Stochastic Networks

Course manual 2025/2026

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

• Stochastic processes and in particular Markov chains.
• Networks of standard M/G/c/K queueing models.
• Migration processes.
• Little's law.
• Reversibility in stochastic networks.
• Stationary behavior of loss networks.
• Solve decentralized optimization problems in networks.
• Characterize the capacity in standard random access networks.
• Effective bandwidth of multiplexed traffic streams.
• Distributed traffic control for small-scale dynamics in networks (e.g., TCP).
• Bandwidth sharing networks.

Teaching methods

• Lecture
• Self-study

Lectures: there are 14 lectures of 2 hours each; in three of these lectures there will be a quiz, two of these lectures will be used as preparation for the midterm test and the final exam.

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

This programme does not have requirements concerning attendance (TER-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%)
2 Quizzes (each 10%)
Resit: Replaces all previous grades

Inspection of assessed work

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

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

Contact information

Coordinator

• prof. dr. R. Nunez Queija

Staff

• prof. dr. R. Nunez Queija