Stochastic Networks

Course manual 2019/2020

Course content

Stochastic Networks theory is a subdomain of Applied Probability. While elementary Queueing Theory studies single service systems, the theory of Stochastic Networks is concerned with the interaction of networks of queueing and service systems and the impact thereof on the performance of the entire network. As the name suggests, the main tool in the understanding of Stochastic Networks are Stochastic Processes, and in particular Markov processes.

The aim of the course is to discuss in detail several topics on Stochastic Networks that have been subject of much research since the late 1970s. Students with special interest in in product-form queueing networks are advised to follow the course 'Multi-class Queues and Stochastic Networks' that is part of the LNMB PhD program.

The course will start with a brief look back at the theory of Markov Chains and elementary queueing theory (see the third year UvA bachelor course 'Markov Chains') and then covers migration processes,
Little's law, reversibility and loss networks, decentralized optimization in networks (with applications to electrical and road traffic networks), random access networks (capacity of distributed protocols using Foster-Lyapunov criteria), effective bandwidth of multiplexed traffic streams (large deviations), distributed traffic control for small-scale dynamics in networks, large-scale dynamics and bandwidth sharing networks. If time permits we will briefly touch on fluid and diffusion limits in stochastic networks.

Study materials

Literature

• Kelly, F., & Yudovina, E. (2014). Stochastic Networks (Institute of Mathematical Statistics Textbooks). Cambridge: Cambridge University Press.
  http://www.statslab.cam.ac.uk/~frank/STOCHNET/LNSN/book.pdf

Objectives

• Recognize networks of standard M/G/c/K queueing models
• Know what stochastic processes and in particular Markov chains are
• Know what migration processes are
• Know Little's law
• Understand reversibility in stochastic networks
• Know stationary behavior of loss networks
• Be able to solve decentralized optimization problems in networks
• Be able to characterize the capacity in standard random access networks
• Know what the effective bandwidth of multiplexed traffic streams is
• Know examples of distributed traffic control for small-scale dynamics in networks (e.g., TCP)
• Know what bandwidth sharing networks are

Teaching methods

• Lecture

Lectures: there are 14 lectures of 2 hours each; in three of these lectures there will be a quizz, one of these lectures will be used for a midterm test

Self-study: students will be provided with additional material for further back ground

Assignments: students use the acquired knowledge to solve problems at home

Learning activities

Attendance

The programme does not have requirements concerning attendance (OER-B).

Additional requirements for this course:

The programme does not have requirements concerning attendance (OER-B), but all material covered in class is mandatory knowledge for the quizzes, intermediate test and exams; not attending a class is left at the student's responsibility

Assessment

Mid term test (30%)
Final exam (50%)
Quizzes (10%; average of 2)
Assignments (10%; average of 2) NOTE: BE AWARE OF THE RULES ON PLAGIARISM AND FRAUD
Resit: Replaces all previous grades

Inspection of assessed work

For the exam: By appointment (made through email) after the grade is made known
For midterm/quizzes/assignments: in class

Assignments

There are three graded assignments handed out during the course; the average of the two highest grades make up for 10% of the final grade. The assignments must be made individually (note the fraud and plagiarism regulations).

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• prof. dr. M.R.H. Mandjes

Staff

• prof. dr. R. Nunez Queija