Given the state of a system -- the number of jobs currently running, their ages and their cluster sizes -- we can use the CLM to estimate the wait time until a given cluster size, n, is available.
We describe the state of the machine at the time of an arrival as
follows: there are p jobs running, with ages 
and cluster
sizes 
(in other words, the ith job has been running on
processors for seconds). We would like to predict
Q(n'), the time until n' additional processors become available,
where 
and 
is the number of free
processors.
In the next two sections we will present ways to estimate the median and mean of Q(n'). Then we will use these values to predict wait times during a trace-driven simulation.