Bayesian Inference on the Steady State Characteristics of Some Advanced Queueing Models

Queuing theory is the mathematical study of queuing, or waiting in lines.

Queues contain customers such as people, objects, or information. Queues

form when there are limited resources for providing a service. A basic queuing

system consists of an arrival process (how customers arrive at the queue, how

many customers are present in total), the queue itself, the service process for

attending to those customers, and departures from the system. Essentials in

modern life would not be possible without queueing theory.

The purpose of this thesis is to address the inferential problems associated

with various single/multi-server queueing models. It is mainly focused on the

estimation of queue parameters like arrival rate, service rate and some important

steady state queue characteristics such as traffic intensity, expected queue

size, expected system size and expected waiting time. The study of queueing

model is basically motivated by its use in communication system and computer

networks. The development of an appropriate stochastic models is one of the

major problem associated with the study of communication systems as it requires

more and more sophistication to manage their complexity.

Queueing theory was developed to provide models to predict the behavior

of the systems that attempt to provide service for randomly arising demand.

The earliest problems studied were those of telephone traffic congestion. The

pioneer investigator was the Danish mathematician, A. K. Erlang, who, in

1909, published "The theory of Probabilities and Telephone Conversations".

In later works he observed that a telephone system was generally characterized

by either Poisson input, exponential service times, and multiple servers,

or Poisson input, constant service times, and a single channel. There

are many valuable applications of the theory, most of which have been well

documented in the literature of probability, operations research, management

science, and industrial engineering. Some examples are traffic flow (vehicles,

aircraft, people, communications), scheduling (patients in hospitals, jobs on

machines, programs on a computer), and facility design (bank, post offices,

amusement parks, fast-food restaurants).