After following this course, students are expected to
- Know the fundamental queueing relations: Little's law, the PASTA property, the Arrival Theorem.
- Know about Markovian queues.
- Know about the M/G/1 and the G/M/1 queue.
- Know about Jackson networks of queues and Kelly/Whittle networks of queues.
- Know about networks of quasi-reversible queues.
- Know about queue disciplines, such as FIFO, PS, LIFO-PR.
- Be able to derive fundamental queueing relations and prove their correctness.
- Be able to formulate a Markov chain model for queueing systems, including open and closed queueing networks.
- Be able to derive the equilibrium distribution of queueing systems and prove correctness of this distribution.
- Be able to evaluate the main performance measures for queueing systems.
This course is about a phenomenon we all have to live with: waiting, in particular in a line (or queue) before receiving some kind of service. Examples include the cashier in a supermarket, the ticket counter at the theatre, and waiting on the phone before an operator is ready to answer your call. But also other entities can 'wait', like data packets before being sent over a communications network, or (semi-)products before being processed further. In all these (and many more) situations it is important to analyze quantities of interest (such as the mean queue length, or the waiting time distribution), as well as means to optimize the performance. Some basic models and techniques are being offered in this course both for single queues and networks of queues. Due to the uncertainties in arrival and service times, probability theory and stochastic processes play an important role in it.
The main topics include:
- Fundamental queueing relations (Little's law, PASTA property, Arrival Theorem)
- Markovian queues such as the M/M/1 queue, and the M/M/c queue
- The M/G/1 and the G/M/1 queue
- Jackson networks of queues
- Kelly/Whittle networks of queues
- Networks of quasi-reversible queues
- Queue disciplines (FIFO, PS, LIFO-PR)