“…does “stream.php” stay open as long as the client is “connected”
to it?”
Yes, and your pseudo-code is a reasonable approach.
“And how do you know when you can END an instance of stream.php?”
In the most typical case, this happens when the user leaves your site. (Apache recognizes the closed socket, and kills the PHP instance.) The main time you might close the socket from the server-side is if you know there is going to be no data for a while; the last message you send the client is to tell them to come back at a certain time. E.g. in your stock-streaming case, you could close the connection at 8pm, and tell clients to come back in 8 hours (assuming NASDAQ is open for quotes from 4am to 8pm). Friday evening you tell them to come back Monday morning. (I have an upcoming book on SSE, and dedicate a couple of sections on this subject.)
“…if this is the case, PHP isn’t a suitable technology for this kind
of server. But all of the demos I’ve seen so far imply that PHP is
just fine for this, which is why I’m so confused…”
Well, people argue that PHP isn’t a suitable technology for normal web sites, and they are right: you could do it with far less memory and CPU cycles if you replaced your whole LAMP stack with C++. However, despite this, PHP powers most of the sites out there just fine. It is a very productive language for web work, due to a combination of a familiar C-like syntax and so many libraries, and a comforting one for managers as plenty of PHP programmers to hire, plenty of books and other resources, and some large use-cases (e.g. Facebook and Wikipedia). Those are basically the same reasons you might choose PHP as your streaming technology.
The typical setup is not going to be one connection to NASDAQ per PHP-instance. Instead you are going to have another process with a single connection to the NASDAQ, or perhaps a single connection from each machine in your cluster to the NASDAQ. That then pushes the prices into either a SQL/NoSQL server, or into shared memory. Then PHP just polls that shared memory (or database), and pushes the data out. Or, have a data-gathering server, and each PHP instance opens a socket connection to that server. The data-gathering server pushes out updates to each of its PHP clients, as it receives them, and they in turn push out that data to their client.
The main scalability issue with using Apache+PHP for streaming is the memory for each Apache process. When you reach the memory limit of the hardware, make the business decision to add another machine to the cluster, or cut Apache out of the loop, and write a dedicated HTTP server. The latter can be done in PHP so all your existing knowledge and code can be re-used, or you can rewrite the whole application in another language. The pure developer in me would write a dedicated, streamlined HTTP server in C++. The manager in me would add another box.