Performance analysis of a multiplexer with the threshold based overload control in ATM networks

In this paper we analyze the performance of a statistical ATM multiplexer with bursty input traffic and two thresholds in the buffer by using queueing model. Two priority levels are considered for source traffic, which is modeled by Markov Modulated Poisson Process to represent the bursty characteristics. Service time distributions of two priority sources are assumed to be same and deterministic for ATM environment. The partial buffer sharing scheme with one threshold may experience a sensitive state change around the threshold. But the proposed multiplexer with two thresholds avoids this hysterical phenominon to improve the system operation.     

Performance analysis of AAL multiplexer with CBR traffic and bursty traffic

This paper models and evaluates the AAL multiplexer to analyze AAL protocol in ATM networks. We consider an AAL multiplexer in which a single periodically deterministic CBR traffic stream and several variable size bursty background traffic streams are multiplexed and one ATM cell stream goes out. We model the AAL multiplexer as aB ^X +D/D/1/K queue and analyze this queueing system. We represent various performance measures such as loss probability and waiting time in the basis of cell and packet.     

On the asymptotic analysis of statistical multiplexers with hyper-bursty arrivals

We consider multiplexers in discrete time fed by the superposition of Ternary Markov Sources. Such sources are the natural extension of the Binary Markov Sources (BMS) recently used to model bursty arrivals in a high speed environment. Unlike BMS, we allow sources to have arbitrary (large) variance in the duration of their OFF (silence) or ON (burst) periods.This paper focuses mainly on the impact of large variability either in the ON or OFF period on the performance. Following some asymptotic analysis, simple results on the tail behavior of the number of cells queued in the multiplexer are given.Our results indicate that ignoring the variability in the ON period may grossly underestimate the cell buildup in the multiplexer queue for all levels of the utilization. Furthermore, the impact of large variability of the OFF period depends very much on the utilization of the system. For a lightly-loaded multiplexer (utilization below a given threshold), the impact of large variability of the OFF period is minimal. However, for a heavy-loaded multiplexer (utilization above the threshold) the impact of the large variability in the OFF period is similar to that of the ON period.     

Performance of an ATM multiplexer queue in the fluid approximation using the Beneš approach

This paper describes a new method for evaluating the queue length distribution in an ATM multiplexer assuming the cell arrival process can be assimilated to a variable rate fluid input. The method is based on a result due initially to Bene allowing the analysis of queues with general input. Its extension to fluid input systems is considered here in the case of a superposition of on/off sources. We derive an upper bound on the complementary queue length distribution. The method is most easily applied in the case of Poisson burst arrivals (infinite sources model). In this case, we derive analytic expressions for the tail of the queue length distribution. A corrective factor is deduced to convert the upper bounds to good approximations. Numerical results justify the accuracy of the method and demonstrate the impact of certain traffic characteristics on queue performance.     

Call Admission: A New Approach to Quality of Service

Quality of service guarantees are an important and much discussed aspect of ATM network design. However, there is no standard definition of quality of service. Moreover, some often-used criteria seem quite crude. We consider call admission to a bufferless ATM multiplexer with on/off sources. A new criterion for a guarantee on average cell loss is proposed. This criterion represents the quality of service from the point of view of the user, and is thus more reliable. We calculate the optimal policy that minimizes blocking subject to the guarantee, when there is only one type of user.The measure of cell-loss we propose is applicable to a wide range of models. It gives rise to a mathematical programming formulation, which we derive explicitly for our case.     

The Markov modulated regulated Brownian motion: A second-order fluid flow model of a finite buffer

A second-order fluid flow model of a queue with finite capacity buffer and variable net input process is presented, based on the previous work of Karandikar and Kulkarni (1995). Queue length is modelled as a Brownian motion whose parameters are controlled by a finite state Markov chain. The process, termed a Markov modulated regulated Brownian motion (MMRBM), provides analytical solutions for steady state queue length distributions, overflow losses and idleness probabilities using boundary regulators. Applications of the model include queues with failure-prone servers and ATM statistical multiplexers with variable traffic loads. This revised version was published online in June 2006 with corrections to the Cover Date.     

