# The WiSE Article Series: Wi-Fi Subtleties Explained (Throughput Algebra)

## The WiSE Article Series: Wi-Fi Subtleties Explained (Throughput Algebra)

By CWNP On 01/04/2013 - 43 Comments

In this first article in a multi-part WiSE Article Series, Bhaskaran Raman explains the formulas you can use to estimate throughput on WLANs.

Guest Blogger: AirTight Networks Author: Bhaskaran Raman, PhD. Series Editor: Tom Carpenter
About the WiSE article series: Wireless is inherently complex; its study spans at least two engineering disciplines: Electrical Engineering and Computer Science. Add to this the nuances of various standards, vendor implementations, RF environments, and protocol interactions, and it is not uncommon to feel a little lost in understanding the various aspects of Wi-Fi network operation. In this series of short articles, we explain various Wi-Fi subtleties, to work toward a better understanding of Wi-Fi network deployments.

## WiSE Article No.1 Wi-Fi Throughput Algebra - Simplified

Network administrators are often faced with the need to do throughput measurements, while evaluating a Wi-Fi network design or deployment. It is well known that measured Wi-Fi throughput falls below the maximum data rate numbers such as 300 Mbps or 450 Mbps, attached to product datasheets. However, what is the throughput number one should expect during the actual measurement? This is often unclear because one gets different throughput numbers at different locations and even different numbers during different runs at the same location. There is also dependence on the Wi-Fi client used for the measurement and its orientation, the measurement software, and various settings in the AP and the measurement software. You may also see different numbers on the Internet, reported by others.

This article simplifies Wi-Fi throughput algebra, to give a rule of thumb for what throughput to expect when taking into account at least the first order factors which affect all environments and tests. So if you measure a number in the neighborhood of this expectation, you know your results are fine. Again, I stress the word neighborhood, because it is not one magic number, but still a good estimate based on fundamental underlying principles. In the case of Ethernet, the measured throughput is just a few percentage points below the link speed: 100 Mbps or 1 Gbps. It is not so simple with Wi-Fi!

We focus here on the various overhead factors in Wi-Fi. As with every protocol, Wi-Fi has payload packaging overheads such as the protocol headers at various layers of the stack. However, Wi-Fi also has other significant causes of overhead.

Imagine a setting where a group of people are talking. Assuming everyone is polite to everyone else, each person, before talking, waits a while to get a chance to talk: check others’ faces, gestures, listen for those whom he or she can’t see, etc. Wi-Fi radios operate pretty similarly. A significant amount of time is spent in this checking: a process known as backoff for collision avoidance. Just as in the case of the group of people, the reason for this mechanism is well grounded: to minimize the chance of collisions, where more than one person (Wi-Fi station) talks (transmits) at the same time.

It turns out that this backoff is a significant overhead in Wi-Fi. As the figure below shows, this overhead can dominate, for a typical Ethernet MTU sized frame (1500 bytes), especially at high 802.11n data rates.

[caption id="" align="aligncenter" width="653"] 802.11 Protocol Overhead[/caption]

Fortunately, 802.11n has the frame aggregation feature suggested in the preceding image, where multiple frames are sent for each backoff process.  Typically 10-20 frames are aggregated together.  Taking this into account, the simplified algebra for the expected Wi-Fi throughput is:

[caption id="" align="aligncenter" width="685"] Aggregated Frame Throughput Formula for UDP[/caption]

While the above formula is a good approximation for the expected throughput using UDP, this is however not the end of the story because we must consider the different impact of TCP-based communications. TCP uses an acknowledgment (ACK) mechanism to achieve reliable data transfer. Here’s the bad news. The ACK packets, which go in the reverse direction as the data, are quite small: 20 bytes IP payload typically. This means, that even with 802.11n frame aggregation, we’re stuck with a high overhead in the reverse direction! And of course, the ACK itself is an overhead, when it comes to measuring the throughput as seen by the end user application.

Adjusting for this TCP ACK overhead, the throughput algebra now stands as:

[caption id="" align="aligncenter" width="686"] Aggregated Frame Throughput Formula for TCP[/caption]

Applying the above algebra, the graph below summarizes the expected throughput numbers, for the various 802.11n data rates at 40 MHz channel width (the data rate of a client depends, roughly, on the signal strength from the AP, and is often shown under the heading “speed” in the Wi-Fi link status).

[caption id="" align="aligncenter" width="600"] Expected Throughput[/caption]

In summary, for high Wi-Fi data rates such as 300 Mbps or 450 Mbps, the expected UDP throughput upper bound is roughly two-thirds of the data rate, while the expected TCP throughput upper bound is roughly half of the data rate. If we add to this further effects such as retransmissions due to packet errors, signal strength and data rate variability, it can go down further by another 20-30% or more. We will discuss these additional factors in later articles in this series. For now, we have a good rule of thumb for the throughput upper bound when you measure throughput using tools such as iPerf, IxChariot, so you’ll know what to expect, and when to feel satisfied.

We matched the above algebra with a large data set generated in AirTight Networks Wi-Fi testing lab on many different enterprise APs and clients at many different data rates and many different configurations, and were surprised to find how good a fit this rule of thumb is to what was measured in practice.

