Queuing
Overall rating: 3.67 Instructor: 3.62 Materials: 4.08 more …
Every networking engineer eventually encounters queues when configuring QoS on network devices. We usually either follow the vendor defaults (hoping they knew what they were doing) or guessing what the correct values might be once we encounter packet drops without ever understanding what it is we’re doing.
Guess what - we’re not the only ones. Queues were studied long before the first networking devices were built, and most things we’d need to know are well understood, but we’re too busy configuring network devices to study them.
We’ll try to fix that gap in this webinar (delivered in multiple live sessions starting on January 15th). Rachel Traylor will start with queuing terminology and basic mathematical principles underlying the models, move to more realistic queuing models, and gently introduce queuing networks and how we build network models from what we’ve learned.
Contents
Queuing Theory Basics
In this webinar, we will aim to get on the same page regarding queuing terminology and basic mathematical principles underlying the models. We’ll discuss characterizations of queues, give an overview of queuing disciplines, and explain Kendall’s notation. From there we will get a bit mathematical and discuss birth-death processes and counting processes, paying particular attention to the Poisson process. We’ll give a brief overview of some common service distributions. We’ll discuss the concept of stochastic balance as a tool for answering common questions engineers ask of queuing models, and apply all this knowledge to the most basic type of queue, the M/M/1 queue.
The final part of the lecture will cover discrete-time queueing, commonly used in different kinds of networking architecture and not commonly covered in many texts. We’ll present some very brief case studies to illustrate that the ideas are actually applied in “real” systems before concluding. Throughout, the assumptions and limitations of these very simple models will be well-emphasized.
Relaxing Assumptions
Building on our knowledge from the first webinar (Queuing Theory Basics), we’ll examine some more realistic assumptions on queuing models. We’ll examine finite capacity queues, priority classes, multiple server models, other service distributions besides exponential. We’ll also gently introduce queuing networks and how we build network models from what we’ve learned thus far. In particular, we’ll discuss Burke’s theorem, and closed/open Jackson networks.
Advanced Queuing Notions
At this point, we’ll spend some time giving an overview of more advanced considerations in queuing, such as non-steady-state queues, an algebraic-topological approach to queuing networks (with examples), differential equation/dynamical flow approaches for estimation, and we’ll spend some time discussing BCMP networks.
The Author
Rachel Traylor is a mathematician whose favorite coworkers are engineers. Her research interests span pure and applied mathematics, but mainly focus on probability theory and its applications to reliability and queueing. She’s invested in closing the disconnect between academic mathematics and the practical world of engineering. She’s held private-sector research positions at Dell EMC, done time as a database administrator for Lockheed Martin Aeronautics, and been an adjunct professor/lecturer at several colleges and universities across the US (Georgia Tech, the University of Texas at Arlington, Marquette University, and Foothill College).
Happy Campers
About the webinar
- i appreciate the opportunity to revisit a academic collegiate style technology presentation. It was and is refreshing to hear a low level foundational description of how the statistical multiplexors work, ( packet routers ).
as to VoQ’s I think she might be interested to consider for example 100 inputs of capacity say of 100Ghz or jigabits, over a two-stage switchinf “fabric / arbiter” trying to determine or schedule to a single output queue(s) on an egress output card/interface which has a capacity of 100Ghz / jigabits ... ie when the entire capacity of the system can be signalled via “back pressure” mechanisms via the center-stage scheduling “arbitration” to the ingresses VoQ system.... Then the magic of VoQ’ng gets groovy
Or so I was told ... once upon a time
thanks for all your great work - Tom Grisham
- Rachel seems very knowledgable in MAth but the problem I could not correlate what she is saying to network queueing. I really would like to understand how long a router or switch buffer the packets how long it would take to send the packet out of the interface how Qos affecting the queuening etc. with math proofs but the session was focused more on the math side of it.
- sinan okay
- I am so glad that finally there are some presentations that go into the mathematical background of networking. Dr. Traylor does an excellent conveying difficult concepts in a clear and practical manner.
- Jim Greene