You want to find the number of logon requests a domain controller has processed.
The following query returns the number of logon requests processed:
> nltest /server:<DomainControllerName> /LOGON_QUERY
The nltest /LOGON_QUERY command is a wrapper around the I_NetLogonControl2 method, and can be useful to determine how many logon requests are being processed by a server. Viewing the results of the command over a period of time and comparing them against a server in the same domain can also tell you if one server is being used significantly more or less than the others.