Figure 5 shows how the numbers of hard faults and
busy signals vary for different values of the threshold 
. The
modem pool sizes simulated are 52 modems for the AT&T Labs trace,
and 1,936 and 2,721 modems for the Telesys July and November traces,
respectively. These modem pool sizes are 90% of the maximum number
of modems needed simultaneously for the Telesys traces. For all three
traces, the modem pool size is such that few busy signals are incurred
for a 600 second threshold. Thus, the sizes are such that they could
very well be used in practice to handle these workloads.
Figure 5: Plots of hard faults (linear scale) and busy signals
(log scale) for all traces under variable threshold (and
). The number of modems for each workload is fixed
to a value that yields few busy signals for a 10 minute
threshold (for the Telesys workloads, this is 90% of the
maximum number of simultaneously connected users in the
trace). The baseline in the busy signal plots is the number of
busy signals incurred with no disconnection policy in
place. For the busy signal plots, often all three curves for
RANDOM, LRU, and CIRG coincide and cannot be distinguished.
For the AT&T Labs trace, the values of examined are between
300 and 900 seconds (5 and 15 minutes, respectively). Since the
environment where the trace was collected had a 15 minute inactivity
timeout, these values seem reasonable. The values are certainly more
aggressive than what would be expected from a typical ISP, but since
the setup uses static IP addresses, the cost of a disconnection is
small (i.e., only the reconnection delay and not the termination of
open sessions). For the Telesys traces, we experimented with threshold
values ranging from 600 seconds (10 minutes) to 2700 seconds (45
minutes). These are more realistic settings for a general purpose ISP
where disconnections are more costly due to the dynamic IP address
assignment.
As we observe in Figure 5, the number of hard faults
may increase for higher threshold values, but not dramatically. LRU
and CIRG remain the best predictors of future idle time, with CIRG
performing slightly better. RANDOM performs significantly worse than
both for all settings that incur a tolerable number of busy signals
(e.g., below 1,000 for the Telesys traces). The number of busy signals
incurred by all policies increases, expectedly, for higher threshold
values. By increasing the minimum inactivity threshold for
disconnections ( ), the number of users who can potentially be
disconnected decreases rapidly (as seen in the histograms of
Figure 2).
We can see from Figure 5 that with 10% fewer modems than the maximum needed simultaneously, we can get a low number of busy signals and hard faults, for high threshold values--over half an hour for the July Telesys trace. The November Telesys trace has worse locality and quickly incurs many busy signals for threshold values above 20 minutes. This is to be expected: users of Telesys who stay idle long, are likely to have dedicated phone lines for modem connections. Nevertheless, the increase of Telesys usage between the Summer and Fall trace is mainly due to students. The percentage of students who can afford dedicated phone lines is lower than the corresponding percentage of faculty and staff. Thus, it is natural to have proportionally fewer users who are idle for long in the November trace. We believe that the July trace is more representative of typical ISP subscribers' behavior than the November trace, but have taken no steps towards verifying this.
