WIMCS is delighted that Professor Maury Bramson (University of Minnesota) will deliver this year's LMS Invited Lectures entitled 'Stability of Queuing Networks' from 12-16th April

A number of invited guest speakers including Professor Adam Letchford (University of Lancaster), Professor Joerg Fliege (University of Southampton) and Professor Jianfeng Feng (University of Warwick) will give additional lectures.

The event is hosted by the University of Swansea. Further details here. The proposed timetable details here.

To register your interest please contact Stephen Williamson. Some funding support for participants is available. Please inquire for more details to Stephen Williamson.

An abstract of the material to be covered in Professor Bramson's Lectures:

Queueing networks constitute a large family of stochastic models, involving "jobs" or "customers" that wait in queues until being served. Once its service is completed, a job moves to the next prescribed queue, with the procedure continuing until the job leaves the network.

Questions involving the stability (that is, positive recurrence) of these models have received substantial attention since the early 1990s. Although the theory is currently incomplete, there are positive criteria for stability as well as examples where stability fails in a nonobvious way. Most of these results pertain to HL networks, where only the first job at a queue receives service at a given time.

In these lectures, we summarize the stability theory for queueing networks, with an emphasis on HL networks. After introducing the basic concepts, we recall some of the classical theory and next give examples of unstable networks. We then develop the technique of fluid limits, which we employ to show stability in different cases. Lastly, we briefly discuss certain more general networks, including in detail the join the shortest queue networks.

The lectures are divided into the following parts:

  • Introduction
  • The Classical Networks
  • Instability of Subcritical Queueing Networks
  • Stability of Queueing Networks
  • Applications
  • Join the Shortest Queue Networks

Much of the material in these lectures can be found in the Springer Lecture Notes volume 1950, "Stability of Queueing Networks", a preliminary version of which can be found at www.math.umn.edu/~bramson/

Wales Institute of Mathematical and Computatuional Sciences