Class Pfqn_looping
D. L. Eager, "Bounding Algorithms for Queueing Network Models of Computer Systems", Ph.D. thesis, Tech. Rept. CSRG-156, University of Toronto, 1984. Looping supplies the initial pessimistic and optimistic estimates that the multiple-class performance bound hierarchy starts from, so it carries a pair of bounds rather than a single fixed point.
It is built on the convolution identity of Zahorjan (1980)
Q_jk(N - 1_c) = [X_j^{+k}(N - 1_c) / X_j(N)] Q_jk(N),
with X_j^{+k}(N - 1_c) estimated from the level-0 multiple-class PBH upper bound B_j and X_j(N) from the optimistic response time R_j^(opt). A HEAP H_j is the class-j congestion that the current queue-length lower bounds have not yet accounted for; it is charged back at the pessimistic inflation factor V_c = max_k D_ck or the optimistic one L_c = min_k D_ck, which are the largest and smallest delays one customer can inflict. The level-0 multiple-class PBH bounds on the mean response time are
J_j(n) = sum_k D_jk, B_j(n) = sum_k D_jk + (sum(n) - 1) max_k D_jk,
i.e. an arriving customer queues behind nobody, respectively behind every other customer in the network at its own worst centre.
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionstatic final classResult of the Looping iteration. -
Method Summary
Modifier and TypeMethodDescriptionstatic Pfqn_looping.Resultpfqn_looping(Matrix L, Matrix N, Matrix Z) static Pfqn_looping.Resultpfqn_looping(Matrix L, Matrix N, Matrix Zin, double tol, int maxiter)
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Method Details
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pfqn_looping
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pfqn_looping
public static Pfqn_looping.Result pfqn_looping(Matrix L, Matrix N, Matrix Zin, double tol, int maxiter)
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