STAT 405 (Stochastic Models for Queues and Networks)
| DESCRIPTION |
The course treats applications of stochastic process models
of time-dependent
systems, specifically systems like computer and telecommunication
networks
where hardware requirements (e.g., numbers of switches and servers)
must
be balanced against the buildup of demand to avoid long backlogs and
degradation
of service. |
| PREREQUISITES |
Math 241 plus
Required: a course in Probability, such as Stat 400, in
which Random Variables are manipulated using Calculus.
Recommended: Math 240 or Math 241. |
| TOPICS |
Review of Probability
Basic concepts of Probability and random
variables
including joint and conditional probability, mass functions and
densities.
Expectations and conditional expectations. Law of Large
Numbers.
Indicator notations and generating functions will be used to develop
intuitive
relations among several types of discrete and continuous random
variables.
(2 weeks)
Poisson & Renewal Processes
Definitions and basic properties.
Memoryless
property and equivalent characterizations of Poisson process. Poisson
process
as renewal process with exponential inter-arrivlas. Renewal
equation
and waiting-time paradoxes. (3 weeks)
Single server Queues with Random (Poisson)
Customer-arrivals.
Formulation of queues as Poisson-related
Markov
processes. Application of renewal and Poisson process theory to
qualitative
behavior of long-term Time and Customer Averages for general
single-server
Queues and random (Poisson) customer-arrivals. (3 weeks)
Markovian models, Equilibrium, & Balance Relations
Balance relations governing equilibrium
behavior
in the general context of Markovian models, leading to formulation of
questions
and derivation of equilibrium properties of special classes of Queueing
Networks. (3 weeks)
Topics in Qualitative Theory of Networds of Queues
Selection of topics emphasizing concrete
calculations
of equilibria for special models, plus Monte Carlo simulations of
queueing
systems. (3.5 weeks)
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| TEXT |
Text(s)
typically used in this course. |
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