On the Shadow Cpu Approximation for Modelling Priority Scheduling in Computer Sy

Cover On the Shadow Cpu Approximation for Modelling Priority Scheduling in Computer Sy
On the Shadow Cpu Approximation for Modelling Priority Scheduling in Computer Sy
Paul G Spirakis
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. L\owever, the cardinality of the system state space grows exponejiCially with the number of service centers, customers and classes. . . _. . ^ _ Although priority schedulir\g. Is very imp, p-rte^nt and basic in most nul ti-prograraming computer sys. Te, ms, . No e, 5tact qlo. Sed form solutions of networks with priorities are yet_kn, own. Jhus, r. Esearchers attempted to efficiently model priority scheduli;^ thr: to minimize Lr (given by (EQl)) under the restriction (R2), or to tninimze ir (g...iven by (EQD), under the constraint (EQl) = (EQ2) . [3CMP, 75] proved that the probability of an aggregate system state S = (npn2, n2) is of the form p(S, B) = C • gi(ni) • g2 (n2, B) • g3(n3) where g^(n^ ) depends only on the conditions at server i. In any LDSM all servers are of type 1 hence (e. G. , for the shadow), -11- g2(n2, B) = eo" no nj k=l where eo is the relative visit count at the shadow, (It could be taken equal to Ut). We conclude that the form of the function to (uinimize is (within a constant) A^ Ao %2~^ BTTT ^ 6(1)6(2) '^' ' '^ S(l)6(2).

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