Performance of discrete-time queueing systems

A general treatment of discrete-time buffers with one randomly interrupted output line

Some remarks on discrete-time buffers with correlated arrivals

A discrete buffered system with infinite buffer size, one single output channel, and periodic opportunities for service (synchronous transmission) is considered in a two-state environment. The output channel is subjected to a random interruption process, which is characterized by a Bernoulli sequence of independent random variables, with probabilities dependent on the environment state. The environment states have random sojourn times with "mixture of geometrics"-type distributions. The arrival process is dependent on the environment state, but arbitrary. For this system, expressions are derived for the probability generating functions of the number of messages in the buffer at various time instants. A number of special cases and possible applications of the model are discussed, and an extended example is given as an illustration of the study.

On Discrete Buffers in a Two-State Environment

A mathematical model for discrete-time buffer systems with correlated output process

A closed-form solution to the buffer design problem is presented by studying a queueing model with a hybrid input traffic arrival process (mixture of Poisson and burst Poisson processes), synchronous output and single server with random interruptions. The queueing model developed is of unified nature as it includes Poisson and burst Poisson arrival processes and the mixture of the two as well. It is shown that, at a modified offered load, the empty buffer probability in an infinite buffer equals that of a finite buffer with actual offered load as its input. The modified offered load is shown to be equal to the carried load of the finite buffer. Thus, it is shown that the expression for the buffer-content state probability of the finite buffer of any length can be directly deduced from that of the infinite buffer, and hence various performance parameters can be evaluated. An integrated digital voice-data system is taken as an example for the model developed. The relationships among buffer size, overflow probability and average message queueing delay due to buffering are portrayed on graphs with the average burst length, the traffic intensity and the input traffic mixture ratio taken as parameters. It is concluded that the burst nature of the input traffic is a very important factor in the buffer design problem.

M. Khalid

Papers

Buffer design in a closed form with hybrid input and random server interruptions