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b(ednesda)m(y)34 b(ev)m(ening.)51 b(Please)34 b(p)s(ost)g(questions)f
(to)h(the)g(newsgroup)0 317 y(\()p Fd(uiuc.class.cs331)p
Fe(\),)27 b(or)j(ask)h(during)d(o\016ce)j(hours)f(\(5:00{8:00pm)j(Th)m
(ursda)m(y)c(in)h(the)g(331)i(lab\).)111 530 y(1.)46
b(There)26 b(are)h(4)f(p)s(erio)s(dic)e(tasks,)k Fc(\034)1343
544 y Fb(1)1408 530 y Fe(through)e Fc(\034)1788 544 y
Fb(4)1827 530 y Fe(,)h(and)f(2)h(data)g(structures)e(shared)h(among)h
(the)f(tasks,)i Fc(D)s(S)3861 544 y Fb(1)227 643 y Fe(and)h
Fc(D)s(S)537 657 y Fb(2)576 643 y Fe(.)40 b Fc(\034)681
657 y Fb(1)720 643 y Fe(,)29 b Fc(\034)814 657 y Fb(2)854
643 y Fe(,)g(and)f Fc(\034)1123 657 y Fb(4)1191 643 y
Fe(share)h Fc(D)s(S)1562 657 y Fb(1)1630 643 y Fe(where)g
Fc(\034)1932 657 y Fb(1)1971 643 y Fe('s)g(critical)f(section)h(is)f
Fc(a)h Fe(ms,)g Fc(\034)3038 657 y Fb(2)3077 643 y Fe('s)g(critical)f
(section)h(is)f Fc(b)227 756 y Fe(ms,)34 b(and)e Fc(\034)617
770 y Fb(4)656 756 y Fe('s)h(critical)f(section)h(is)f
Fc(c)h Fe(ms.)48 b Fc(\034)1753 770 y Fb(2)1826 756 y
Fe(and)32 b Fc(\034)2045 770 y Fb(3)2117 756 y Fe(share)h
Fc(D)s(S)2492 770 y Fb(2)2564 756 y Fe(where)f Fc(\034)2869
770 y Fb(2)2908 756 y Fe('s)h(critical)f(section)h(is)f
Fc(d)h Fe(ms)227 868 y(and)d Fc(\034)444 882 y Fb(3)483
868 y Fe('s)h(critical)e(section)h(is)g Fc(e)g Fe(ms.)227
1019 y Fc(a)p Fe(,)j Fc(b)p Fe(,)g Fc(c)p Fe(,)g Fc(d)p
Fe(,)h(and)d Fc(e)i Fe(are)f(all)g(p)s(ositiv)m(e)f(in)m(tegers.)47
b(Do)33 b(not)f(mak)m(e)h(an)m(y)g(assumptions)e(ab)s(out)h(their)f
(relativ)m(e)227 1132 y(sizes.)45 b(The)31 b Fc(max)h
Fe(function)e(ma)m(y)i(b)s(e)g(used)e(in)h(y)m(our)h(answ)m(ers.)44
b(It)32 b(accepts)h(an)m(y)f(n)m(um)m(b)s(er)f(of)h(argumen)m(ts)227
1245 y(and)e(returns)f(the)i(largest)f(one.)41 b(F)-8
b(or)32 b(example,)e Fc(max)p Fe(\(5)p Fc(;)15 b Fe(20\))27
b(=)e(20)32 b(and)d Fc(max)p Fe(\(100)p Fc(;)15 b Fe(54)p
Fc(;)g Fe(8\))30 b(=)25 b(100.)227 1395 y(Assuming)37
b(that)i(semaphores)g(can)g(b)s(e)f(nested,)j(what)d(are)h(the)g(w)m
(orst)g(case)g(blo)s(c)m(king)f(times)g(of)h(eac)m(h)227
1508 y(task)d(under)e(the)h(Basic)g(Priorit)m(y)f(Inheritance)h(Proto)s
(col)g(\(BIP\))h(and)e(the)i(Priorit)m(y)e(Ceiling)f(Proto)s(col)227
1621 y(\(PCP\)?)111 1808 y(2.)46 b(There)24 b(are)i(four)e(p)s(erio)s
(dic)e(tasks)j(with)e(the)i(follo)m(wing)e(computation)i(times)f(\()p
Fc(C)7 b Fe(\),)26 b(p)s(erio)s(ds)d(\()p Fc(T)13 b Fe(\),)26
b(blo)s(c)m(king)227 1921 y(times)39 b(\()p Fc(B)5 b
Fe(\),)43 b(and)c(pre-p)s(erio)s(d)e(deadlines)h(\()p
Fc(D)s Fe(\).)68 b(The)40 b(con)m(text)h(switc)m(hing)d(time)i(is)e
Fc(S)46 b Fe(=)3451 1885 y Fb(1)p 3451 1900 36 4 v 3451
1952 a(2)3496 1921 y Fe(.)69 b(Use)40 b(the)227 2034
y(Utilization)29 b(Bound)h(and)g(Exact)h(tests)g(as)g(needed)f(to)h
(determine)e(if)h(the)g(task)h(set)g(is)f(sc)m(hedulable.)p
1505 2183 1118 4 v 1503 2296 4 113 v 1555 2262 a Ff(T)-9
b(ask)p 1814 2296 V 1831 2296 V 126 w Fc(C)p 2021 2296
V 151 w(T)p 2257 2296 V 148 w(B)p 2430 2296 V 110 w(D)p
2621 2296 V 1505 2299 1118 4 v 1505 2315 V 1503 2428
