Other users have reported high ping times with various game servers.
Do you know the host name or ip address of the game server? At different times of the day, you could do a ping of the hostname/ip address as well as tracert -d of hostname/ipaddress. Most of the day, you'll probably have good response times. When response time is bad, the tracert will show where the network delays are. Do tracert without the -d and it will show the hostname of the routers in the network path, which might point to the organisation causing the problem.
You might like to check out this post:
Seems to be a very common issue at the moment with TPG. I also go from playing games wired and getting around 40ms ping to their servers, then as soon as it hits 7pm, my ping is all of a sudden hanging around 200ms in the same game making it next to impossible for me to play any game online at night, which is when I usually do most my online gaming.
I have tried for several nights on end to try to contact TPG phone support about this issue, but after several hours on hold every night, I have to give up and go to bed. Even the moderator in these forums seems to just ask the same questions in every thread about it and assumes it is all an end user issue, when quite clearly it isn't. I have read people in other online forums saying that they have just switched from TPG to an alternate Internet provider and their issue was solved, so I am thinking about doing the same thing seing as though TPG's support is absolutely horrible and doesn't seem to have any interest in solving this issue.