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ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 8.17 An ex<strong>amp</strong>le of partial flow (a), which causes a deadlock in (b). The input ratio of path [p2 t2 p3 t3<br />

p4] is 2, and that of path [p2 t5 p5 t6 p4] is 4.<br />

Since each PSP of and is exclusive to each other in its own set, the sum of v’s must equal w; i.e.,<br />

We thus obtain<br />

t2<br />

t3<br />

X g1 j 1<br />

2<br />

�<br />

p3<br />

�<br />

tjs�X j1g 1<br />

X j1 g 1<br />

(a) (b)<br />

p4<br />

2<br />

p1<br />

t1<br />

p2<br />

t7<br />

t8<br />

4<br />

2<br />

p6<br />

t5<br />

p5<br />

t6<br />

� vgs � w and � vjs � w.<br />

t gs �X g1 j 1<br />

�( tjs)Rj1js t2<br />

t3<br />

t gs �X g1 j 1<br />

f<br />

�( tgs)Rg1g f<br />

f<br />

t s<br />

gs�X ( w)<br />

( R g1j g1s) Rg1 s<br />

1<br />

f<br />

-------------------------------------- � --------------------- f � ------- f �<br />

[ Rg1 j ]�.<br />

1<br />

f ( w)<br />

( Rj1 s)<br />

Rj1 s<br />

2<br />

p3<br />

p4<br />

2<br />

p1<br />

t1<br />

p2<br />

t7<br />

t8<br />

4<br />

2<br />

p6<br />

t5<br />

p5<br />

t6

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