Graphics Programs Reference
In-Depth Information
Table 7.1: Specification of the transitions of the Central Server Model of
Fig.
7.1
transition
rate
semantics
transition
weight
priority
ECS
TERM
0.1
infinite-server
getCPU
1
1
1
CPU
1.0
infinite-server
getDISK
1
1
2
DISK
0.8
infinite-server
complete
1
1
3
I/O
9
1
3
Table 7.2: Initial marking of the Central Server Model of Fig.
7.1
place
initial marking
think
6
CPUidle
1
DISKidle
1
(transition CPU fires) proceeds to a selection point where, with a certain
probability, it decides to continue requesting service from the I/O subsys-
tem; with a complementary probability, the job leaves the central system
and the corresponding customer starts a new thinking period (immediate
transition complete is chosen to fire). The disk representing the I/O subsys-
tem is used in a single server manner and the waitDISK place represents the
disk queue. No specific policy is specified for this queue and a random order
is assumed to fit the purposes of the analysis as long as the actual discipline
excludes preemption.
A structural analysis of this basic model shows that it is bounded and live,
and that its initial marking is a home state. Using the algebraic tech-
niques discussed in Chapter
2,
three P semi-flow vectors can be identified
(PS
1
= think + waitCPU + useCPU + choose + waitDISK + useDISK,
PS
2
= CPUidle + useCPU, and PS
3
= DISKidle + useDISK). The first
P semi-flow corresponds to the possibilities that customers have of moving
throughout the net and it identifies the possible execution cycle of jobs; it
generates a P-invariant with token count of 6 that proves the conservation
of customers in the system. The second P semi-flow corresponds to the CPU
cycle through idle and busy states. The third corresponds to the DISK cy-
cle: the disk may also be either idle or busy. These last two P semi-flows
generate two P-invariants with token count of 1. Since all the places of
the GSPN are covered by P semi-flows, the net is structurally bounded: its
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