I list the follows for our study on power-efficient
network processor design.

First, there are two important conclusions [1] for discrete voltage 
levels on voltage scaling, considering only dynamic power: 

(i). There exist one unique optimal Vdd for any task with 
deadline and execution time such as total energy is minimized. 
Under such optimal Vdd the task execution time is equal to 
its deadline.

(ii). If the unique optimal Vdd is not available in the 
discrete voltage level case, at most two Vdds are enough 
to achieve the optimal energy. 

We first need to extend both conclusions to include leakage power.
With leakage power involved, it has been proved that there exists
a critical Vdd denoted as Vc (and the corresponding frequency Fc) 
such that the overall energy consumption is minimized [2]. Further 
increasing or decreasing from such critical Vdd will increase total 
energy. Therefore, for conclusion (i), if the speed of Fc can meet
the deadline, obviously Vc is the optimal Vdd. Otherwise, since
in the vdd range of [Vc, Vmax] the total energy is still a convex
function of Vdd, we can prove that conclusion (i) still hold, which
I have already done. For conclusion (ii), by limiting ourselves
in the vdd range of [Vc, Vmax] we can prove it even with the consideration
of leakage power.

After that, we may consider the following problems step by step. 
For each problem, we try our best to come up with analytical solution. 
If not possible, we need to develop some deterministic algorithms.

1. fixed workload with constant task rate R, continuous Vdd scaling, 
total number of PEs M, given QoS Decide the task rate r_i on each PE 
where the sum of r_i for i = 1 to M is equal to R, and the Vdd of each PE, 
to minimize the total system energy. 

I have some analytical derivations and they show that the answer is 
not trivial and it is not the case when all PEs have the same 
setting to minimize total energy. I am working on further details.

2. same conditions as problem 1, except for discrete Vdd levels 
Two things to decide: (i) the voltage setup problem, how to design 
the available vdd levels; and (2) voltage scaling: decide the task 
rate on each PE and the Vdd of each PE. Here the first thing (voltage 
setup problem) is similar to the ICCAD'03 paper I presented. The 
second thing is similar to the first problem but we have to consider 
discrete Vdd levels.

3. same conditions as problem 2, except that the task rate is no long 
a constant, but with probability density function, for variable workload. 
Decide the same two things as those in problem 2. Here the voltage setup 
problem can be solved by the method I proposed in last weekly report. 
The second thing is the same as that in problem 2.

4. VSVP problem: based on the conditions in problem 3, how to decide Vdd domains 
to minimize power supply cost. Some cost function of power domain is necessary.

[1] T. Ishihara and H. Yasuura, "Voltage scheduling problem for dynamically
variable voltage processors", ISLPED'98
[2] R. Jejurikar and C. Pereira and R. Gupta, "Leakage aware dynamic voltage
scaling for real-time embedded systems", DAC'04