Guaranteed approximation of Markov chains with applications to multiplexer engineering in ATM networks

Discrete Markov chains are applied widely for analysis and design of high speed ATM networks due to their essentially discrete nature. Unfortunately, their use is precluded for many important problems due to explosion of the state space cardinality. In this paper we propose a new method for approximation of a discrete Markov chain by a chain of considerably smaller dimension which is based on the duality theory of optimization. A novel feature of our approach is that it provides guaranteed upper and lower bounds for the performance indices defined on the steady state distribution of the original system. We apply our method to the problem of engineering multiplexers for ATM networks.     

Overflow and loss probabilities in a finite ATM buffer fed by self-similar traffic

In [13], real-time measurements from LANs, variable-bit-rate video sources, ISDN control-channels, the World Wide Web and other communication systems have shown that traffic exhibits a behaviour of self-similar nature. In this paper, we give new lower bounds to buffer-overflow and cell-loss probabilities for an ATM queue system with a self-similar cell input traffic and finite buffer. The bounds are better than those obtained in [20], in an important region of parameters. As in [20], they decay hyperbolically with buffer size, when the latter goes to infinity. However, in some region, a factor which accompanies the decay is higher in this paper than in [20]. This revised version was published online in June 2006 with corrections to the Cover Date.     

Performance analysis of virtual circuit connections for bursty data sources in ATM networks

ATM is a packet-like transmission mode that has been proposed for BISDN. It is characterized by an asynchronous slotted transmission mechanism that provides a high bandwidth, low delay connection-oriented transport service to the end user. In this paper, we provide an analytical approach for determining the performance of a virtual circuit connection for data transmission in a high-speed ATM network with finite buffers at the network nodes. The analysis assumes that the network operates using thebest effort delivery strategy and that the end-to-end virtual circuit is responsible for guaranteeing the integrity of the connection. Since the normal Markovian assumptions do not apply, a concise exact solution is impossible to obtain. This provides motivation for developing approximate techniques such as those found in Whitt's QNA paper that allow us to use general distributions for the traffic streams and service times. However, even these techniques assume infinite buffer capacities and hence cannot model buffer overflow. We have therefore developed a hybrid model that allows us to incorporate finite buffers at the nodes. This enables us to study the effect on the performance of both link errors and buffer overflow in conjunction with an end-to-end packet loss recovery scheme.This work was supported in part by a grant from AT&T and in part by NSF under Grant No. 8914447.Work done while at the University of Pennsylvania, Philadelphia, PA 19104, USA     

Stochastic models of space priority mechanisms with Markovian arrival processes

In this paper, we study a single-server queue with finite capacity in which several space priority mechanisms are implemented. The arrival process is the general Markovian arrival process (MAP) which has been used to model the bursty arrival processes commonly arising in communication applications. The service times are generally distributed. These buffer mechanisms enable the Asynchronous Transfer Mode (ATM) layer to adapt the quality of the cell transfer to the quality of service requirements of the specific broadband ISDN services and to improve the utilization of the network resources. This is done by a selective discarding of cells according to the class they belong to. Computable expressions for various performance parameters are obtained. Numerical results are given for the case of a two-state Markov-modulated Poisson process (MMPP) and deterministic service times. The values derived can be used to evaluate the benefits of using priorities in an ATM network when the traffic is bursty and to make a comparative study of the buffer mechanisms. These results extend the models previously developed, which were limited to Poisson arrivals.     

