#### Date of Award

Spring 1976

#### Document Type

Thesis

#### Department

Mathematics, Engineering & Computer Science

#### First Advisor

Ronald Knoshaug

#### Second Advisor

Alfred Murray

#### Third Advisor

John Semmens

#### Abstract

The problem I have chosen is a sequential service problem which is a type of stochastic process. The system has two servers A and B. A customer will enter only if A is free. Once A has served the customer, he will then be served by B If B is free or leave if B is busy. The objectives of the problem are to find the average number of customers entering the system, how many of these are served by B, the average number of customers present, and the average amount of time spent in the system. The Poisson process determines the arrival rate of customers. The servers serve with exponential rates.

Stochastic processes can be defined two ways, one of which is mathematically oriented and the other oriented towards the non-mathematician. A stochastic process is the mathematical abstraction of an empirical process whose development is governed by probabilistic laws. A stochastic process is any probability process, that is, any process running along in time and controlled by probabilistic laws.J Karkov chains are a type of stochastic process. They are used- to describe probability systems in which the results are dependent on the previous events. The system has fixed conditional probabilities pij of Ek given that Ej has occurred at the preceding trial and the probabilities of sample sequences are defined in terms of an initial probability distribution for the states EK=0.

#### Recommended Citation

Kane, John, "Stochastic Processes With Emphasis On Random Walks" (1976). *Mathematics, Engineering and Computer Science Undergraduate Theses*. 113.

https://scholars.carroll.edu/mathengcompsci_theses/113