Have you seen our High Density WLANs for Auditoriums design guide?
http://www.arubanetworks.com/wp-content/uploads/dg_highdensity_vrd.pdf
I'm the lead author of this VRD, and even though it is now a couple years old the design principles have repeatedly proven out. We are using the capacity planning techniques in here in much much larger venues such as football stadiums.
Let's talk about some key client behaviors, and about capacity planning.
Channel capacity diminishes rapidly if the client population is "unhappy" with the SNR environment (among other factors). Apple devices especially. What happens is they go into a more aggressive roaming mode, probing on all channels. So a single device can negatively affect capacity on multiple channels until it settles down. Scale that up to 10K or 20K devices and it becomes a significant effect. And unfortunately, the SNR these devices prefer is pretty "warm" - at least 20dB.
So in the pantheon of design tradeoffs that must be made in an LPV, it turns out that running "hotter" can actually increase system capacity even though it increases self-interference. Aruba is capable of mitigating this to a degree with our "Cell Size Reduction" feature. CSR synthetically reduces RX sensitivity on the AP and therefore forces much much smaller cells.
With this in mind, let us talk about capacity planning.
At Aruba, we teach customers to think in terms of two different capacity metrics. “Associated User Capacity” and “Active User Capacity”. “Associated user capacity” is how many “slots” the system has for client devices (whether they are transmitting or not). Think of this as a form of CAC. “Active user capacity” is the subset of those devices that can attempt to transmit at the same time and still achieve the minimum throughput target the customer has set.
You control Associated User Capacity by deciding how many APs there are and what the “max client association” setting is in the relevant SSID profiles. If we have 100 dual-radio APs, and each radio is configured to support 200 associations, this means we can accommodate 100*2*200 = 40,000 devices.
It’s really not possible to “control” Active User Capacity. Because there is minimal channel reuse in LPVs as Ken and others have correctly observed. In fact, the more Associated Users you have, the lower your Active User Capacity due to increased control plane load and CSMA/CA contention. However, it is possible to calculate and/or measure empirically how Active User Capacity varies as the number of Associated Users on a a channel increases.
At the end of the day, what most customers care most about is hitting the Associated User Capacity target. Fortunately, this goes hand in hand with the desire of clients to have relatively high SNR levels because the only way to meet both needs is to have a relatively large number of APs. Much higher than any rational WLAN engineer would normally put in a single collision domain. But in practice it does work.
Coming back to clients, we can see that having APs that are stable in the face of 200+ associations per radio, and a control plane that can handle tens of thousands of clients with perhaps a dozen UDP/TCP sessions each including video is actually what separates "stadium grade" WLAN solutions from mere "enterprise grade". These things can be easily tested by customers in bakeoffs, and of course on game day. We're replacing a lot of competitor deployments in stadiums that couldn't handle the load during the highest-attendance games.
A broader challenge for the industry as a whole is to improve the level of cooperative control between infrastructure and clients to jointly make better decisions that benefit everybody in the environment. There are features we'd like to see on smart devices that have the potential to use the air in a vastly more efficient manner.