Some remarks:
• Above, we have talked only about single client throughput; with multiple clients, various effects can come into play depending on the configuration, some enhancing overall throughput, but most reducing it.
• The above formulas can also be applied to the data rates corresponding to the 20 MHz operation.
• It is beyond the scope of this article to talk about possible causes of throughput degradation, when the measured throughput is well below the expected number, because the possibilities here are too many.

Bhaskaran Raman is a scientist at AirTight Networks, working on high performance Wi-Fi architecture. Bhaskar received his M.S. and Ph.D. in Computer Science from the University of California, Berkeley, in 1999 and 2002 respectively, and his B.Tech in CSE from IIT Madras, India in May 1997. He was a faculty in the CSE department at IIT Kanpur from 2003-07. Since July 2007, he has been a professor at the CSE. Tagged with: Wi-Fi, data rate, tom carpenter, WiSE, throughput, airtight networks

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Manfred said he didn't know that the Marlins' new owners planned to tear it washington nationals jersers down
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"We did not have player-specific plans from the Miami Marlins or any other team that has been in the ownership miami marlins jersers process. Those are decisions that the individual owners make, and they do not have to be cleared by us or approved by us. ... Those are local decisions that really are not part of the approval process. Those are decisions that the individual owners make, and they do not have to be cleared with us or approved by us."

Manfred went on to say that he didn't receive a payroll plan from the Marlins until two days prior to his interview with Le Batard. More: "We don't get into, are you going to trade 'Player X' or 'Player Y' at a particular point in time, nor do we ask them to make a commitment to people before they even got in and made an evaluation of their talent level, their ability to win with the people that st. louis cardinals jersers they have. That's just not how the ownership process works."
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A source directly involved in the Marlins sales chicago white sox jersers process, after hearing the Le Batard cincinnati reds jersers interview, said, via text: "Commissioner said was not aware of [Jeter] plan to slash payroll. Absolutely not true. They request and receive the operating plan from all bidders.

"Project Wolverine [the name for Jeter's plan] called chicago white sox jersers on his group to reduce payroll to \$85 million. This was vetted and approved by MLB prior to approval by MLB. Every [Jeter] investor and non investor has the Wolverine financial plan of slashing payroll to \$85 million. Widely circulated."

First off, "Project Wolverine" is ludicrously self-important and sinister-sounding, as budget strategies go. That's the name of a secret NSA laboratory deep under the Caballo Mountains in New Mexico, not a financial schematic. Do better, Jeets. Anyhow, there's enough careful phrasing in Manfred's comments ("operating-level decisions," "'Player X' or 'Player Y'") to give him some plausible deniability. However, the idea that he didn't know about plans to engage in yet another demo job by Marlins owners strains credulity.

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Keith Parsons Says:
07/17/2013 at 17:30pm
I was just wondering what font you used in the graphics? It is readable and yet still kind of 'fun'...

Thanks

Says:
02/02/2013 at 04:23am
Can you please update the graphics to reflect the correct values, Thanks!

Bhaskaran Raman Says:
01/07/2013 at 19:33pm

(I'm sorry I've trouble posting individual replies for some reason)Thanks to all who have read and commented.
To Wi-Friend:Thanks.  Yes, the expected throughput numbers have indeed been very useful in my work too, to achieve experimental control.
To Albert Pinto:Thanks for asking about this subtle difference.The difference arises because a typical UDP header has 8 bytes of header, while a typical TCP header has 20 bytes, or an additional 12 bytes.
To Wlanman:Thanks a lot for asking.  Here's some explanation of the constants:
• The 84 microseconds of bulk ACK time consists of 16 microseconds of SIFS (Short Inter Frame Spacing) gap as well as 68 microseconds for transmission of the bulk ACK bytes
• The 68 microseconds of header overhead is composed of 36 microseconds of phy layer overhead (independent of the MCS data rate), and MAC(34)+Link(8)+IP(20)+20(TCP) bytes of header sent at the chosen 802.11n data rate.
• The gap before transmission consists of 34 microseconds of DIFS (DCF Inter Frame Spacing) and 67.5 microseconds of random backoff (there's a typo in the graphics, sorry for that; but it doesn't change the results much).  The DIFS itself consists of 16 microseconds of SIFS and two slot times of 9 microseconds each.  The 67.5 microseconds comes from a random backoff of 0-15 slots, or an average of 15/2*9 microseconds.
• The constants like DIFS, SIFS, slot time have further breakup, and are defined in the standard.

Howard Higgins Says:
01/06/2013 at 13:15pm

I am familiar with the phrase "the intermediate steps are left to the student...", but it would have been nice if there were more explanation behind a couple of the constants.

Don't take me wrong, I'll be making up an Excel spreadsheet using your results.

Says:
01/05/2013 at 12:09pm
I do not understand how the number changes from 70 to 82 in image for "Aggregated Frame Throughput Formula for TCP". Otherwise the article is very well written. Thanks!

Says:
01/04/2013 at 11:45am

I know from personal experience that Wi-Fi testing can get quite dizzying,
especially due to so many moving parts and due to RF being involved. I always
look for ways to verify test numbers against basic principles, because you can
never tell what test tool is doing internally. Such algebra coming from
fundamental networking principles are nice tools to make sense of Wi-Fi
performance numbers and to also assist in Wi-Fi network design.

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