Graphics Programs Reference

In-Depth Information

Figure A.3: State transition diagram of the single processor model

Note that the first two equations are linearly dependent, so that one can be

discarded.

The steady-state distribution can immediately be found to be:

q

p + q
,

p

p + q

η =

this means that at steady-state the probability of the processor being ex-

ecuting in its private memory is

q

p + q
, that the mean recurrence time of

state 2 is
p + q

p
cycles, and that the average number of common memory

access cycles between two consecutive private memory accesses is
p

q
.

Let us now return to the two-processor system: name the two processors

A and B, and characterize the workloads of the two processors similarly to

what was done above, adding subscripts to identify the two processors (i.e.,

use p
A
to denote the common memory access probability of processor A,

and so on).

The system can now be in the following five states:

1. both processors are executing in their private memories;

2. processor B is executing in its private memory, and processor A is

accessing the common memory;

3. processor A is executing in its private memory, and processor B is

accessing the common memory;

4. processor B is waiting for the common memory, and processor A is

accessing the common memory.

5. processor A is waiting for the common memory, and processor B is

accessing the common memory;

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