web page shows 507 insufficient storage once in a while

I have a website up and running. The website worked fine on localhost with no such errors but after I put it online it started showing 507 insufficient storage page whenever two or three users used the same page at the same time.
For example there is a webpage chat.php which runs an ajax request to update the chats every 700 milliseconds. Side by side two ajax requests keep checking for messages and notifications. These ajax requests are completed using javascript's setInterval method. When this page is accessed concurrently by two or more users the page does not load and shows the error and sometimes the page shows 429 too many requests error. So at the same time maximum 4 requests can occur at the user's end and that too if the scripts run at the same time. Could this occur because of the limited entry processes? The hosting provides me with 10 limited entry processes by default. Please reply and leave a comment if you want me to post the setInterval method code even though I think the problem is something else here.