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).