It looks more like a server problem to me. For some reason it doesn't have the resources to service requests. Why, I couldn't say. It could be something else running on the server, it could be a programming error, it could even be a low-grade DoS attack.
The first responses seem to be assuming that your server had been compromised and was being used for a DoS attack.
DDoS is Distributed DoS - rather than one host attacking dozens are used. The usual source is a "botnet" - malware infiltrated onto a large number of unsuspecting people's computers, enabling remote control for various malign purposes.