behavior of the ATM switch approach those for a product form queueing network and that the steady-state probabilities of such an ATM switch approach the product-form solution as the cell length tends to zero. Last, a numerical investigation shows that the approximation yields good results, even when the packet lengths are not well described by Coxian distributions     

A simplified performance evaluation for bursty multiclass trafficin ATM systems

In broadband ISDN with ATM, various kinds of traffic, such as voice, data and video, share the common transmission resource. For such multiclass traffic systems, it is necessary to evaluate the grade of service (GOS) for individual traffic. In particular, for the ATM networks integrating voice and video which are of bursty property and delay sensitive, the individual performance evaluation for the mixed bursty traffic an important problem. The authors propose a simplified evaluation of the individual mean waiting time for the bursty multiclass systems appearing in the ATM network and show numerical examples for voice/video system