A Priority Discrete Queueing Model for Multimedia Multiplexers

Multiplexers have been extensively modeled as discrete time queueing systems. In this article, we model a multimedia multiplexer handling traffic of two classes. One class represents real-time traffic, e.g., packets of live audio or video transmissions, and the other nonreal-time traffic, e.g., packets of file transfer transmissions. These packets arrive into the multiplexer in batches. In each time slot, one batch of each class arrive. The multiplexer gives service priority to class-1 packets over class-2. The demands of each class are in conflict with that of the other, and thus they are treated by the multiplexer differently. The multiplexer is thus modeled as a (preemptive) priority discrete queueing system with simultaneous batch arrivals and geometric service time. The system occupancy is analyzed and the joint probability generating function (PGF) of the number of packets of each class is derived. From this PGF, marginal PGFs of interest are obtained. The results for deterministic service time, most suitable for ATM purposes, are readily obtainable as a special case from the results of this article.     

Burst reducing servers in ATM networks

We study a stream of traffic or message as it is transferred over an ATM connection consisting of burst reducing servers. A message is modeled as a deterministic fluid flow, and an ATM node is modeled as a server which allocates bandwidth to messages. A message's burstiness curve b() is the buffer size needed to prevent cell loss if it is served at rate. A server is burst reducing if its output message is always less bursty than the input message. Two popular bandwidth allocation schemes — the fixed rate and the leaky bucket server — are shown to be burst reducing. We also present a new class of burst reducing servers, the affine servers. We derive buffer requirements along a multi-hop connection and the final fluid flow reaching the destination as a message goes through a sequence of burst reducing servers. Finally, we suggest an approach to defining service quality.Part of this work was presented at Globecom'91, December 1991, and Infocom'93, March 1993.     

Queueing at large resources driven by long-tailed M/G/∞-modulated processes

We analyze the queue at a buffer with input comprising sessions whose arrival is Poissonian, whose duration is long-tailed, and for which individual session detail is modeled as a stochastic fluid process. We obtain a large deviation result for the buffer occupation in an asymptotic regime in which the arrival rate nr, service rate ns, and buffer level nb are scaled to infinity with a parameter n. This can be used to approximate resources which multiplex many sources, each of which only uses a small proportion of the whole capacity, albeit for long-tailed durations. We show that the probability of overflow in such systems is exponentially small in n, although the decay in b is slower, reflecting the long tailed session durations. The requirements on the session detail process are, roughly speaking, that it self-averages faster than the cumulative session duration. This does not preclude the possibility that the session detail itself has a long-range dependent behavior, such as fractional Brownian motion, or another long-tailed M/G/∞ process. We show how the method can be used to determine the multiplexing gain available under the constraint of small delays (and hence short buffers) for multiplexers of large aggregates, and to compare the differential performance impact of increased buffering as opposed to load reduction. This revised version was published online in June 2006 with corrections to the Cover Date.     

Tandem queues with deterministic service times

In this paper we consider a tandem queueing model for a sequence of multiplexers at the edge of an ATM network. All queues of the tandem queueing model have unit service times. Each successive queue receives the output of the previous queue plus some external arrivals. For the case of two queues in series, we study the end-to-end delay of a cell (customer) arriving at the first queue, and the covariance of its delays at both queues. The joint queue length process at all queues is studied in detail for the 2-queue and 3-queue cases, and we outline an approach to the case of an arbitrary number of queues in series.Part of the research of this author has been supported by the European Grant BRA-QMIPS of CEC DG XIII.The research of this author was done during the time that he was affiliated with CWI, in a joint project with PTT Research.     

Chernoff bounds for mean overflow rates

A number of independent traffic streams arrive at a queueing node which provides a finite buffer and a non-idling service at constant rate. Customers which arrive when the buffer is full are dropped and counted as overflows. We present Chernoff type bounds for mean overflow rates in the form of finite-dimensional minimization problems. The results are based on bounds for moment generating functions of buffer and bandwidth usage of the individual streams in an infinite buffer with constant service rate. We calculate these functions for regulated, Poisson and certain on/off sources. The achievable statistical multiplexing gain and the tightness of the bounds are demonstrated by several numerical examples.     

