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Department of Mathematics and Applications
"Renato Caccioppoli"


Stochastic Processes and Applications (mod. 2)

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Stochastic Processes
and Applications (mod. 2)

Credits

6

Prerequisites

None.

Examination method

Passing an integrated examination, possibly divided into several tests, on the contents of Stochastic Processes and Applications mod. 1 and Stochastic Processes and Applications mod. 2

Learning
objectives

The course aims to introduce students to the study of continuous-time stochastic processes with a discrete state space. Particular attention will be paid to queueing theory through the formulation and analysis of mathematical-probabilistic and simulation models suitable for describing real systems in which a generic user requests a particular service and must wait in some kind of queue (or waiting line) if the server is not immediately available. Finally, a further objective is to enable students to simulate a service system on their own, appropriately linking and using methods and theories specific to the discipline.

Contents

Service systems. Distributions of interarrival times and service times. Performance measures. Little’s laws. Poisson process. Birth-death processes. Markov chains. Queues: M/M/1, M/M/1 with clearing, M/M/1/K, M/M/s, M/M/∞, M/D/1, M/G/1, GI/M/1. Generation of random numbers and random variables. Further topics in estimator theory, statistical hypothesis testing and the Monte Carlo method. Simulation of a service system.