It is, in a sense, unfair to compare a replacement policy with a policy that proactively disconnects users even when the modem pool is not fully utilized. A replacement policy is always going to inconvenience fewer users while incurring the same number of busy signals. It is, however, interesting to quantify how much better the replacement approach is in a practical setting. Since fixed-idle-threshold disconnection policies are widespread, we show the results of a single experiment below, just as a point of reference. We will not, however, insist on such comparisons any further in the rest of the paper. If keeping users connected has no cost, the replacement approach clearly results in much less inconvenience for users.
Figure 3: Log plot of hard faults for three replacement
policies and a fixed idle threshold policy.
Figure 3 shows the numbers of hard faults incurred when
simulating a fixed-idle-threshold disconnection policy and three
replacement policies for our first Telesys trace. The simulated modem
pool has 1,936 modems (this number is 90% of the maximum number of
users who are connected simultaneously in this trace). The threshold
value, 
, varies from 600 to 2700 seconds (10 to 45
minutes). (Recall that 
is the minimum idle time before a user
becomes eligible for disconnection.) For all values of the threshold,
the replacement algorithms incur at least one order of magnitude fewer
hard faults.
In examining Figure 3 (as well as figures that follow) it
may seem awkward that the number of hard faults can rise for higher
thresholds. Recall, however, that the figures shown are produced for
. When the threshold increases, 
also increases,
thus causing many soft faults to be considered hard faults.