Connection admission control for constant bit rate traffic at a multi‐buffer multiplexer using the oldest‐cell‐first discipline

Consider an ATM multiplexer where M input links contend for time slots on an output link which transmits C cells per second. Each input link has its own queue of size B cells. The traffic is delay sensitive so B is small (e.g., B=20). We assume that each of the M input links carries Constant Bit Rate (CBR) traffic from a large number of independent Virtual Connections (VCs) which are subject to jitter. The fluctuations of the aggregate traffic arriving at queue i, i=1,...,M, is modeled by a Poisson process with rate λ_i. The Quality of Service (QoS) of one connection is determined in part by the queueing delay across the multiplexer and the Cell Loss Ratio (CLR) or proportion of cells from this connection lost because the buffer is full. The Oldest‐Customer(Cell)‐First (OCF) discipline is a good compromise between competing protocols like round‐robin queueing or serving the longest queue. The OCF discipline minimizes the total cell delay among all cells arriving at the contending queues. Moreover, the CLR is similar to that obtained by serving the longest queue. We develop QoS formulae for this protocol that can be calculated on‐line for Connection Admission Control (CAC). These formulae follow from a simple new expression for the exact asymptotics of a M/D/1 queue. This revised version was published online in June 2006 with corrections to the Cover Date.     

A traffic control algorithm for Clos network type ATM switches

This paper presents a new traffic control algorithm for asynchronous transfer mode (ATM) switches composed of Clos network type switch fabric. In most traffic control algorithms previously proposed, an ATM switch has been considered as a single node, although the switch fabric of an ATM switch is usually of a network type. In this paper, we suggest a new control algorithm that is designed not only for the ATM network but also for the switch fabric and that can maintain high speed even in cases where buffer capacity of the switch fabric is limited. Main modules of the suggested algorithm are a traffic status detection mechanism based on non-parametric statistical tests, a cell-loss detection mechanism, and a cluster-based fair share computation procedure. Results of simulation experiments show that the suggested algorithm satisfactorily adjusts traffic rate of available bit rate services according to changes in traffic rate used by quality of service (QoS) guaranteed services. The results also show that the algorithm prevents cell losses relatively well and keeps the delay time of QoS guaranteed services short enough.     

Bounding the performance of tandem queues with finite buffer spaces

We consider a queueing system with three single servers in tandem with two intermediate buffer storages of finite capacity. The processing times are exponentially distributed and the first server has unlimited number of customers in front of it. Using a negative dependence property between the number of customers at the first and second buffer storages we show that a popular form of decomposition approach applied to this model, indeed, provides a lower bound for its performance. The approach used here to establish the bound is new and could be extended to establish bounds for other types of tandem queues with finite buffer spaces.     

On the departure process of a leaky bucket system with long-range dependent input traffic

Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range dependence, it is important to study the possible implications that such traffic may have for the design and performance of these networks. In particular, an important question is whether the offered traffic preserves its long-range dependent nature after passing through a policing mechanism at the interface of the network. One of the proposed solutions for flow control in the context of the emerging ATM standard is the so-called leaky bucket scheme. In this paper we consider a leaky bucket system with long-range dependent input traffic. We adopt the following popular model for long-range dependent traffic: Time is discrete. At each unit time a random number of sessions is initiated, having the distribution of a Poisson random variable with mean λ. Each of these sessions has a random duration τ, where the integer random variable τ has finite mean, infinite variance, and a regularly varying tail, i.e., P(τ >К) ~ К^-Lα L(К), where 1 < α < 2 L(·) is a slowly varying function. Once a session is initiated, it generates one cell at each unit of time until its termination. We examine the departure process of the leaky bucket policing mechanism driven by such an arrival process, and show that it too is long-range dependent for any token buffer size and any - finite or infinite - cell buffer size. Moreover, upper and lower bounds for the covariance sequence of the output process are established. The above results demonstrate that long-range dependence cannot be removed by the kinds of flow control schemes that are currently being envisioned for broadband networks. This revised version was published online in June 2006 with corrections to the Cover Date.