If the provider's web server is configured to use Keep-Alive extension to HTTP protocol (HTTP 1.1), there can be a big delay in the response time from the provider. By default Apache is configured to use Keep-Alive for 5 seconds. This is the delay after which the response will come back to the consumer. If you have this issue of delayed result, you can pass in HTTP headers when calling $consumer->fetch():
$consumer = new OAuth("consumer_key", "consumer_secret", OAUTH_SIG_METHOD_HMACSHA1, OAUTH_AUTH_TYPE_FORM);
$consumer->fetch('http://example.com/api/', null, OAUTH_HTTP_METHOD_POST, array('Connection'=>'close'));
Then the provider will send the result immediately after it's ready with the processing and the connection will be closed. Unfortunately, when calling $consumer->getRequestToken() and $consumer->getAccessToken() there's no way provided to pass in HTTP headers and this delay (if present) cannot be avoided, or at least we could not find a way to avoid it.
The solution that worked for us is to send this header from the provider when returning result to the consumer:
$result = 'oauth_callback_accepted=true&oauth_token=' . $this->urlencode($token->oauth_token) .
header('HTTP/1.1 200 OK');
This can work if you have the possibility to modify the code of the provider, e.g. if you are the provider yourself or if you can talk with the people that develop it and ask them to send this header for your request.