Exponential Upper Bounds via Martingales for Multiplexers with Markovian Arrivals.

We obtain explicit upper bounds in closed form for the queue length in a slotted time FCFS queue in which the service requirement is a sum of independent Markov processes on the state space {O, 1}, with integral service rate. The bound is of the form P[queue length ≥ b] ≤ cy^(-b) for any b ≥ 1 where c 1 are given explicitly in terms of the parameters of the model. The model can be viewed as an approximation for the burst-level component of the queue in an ATM multiplexer. We obtain heavy traffic bounds for the mean queue length and show that for typical parameters this far exceeds the mean queue length for independent arrivals at the same load. We compare our results on the mean queue length with an analytic expression for the case of unit service rate, and compare our results on the full distribution with computer simulations

Queues with superposition arrival processes in heavy traffic

AbstractTo help provide a theoretical basis for approximating queues with superposition arrival processes, we prove limit theorems for the queue-length process in a Σ GIi/G/s model, in which the arrival process is the superposition of n independent and identically distributed stationary renewal processes each with rate n−1. The traffic intensity ρ is allowed to approach the critical value one as n increases. If n(1−ρ)2 → c, 0 < c < ∞, then a limit is obtained that depends on c. The two iterated limits involving ρ and n, which do not agree, are obtained as c → 0 and c → ∞

Optimization of resources for H.323 endpoints and terminals over VoIP networks

Abstract: We suggest a method of optimizing resource allocation for real time protocol traffic in general, and VoIP in particular, within an H.323 environment. There are two options in the packet network to allocate resources: aggregate peak demand and statistical multiplexing. Statistical multiplexing, our choice for this case, allows the efficient use of the network resources but however exhibits greater packet delay variation and packet transfer delay. These delays are often the result of correlations or time dependency experienced by the system’s queue due to the variations observed in different point processes that occur at a point of time. To address these issues, we suggest a queuing method based on the diffusion process approximated by Orstein-Ulenbeck and the non-validated results of Ren and Kobayashi

Markovian queues with correlated arrival processes

In an attempt to examine the effect of dependencies in the arrival process on the steady state queue length process in single server queueing models with exponential service time distribution, four different models for the arrival process, each with marginally distributed exponential interarrivals to the queueing system, are considered. Two of these models are based upon the upper and lower bounding joint distribution functions given by the Fréchet bounds for bivariate distributions with specified marginals, the third is based on Downton’s bivariate exponential distribution and fourthly the usual M/M/1 model. The aim of the paper is to compare conditions for stability and explore the queueing behaviour of the different models

Some aspects of traffic control and performance evaluation of ATM networks

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