214 research outputs found

    Rigorous Bounds for Loss Probabilities in Multiplexers of Discrete Heterogenous Markovian Sources

    Get PDF
    Exponential upper bounds of the form P[queue ā‰„ b] ā‰¤ Ļ†y^(-b) are obtained for the distribution of the queue length in a model of a multiplexer in which the input is a heterogeneous superposition of discrete Markovian on-off sources. These bounds are valid at all queue lengths, rather than just asymptotic in the limit bā†’āˆž. The decay constant y is found by numerical solution of a single transcendental equation which determines the effective bandwidths of the sources in the limit bā†’āˆž. The prefactor Ļ† is given explicitly in terms of y. The bound provides a means to determine rigorous corrections to effective bandwidths for multiplexers with finite buffers

    Asymptotic buffer overflow probabilities in multiclass multiplexers : part I : the GPS policy

    Get PDF
    Cover title.Includes bibliographical references (p. 34-37).Supported by a Presidential Young Investigators award. DDM-9158118 Matching funds from Draper Laboratory. Supported by ARO. DAAL-03-92-G-0115Dimitris Bertsimas, Ioannis Ch. Paschalidis, John N. Tsitsiklis

    Exponential Bounds for Queues with Markovian Arrivals

    Get PDF
    Exponential bounds P[queue ā‰„ b] ā‰¤ Ļ†e^(-Ī³b) are found for queues whose increments are described by Markovian Additive Processes. This is done application of maximal inequalities to exponential martingales for such processes. Through a thermodynamic approach the constant Ī³ is shown to be the decay rate for an asymptotic lower bound for the queue length distribution. The class of arrival processes considered includes a wide variety of Markovian multiplexer models, and a general treatment of these is given, along with that of Markov modulated arrivals. Particular attention is paid to the calculation of the prefactor Ļ†

    Some aspects of traffic control and performance evaluation of ATM networks

    Get PDF
    The emerging high-speed Asynchronous Transfer Mode (ATM) networks are expected to integrate through statistical multiplexing large numbers of traffic sources having a broad range of statistical characteristics and different Quality of Service (QOS) requirements. To achieve high utilisation of network resources while maintaining the QOS, efficient traffic management strategies have to be developed. This thesis considers the problem of traffic control for ATM networks. The thesis studies the application of neural networks to various ATM traffic control issues such as feedback congestion control, traffic characterization, bandwidth estimation, and Call Admission Control (CAC). A novel adaptive congestion control approach based on a neural network that uses reinforcement learning is developed. It is shown that the neural controller is very effective in providing general QOS control. A Finite Impulse Response (FIR) neural network is proposed to adaptively predict the traffic arrival process by learning the relationship between the past and future traffic variations. On the basis of this prediction, a feedback flow control scheme at input access nodes of the network is presented. Simulation results demonstrate significant performance improvement over conventional control mechanisms. In addition, an accurate yet computationally efficient approach to effective bandwidth estimation for multiplexed connections is investigated. In this method, a feed forward neural network is employed to model the nonlinear relationship between the effective bandwidth and the traffic situations and a QOS measure. Applications of this approach to admission control, bandwidth allocation and dynamic routing are also discussed. A detailed investigation has indicated that CAC schemes based on effective bandwidth approximation can be very conservative and prevent optimal use of network resources. A modified effective bandwidth CAC approach is therefore proposed to overcome the drawback of conventional methods. Considering statistical multiplexing between traffic sources, we directly calculate the effective bandwidth of the aggregate traffic which is modelled by a two-state Markov modulated Poisson process via matching four important statistics. We use the theory of large deviations to provide a unified description of effective bandwidths for various traffic sources and the associated ATM multiplexer queueing performance approximations, illustrating their strengths and limitations. In addition, a more accurate estimation method for ATM QOS parameters based on the Bahadur-Rao theorem is proposed, which is a refinement of the original effective bandwidth approximation and can lead to higher link utilisation

    Fast simulation of packet loss rates in a shared buffer communications switch

    Get PDF
    This paper describes an efficient technique for estimating, via simulation, the probability of buffer overflows in a queueing model that arises in the analysis of ATM (Asynchronous Transfer Mode) communication switches. There are multiple streams of (autocorrelated) traffic feeding the switch that has a buffer of finite capacity. Each stream is designated as either being of high or low priority. When the queue length reaches a certain threshold, only high priority packets are admitted to the switch's buffer. The problem is to estimate the loss rate of high priority packets. An asymptotically optimal importance sampling approach is developed for this rare event simulation problem. In this approach, the importance sampling is done in two distinct phases. In the first phase, an importance sampling change of measure is used to bring the queue length up to the threshold at which low priority packets get rejected. In the second phase, a different importance sampling change of measure is used to move the queue length from the threshold to the buffer capacity

    Asymptotic buffer overflow probabilities in multiclass multiplexers : part II : the GLQF policy

    Get PDF
    Cover title.Includes bibliographical references (p. 33-35).Supported by a Presidential Young Investigator Award. DDM-9158118 Matching funds from Draper Laboratory. Supported by ARO. DAAL-03-92-G-0115Dimitris Bertsimas, Ioannis Ch. Paschalidis, John N. Tsitsiklis

    Multiplexing regulated traffic streams: design and performance

    Get PDF
    The main network solutions for supporting QoS rely on traf- fic policing (conditioning, shaping). In particular, for IP networks the IETF has developed Intserv (individual flows regulated) and Diffserv (only ag- gregates regulated). The regulator proposed could be based on the (dual) leaky-bucket mechanism. This explains the interest in network element per- formance (loss, delay) for leaky-bucket regulated traffic. This paper describes a novel approach to the above problem. Explicitly using the correlation structure of the sourcesā€™ traffic, we derive approxi- mations for both small and large buffers. Importantly, for small (large) buffers the short-term (long-term) correlations are dominant. The large buffer result decomposes the traffic stream in a stream of constant rate and a periodic impulse stream, allowing direct application of the Brownian bridge approximation. Combining the small and large buffer results by a concave majorization, we propose a simple, fast and accurate technique to statistically multiplex homogeneous regulated sources. To address heterogeneous inputs, we present similarly efficient tech- niques to evaluate the performance of multiple classes of traffic, each with distinct characteristics and QoS requirements. These techniques, applica- ble under more general conditions, are based on optimal resource (band- width and buffer) partitioning. They can also be directly applied to set GPS (Generalized Processor Sharing) weights and buffer thresholds in a shared resource system

    Sharp Bounds in Stochastic Network Calculus

    Full text link
    The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper it is uncovered that for bursty arrival processes (specifically Markov-Modulated On-Off (MMOO)), whose amenability to \textit{per-flow} analysis is typically proclaimed as a highlight of SNC, the bounds can unfortunately indeed be very loose (e.g., by several orders of magnitude off). In response to this uncovered weakness of SNC, the (Standard) per-flow bounds are herein improved by deriving a general sample-path bound, using martingale based techniques, which accommodates FIFO, SP, EDF, and GPS scheduling. The obtained (Martingale) bounds gain an exponential decay factor of O(eāˆ’Ī±n){\mathcal{O}}(e^{-\alpha n}) in the number of flows nn. Moreover, numerical comparisons against simulations show that the Martingale bounds are remarkably accurate for FIFO, SP, and EDF scheduling; for GPS scheduling, although the Martingale bounds substantially improve the Standard bounds, they are numerically loose, demanding for improvements in the core SNC analysis of GPS
    • ā€¦
    corecore