Graphics Programs Reference
In-Depth Information
End of
p
ext_req_1
p
ext_req_n
requests
Requests
from
from
p
loc_rdy
neighbours
neighbours
t
p
start_req_n
T
req_exe_n
loc_ex
Requests
T
end_req_n
to
neighbours
End of
requests
(a)
(b)
Figure 11.2: Basic model of the processing elements
11.2
Single Processor Model
The basic structure of the GSPN model of each processing unit is shown in
Fig.
11.2.
It is composed of two different subnets. The first one, labelled
(a), describes the local activity of the task (modelled by the timed transition
T
loc ex
with rate λ) along with the issuing of the service requests towards
the neighbours. The second subnet (b), models the service provided by the
processor to requests from neighbours.
In subnet (b), for any direct neighbour the model must include a place to
describe the pending requests (p
ext req n
for the nth neighbour), an imme-
diate transition (t
start req n
) to model the granting operation, and a place
(p
req exe n
) followed by a timed transition (T
end req n
) with rate µ describing
the service operation. Once service has been completed, a token is returned
to the requesting neighbour, where the task is inserted in the ready-task
pool (place p
loc rdy
of subnet (a)).
The specific process interaction and scheduling policies determine whether
a local computation is resumed or further external requests (if pending) are
served next. These policies are modelled by subnet (a) (not yet specified)
and by the priority of transitions t
start req n
. In any case, the activity of
each processor alternates between execution of local tasks (subnet (a)) and
service of external requests (subnet (b)).
Two basic interaction policies will be considered in the following:
•
preemptive interaction: requests coming from the neighbours are served
with higher priority than the local activity, i.e., requests are preemp-
tive;
•
non-preemptive interaction: requests are not preemptive, but are served
at the end of the local operation.
All models in this section refer, for ease of representation, to a processor with
two neighbours. We first discuss two simplified models considering only one
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