That is peculiar. I'll need a bit more info before I can try to help debugging the problem.
When you say you have 3 web services, I'm assuming you mean that you have 3 services (or modules) deployed on AppScale. Is that correct, or are you referring to services that are external to the deployment?
When you use the word transactions, are you referring to datastore transactions, or do you just mean concurrent HTTP requests to the application instances? There are no general limits on concurrent datastore transactions or application requests, but I just want to make sure I'm understanding the situation correctly.
Do you know which process is raising the "Deadline exceeded" error? For example, is it raised while one of the services is trying to make an API call (to the datastore, for example)? Is it one of the web services raising the error while waiting for a response from one of the other web services? Is it your local client that is making the concurrent HTTP requests?