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.


This webinar is part of Networking Fundamentals roadmap and accessible with standard subscription

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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 TraylorDr. Rachel Traylor is a professional private-sector mathematician and the cofounder of the Math Citadel, a research and consulting firm specializing in mathematical consulting. She received her PhD in mathematics from the University of Texas at Arlington, a MS Statistics and BS Applied Mathematics from Georgia Tech. Her research interests include probability theory, reliability, and queuing theory; in particular, she’s been very interested in sequences of dependent random variables. She’s a former senior research scientist for Dell EMC, former university lecturer in mathematics and statistics (Foothill College, University of Texas at Arlington, Georgia Tech), and former DBA/Quality Analyst at Lockheed Martin. She has 6 pending patents and 9 academic publications in the fields of probability and reliability theory.

More about Rachel…

Happy Campers

About the webinar

This was way to mathematical for me

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