Markov chains model random processes that run over a finite or countably infinite number of steps. Researchers tend to write such models in terms of transition matrices -- matrices that state the likelihood of certain states for a successive step. One common example of a Markov chain application is weather forecasting. The probability of it raining tomorrow can be predicted well if you use the information that you have today: whether it is raining today. You can then design a set of probability matrices based on the current weather situation to predict tomorrow's weather.
Poisson processes are important for designing models of real-world uncommon phenomena. They are primarily found in operations research problems that deal with unlikely or rare situations, such as earthquakes, textbook typos or the breakdown of machines. These Poisson processes allow researchers to calculate the probability of the events and account for them in the design of policies. For example, insurance companies create Poisson processes for a variety of damaging situations. This allows the insurance companies to rationally price their policies to account for such rare events.
Queuing theory includes a class of models that deal with how customers arrive to, wait in and leave a facility or service. These models allow researchers to understand and predict the development of customer service. Operations researchers use these models to design queuing methods for businesses and computer systems. Important results of queuing models are the average amount of customers a company can expect at one time, the optimal number of servers the company needs and the speed at which a customer should be served.
Reliability theory's name comes from the idea of product reliability. This theory primarily deals with modeling the probability of a system's functioning or failing. Because many systems in business and other fields related to operations research contain many components, it is difficult to analyze how likely the whole system is to fail based on these individual components. Reliability theory handles this task, allowing designers to know how to more efficiently create products, allowing companies to optimize warranties and return policies.