you need more ram it seems. I would make it 4 gigs of ram rather then 2 gig. Do this in the server.properties file. Open it with note pad to edit. server_memory=4000 I use 8000 myself. It depends how much ram your server has.
I highly recommend to do it in a power of two.
So that would be, for example: 1024, 2048, 4096, 6144, 8192, and so on. Personally, I'd go for 4096 if it's a small server and you are starting out. You can increase the allocated RAM as needed.