This paper revisits the classical model of ATM multiplexing. We exhibit an \exact" discrete-time model for the output queue of the switch, taking into account all peculiarities of the hardware functions, especially all synchronization-related features. The model however happens to present a complexity proportional to both the queue size and the number of inputs. A batch arrival model can be bui...

We introduce a general non-Gaussian, self-similar, stochastic process called the fractional Lévy motion (fLm). We formally expand the family of traditional fractal network traffic models, by including the fLm process. The main findings are the probability density function of the fLm process, several scaling results related to a singleserver infinite buffer queue fed by fLm traffic, e.g., scalin...

| We present simple exponential approximations to the transient behavior of the stable M=M=1 queue. The approximations are optimal in a least-squares sense, and we nd them to agree well with exact results. Our approach can be used to derive approximations for any time-dependent quantity with a known Laplace transform, e.g., the probability distribution and the moments of the queue size, of the ...

The M/M/1 retrial queue with working vacations and negative customers is introduced. The arrival processes of positive customers and negative customers are Poisson. Upon the arrival of a positive customer, if the server is busy the customer would enter an orbit of infinite size and the orbital customers send their requests for service with a constant retrial rate. The single server takes an exp...

We extend the analysis of queueing systems for real-life situations, where the arrival pattern of customers is unknown. In real systems, we must understand how the choice of a method of estimation influences the configuration of the system. Using kernel smoothing, we evaluate algorithms to estimate performance measures of a GI/M/c/N system, including the invariant probability distribution of th...

Time dependent system size probabilities of a birth and death process related to the Rogers-Ramanujan continued fraction are obtained. The range for the parameter in this continued fraction is obtained to ensure the positivity of the recursively defined birth and death rates. The general behavior of the birth and death rates is described and the asymptotic behavior of the transition probabiliti...

We extend the analysis of queueing systems for real-life situations where the arrival pattern of customers is unknown. In real systems, we must understand how the choice of a method of estimation influences the configuration of the system. Using kernel smoothing, we evaluate algorithms to estimate performance measures of a GI X /M/c/N system, including the invariant probability distribution of ...

In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded M...

In traditional batch-service queueing systems, the mean service time of batches are generally assumed to be constant. However, in numerous applications this assumption may not appropriate. telecommunication networks, transmission rates depend on number packets batch which can framed as batch-size-dependent queue. The objective paper is focus both queue and server content distribution an infinit...