Performance of discrete-time queueing systems

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

We develop a mathematical analysis for the steady state performance of a system where voice calls and data packets are transmitted over the same channel The voice calls have priority over the data packets, in that the data packets are transmitted only when there are no voice calls present in the system or the voice conversation is in a long silent period

Data Performance in a System Where Data Packets are Transmitted During Voice Silent Periods--Single Channel Case

A queueing model with finite buffer size, mixed input traffic (Poisson and burst Poisson arrivals), synchronous transmission and server interruptions through a Bernoulli sequence of independent random variables is studied. Using average burst length, traffic intensity and input traffic mixture ratio as parameters, the relationships among buffer size, overflow probability and expected message queueing delay are obtained. An integrated digital voice-data system with synchronous time division multiplexing (STDM) for a large number of voice sources and mixed arrival process for data messages is considered as an application for this model. The results of this study are portrayed on graphs and may be used as guidelines in buffer design problems in digital voice-data systems. The queueing model developed is quite general in a sense that it covers pure Poisson and burst Poisson arrival processes and the mixture of the two as well.

Buffer Behavior for Mixed Arrivals and Single Server with Random Interruptions

Analysis of an infinite buffer system with random server interruptions

A queueing model with finite buffer size, Poisson arrival process, synchronous transmission and server interruptions is studied through a Bernoulli sequence of independent random variables. An integrated digital voice-data system with Synchronous Time-Division Multiplexing (STDM) for voice sources and Poisson arrival process for data messages is considered as an application for this model. The relationships among overflow probabilities, buffer size and expected queueing delay due to buffering for various traffic intensities are obtained. The results of this study are portrayed on graphs and may be used as guide lines for the buffer design in digital voice-data systems. Although this study arose in the design of a buffer for digital voice-data systems, the queueing model developed is quite general and may be useful for other industrial applications.

C. Saxena

Papers

Finite Buffer Behavior with Poisson Arrivals and Random Server Interruptions