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The adaptive dual threshold (ADT) policy
The key idea in the design of the ADT policy is that, in contrast to
the T1T2 policy, the ADT policy is always operating as a T1
policy, but unlike the standard T1 policy, the value of adapts,
depending on the length of queue 2, to provide static robustness.
Specifically, the ADT policy
behaves like the T1 policy with parameter if the length of queue 2 is
less than and otherwise like the T1 policy with parameter , where
.
We will see that the ADT policy, unlike the T1T2 policy, is far superior to the T1 policy with
respect to static robustness, due to the dual thresholds on queue 1.
In addition, one might also expect that the mean response time of the
optimized ADT policy will significantly improve upon that of the optimized T1
policy, since the ADT policy generalizes the T1 policy (the ADT policy
is reduced to the T1 policy by setting
).
However, this turns out to be largely false, as we see below.
Formally, the ADT policy is characterized by the following rule.
Definition 19
The ADT policy with parameters (
)
operates as the T1 policy with parameter if ;
otherwise, it operates as the T1 policy with parameter .
Below, the ADT policy with parameters (
) is also
denoted by the ADT(
) policy.
Figure 7.9:
Figure shows whether server 2 works on jobs from queue 1 or queue 2 as
a function of and
under the ADT policy with parameters
.

Figure 7.9 shows the jobs processed by server 2 under
the ADT policy as a function of and . At high enough
and , usually exceeds , and the policy
behaves similar to the T1 policy with parameter . Thus, the stability
condition for the ADT policy is the same as
that for the T1 policy with parameter . The following theorem can be
proved in a similar way as Theorem 14.
Theorem 19
The stability condition for the ADT policy with parameters (
)
is given by the stability condition for the T1 policy with parameter
(Theorem 14).
Subsections
Next: Static robustness of the
Up: Static robustness and mean
Previous: T1T2 policy
Contents
Takayuki Osogami
20050719