4 113 v 1621 2395 a(\034)1661 2409 y Fb(1)p 1814 2428
V 1831 2428 V 1882 2395 a Fe(15)p 2021 2428 V 101 w(100)p
2257 2428 V 115 w(6)p 2430 2428 V 114 w(30)p 2621 2428
V 1505 2432 1118 4 v 1503 2545 4 113 v 1621 2511 a Fc(\034)1661
2525 y Fb(2)p 1814 2545 V 1831 2545 V 1882 2511 a Fe(70)p
2021 2545 V 101 w(150)p 2257 2545 V 115 w(3)p 2430 2545
V 114 w(20)p 2621 2545 V 1505 2548 1118 4 v 1503 2661
4 113 v 1621 2627 a Fc(\034)1661 2641 y Fb(3)p 1814 2661
V 1831 2661 V 1882 2627 a Fe(20)p 2021 2661 V 101 w(200)p
2257 2661 V 115 w(4)p 2430 2661 V 114 w(10)p 2621 2661
V 1505 2664 1118 4 v 1503 2777 4 113 v 1621 2743 a Fc(\034)1661
2757 y Fb(4)p 1814 2777 V 1831 2777 V 1882 2743 a Fe(26)p
2021 2777 V 101 w(275)p 2257 2777 V 115 w(0)p 2430 2777
V 114 w(10)p 2621 2777 V 1505 2780 1118 4 v 1914 2859
a Fc(S)31 b Fe(=)25 b(0)p Fc(:)p Fe(5)111 3107 y(3.)46
b(There)24 b(are)i(four)e(p)s(erio)s(dic)e(tasks)j(with)e(the)i(follo)m
(wing)e(computation)i(times)f(\()p Fc(C)7 b Fe(\),)26
b(p)s(erio)s(ds)d(\()p Fc(T)13 b Fe(\),)26 b(blo)s(c)m(king)227
3220 y(times)k(\()p Fc(B)5 b Fe(\),)31 b(and)f(pre-p)s(erio)s(d)e
(deadlines)g(\()p Fc(D)s Fe(\).)41 b(The)30 b(con)m(text)i(switc)m
(hing)d(time)h(is)g Fc(S)g Fe(=)25 b(1)p Fc(:)p Fe(5.)p
1511 3391 1105 4 v 1509 3504 4 113 v 1561 3470 a Ff(T)-9
b(ask)p 1821 3504 V 1838 3504 V 126 w Fc(C)p 2028 3504
V 151 w(T)p 2264 3504 V 148 w(B)p 2437 3504 V 104 w(D)p
2614 3504 V 1511 3507 1105 4 v 1511 3524 V 1509 3637
4 113 v 1627 3603 a(\034)1667 3617 y Fb(1)p 1821 3637
V 1837 3637 V 1889 3603 a Fe(37)p 2028 3637 V 100 w(100)p
2264 3637 V 115 w(0)p 2437 3637 V 130 w(0)p 2614 3637
V 1511 3640 1105 4 v 1509 3753 4 113 v 1627 3719 a Fc(\034)1667
3733 y Fb(2)p 1821 3753 V 1837 3753 V 1889 3719 a Fe(60)p
2028 3753 V 100 w(200)p 2264 3753 V 115 w(0)p 2437 3753
V 130 w(0)p 2614 3753 V 1511 3756 1105 4 v 1509 3869
4 113 v 1627 3835 a Fc(\034)1667 3849 y Fb(3)p 1821 3869
V 1837 3869 V 1889 3835 a Fe(55)p 2028 3869 V 100 w(250)p
2264 3869 V 115 w(0)p 2437 3869 V 130 w(0)p 2614 3869
V 1511 3873 1105 4 v 1509 3985 4 113 v 1627 3952 a Fc(\034)1667
3966 y Fb(4)p 1821 3985 V 1837 3985 V 1911 3952 a Fe(1)p
2028 3985 V 123 w(850)p 2264 3985 V 115 w(0)p 2437 3985
V 130 w(0)p 2614 3985 V 1511 3989 1105 4 v 1914 4068
a Fc(S)31 b Fe(=)25 b(1)p Fc(:)p Fe(5)227 4310 y Fa(Note:)39
b(As)26 b(it)g(is)h(written,)h(this)f(pr)-5 b(oblem)29
b(r)-5 b(e)g(quir)g(es)27 b(that)h(the)e(exact)h(test)g(b)-5
b(e)26 b(c)-5 b(arrie)g(d)29 b(out)d(quite)g(far.)41
b(L)-5 b(etting)227 4423 y Fc(T)280 4437 y Fb(4)352 4423
y Fa(b)g(e)33 b(800)h(inste)-5 b(ad)34 b(of)f(850)h(wil)5
b(l)32 b(make)h(things)h(simpler)f(at)h(the)f(end.)42
b(Why?)266 4636 y Fe(\(a\))k(Use)36 b(the)g(Utilization)f(Bound)g(and)g
(Exact)i(tests)f(as)g(needed)f(to)i(sho)m(w)f(that)g(the)g(task)g(set)g
(is)f Fa(not)427 4748 y Fe(sc)m(hedulable.)261 4895 y(\(b\))45
b(Devise)39 b(a)f(p)s(erio)s(d)e(transformation)i(that)g(mak)m(es)h
(the)g(task)f(set)h(sc)m(hedulable.)63 b(Sho)m(w)37 b(that)i(y)m(our)
427 5008 y(transformation)30 b(w)m(orks.)1927 5589 y(1)p
eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF