PhD students follow the extended version of the course under course code EP3340.

PhD students need to participate in dedicated seminar sessions, and need to complete an individual project, instead of the project designed for the master students. PhD students need to complete all other moments in the course, such as the home assignments and the exam.

Advanced material, covered only by PhD students:

A1.Poisson Process: equivalent definitions of the Poisson process, construction of a Poisson process, relationship to Geometric distribution and Uniform distribution. Extensions considering homogeneity and higher dimensions. Use of Poisson Process assumption in the research literature.

A2.Analysis of both discrete and continuous time MCs in transient state. Ergodicity and stability, proof of conditions for these.

A3. Finding steady state via generating function.

A4.Non-Markovian queuing systems, renewal theory, embedded Markov chains. The derivation of the Pollaczek-Khinchin transform equations through the use of embedded Markov chains.

A5.Outlook: Optimal control of queues or Markov decision process

A.6. Small project: queuing theory model formulation (and maybe solution of model) of a problem closely related to the research of the PhD student. Example project 1, Example project 2 (ca, one week of work)