A complicated dance
Thursday, February 18, 2010
11:49 AM
A complicated dance
Response time P depends upon tserver. 
tserver depends upon load and schedule.
Schedule is determined by λrequest = request arrival rate. 
Over a long enough time, Little's law says that (average) tserver= mean time in system = Wrequest = Lrequest/λrequest. 
But equivalently, WCPU=LCPU/λCPU and we know LCPU, but not Lrequest. 
We do not know Wrequest, but we do know it is proportional to WCPU (via some unknown constant),  which is proportional to LCPU, which is the output of the UNIX uptime command. 
Thus we know that uptime load is proportional to Wrequest, which is internal response time, but we do not know the proportion. 