Get a copy of netperf -
www.netperf.org/ftp.netperf.org and configure it for histograms --enable-histograms, then run a TCP_RR test with a verbosity level of 2 and look at the resulting histogram and transaction per second rate. Pick a request/response size similar to that of the pings you were sending.
Or... on the client, run tcpdump and look at the packet trace