Queuing

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 studies 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.

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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.

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…