Queuing theory and queuing analysis are based on the use of probability theory and the concept of random variables. We utilize the concepts embodied in probability in a number of different ways. For example, we may ask what the probability is of the Boston Bruins winning the Stanley Cup this year. How likely is George W. Bush to be reelected after the events of this year? How likely is it to snow on the top of Mt. Washington in New Hampshire in January of this year? Most of the time a general answer would suffice. For example, it is highly probable that snow will fall sometime in January on Mt. Washington. Conversely, based on the last 30 years of frustration, it is also highly unlikely that the Boston Bruins will win the Stanley Cup this year. Probability theory allows us to make more precise definitions for the probability of an event occurring based on past history or on specific available measurements, as we will see. In this chapter, we will introduce the concepts of probability, joint probability, conditioned probability, and independence. We will then move on to probability distributions, stochastic processes, and, finally, the basics of queuing theory.

Before discussing queuing analysis, it is necessary to introduce some concepts from probability theory and statistics. In basic probability theory, we start with the ideas of random events and sample spaces. Take, for instance, the experiment that involves tossing a fair die (an experiment typically defines a procedure that yields a...