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## Single-threshold allocation policies: T1 and T2

The T1 and T2 policies are formally defined as follows:

Definition 16   Let (respectively, ) denote the number of jobs at queue 1 (respectively, queue 2). The T1 policy with parameter is characterized by the following set of rules, all of which are enforced preemptively (preemptive-resume):
• Server 1 serves only its own jobs.
• Server 2 serves jobs from queue 1 if either (i) or (ii) & . Otherwise, server 2 serves jobs from queue 2.
To achieve maximal efficiency, we assume the following exceptions. When and , the job is processed by server 2 if and only if . Also, when and , the job in queue 1 is processed by server 2 if and only if regardless of the number of type 2 jobs.

Definition 17   The T2 policy with parameter is characterized by the following set of rules, all of which are enforced preemptively (preemptive-resume):
• Server 1 serves only its own jobs.
• Server 2 serves jobs from queue 1 if . Otherwise server 2 serves jobs from queue 2.
When and , we allow the same exception as in the T1 policy.

Below, the T1 policy with parameter is also denoted by the T1() policy, and the T2 policy with parameter is also denoted by the T2() policy.

Figure 7.2: Figure shows whether server 2 works on jobs from queue 1 or queue 2 as a function of and under (a) the T1 policy with parameter and (b) the T2 policy with parameter .
 (a) T1 policy
 (b) T2 policy

Figure 7.2 shows the jobs processed by server 2 as a function of and (a) under the T1 policy and (b) under the T2 policy. Note that the T1(1) policy is the c rule when , and the T1() policy is the c rule when ; thus the rule falls within the broader class of T1 policies.

Next: Stability under single-threshold allocation Up: Static robustness and mean Previous: Static robustness and mean   Contents
Takayuki Osogami 2005-07-19