Stochastic process fundamentals - Modelling with Generalised Stochastic Petri Nets - page 270

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;