Package jline.api.pfqn.nc
package jline.api.pfqn.nc
Normalizing constant algorithms for Product Form Queueing Networks.
This package provides algorithms for computing the normalizing constant in product-form queueing networks, which is essential for deriving steady-state probabilities and performance metrics.
- Since:
- LINE 2.0
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ClassesClassDescriptionPlacement-order logic of a pass-and-swap (P&S) / order-independent network with swap graph H.Derive the GLOBAL placement-order DAG H of a closed two-station pass-and-swap (P&S) tandem 1->2->1 directly from its swap graph, for use with
Pfqn_pas_is.Adaptive Gauss-Hermite quadrature of the simplex factor of the McKenna-Mitra integral.Computes g(K) of a multichain closed product-form network with single-server and (optionally) infinite-server queues by numerically inverting its p-dimensional generating function (Choudhury, Leung and Whitt, 1995, eq.Computes g(K) of a multichain closed product-form network with limited load-dependent (LLD) stations and (optionally) infinite-server delay by numerically inverting its p-dimensional generating function (Bertozzi-McKenna eqs.Accelerations and their parameters; the defaults are the paper's.Computes G(N) of a closed product-form network made of an aggregated infinite-server (delay) node and any number of LIMITED JOINT-DEPENDENT stations.Computes G(N) of a closed product-form network made of an aggregated infinite-server (delay) node and any number of order-independent (OI) / pass-and-swap stations with empty swap graph, by inverting G(z) = exp(sum_r Z_r z_r) prod_i F_i(z), F_i(z) = sum_n Phi_i(n) z^n, with Phi_i the v-weighted balanced-fairness balance function of station i, mu_i(n) Phi_i(n) = sum_{r: n_r>0} v_{i,r} Phi_i(n - e_r).Triple of (A, B, DA) coefficient matrices.Exact passage-time density, distribution and moments along an OVERTAKE-FREE PATH of a closed single-chain tree-like product-form network.Result of the DNC evaluation at a real population.Result of the closed form, mirroring [lG, G, method, lossDigits].Signed log-sum-exp of S = sum_i s_i exp(l_i): log|S|, sign(S), digits lost.Importance-sampling (IS) estimate of the normalizing constant of a closed LOAD-INDEPENDENT product-form queueing network with M single-server queues of per-class demand L and an aggregated delay of think time Z.Importance-sampling (IS) estimate of the normalizing constant of a closed LOAD-DEPENDENT product-form queueing network.Exact normalizing constant of a closed multiclass product-form network whose state space carries arbitrary linear integer constraints.Markov chain Monte Carlo estimator of the class throughputsX(r) = G(N-e_r)/G(N)and of the mean queue lengthsQ(i,r)of a CLOSED multiclass product-form (BCMP, no type changes) network, by the REGULARIZATION algorithm ofCompute the normalizing constant of a repairmen model using Gauss-Laguerre integration.The two names denote the SAME routine because the balanced-fairness recursion Phi_i(0) = 1, mu_i(n) Phi_i(n) = sum_{r: n_r>0} v_{i,r} Phi_i(n - e_r) never inspects the structure of mu_i: it evaluates the handle at the full count vector n.Normalizing constant via the saddle-tilted Edgeworth (NRE) approximation.MATLAB's[lG,G,lGs,vsad]: the constant, the saddlepoint term on its own and the tilt the expansion was taken about.Importance-sampling (IS) estimate of the normalizing constant of a SINGLE communicating class of a closed two-station pass-and-swap (P&S) / order-independent (OI) tandem with swap graph H (Casale, Comte and Dorsman, 2026).Result ofPfqn_pas_is.pfqn_pas_is(int[], java.util.List<java.util.function.ToDoubleFunction<int[]>>, int[][], long, long, boolean): G, log G, and (2 x R) mean queue lengths.Permanent of a demand matrix, with optional column multiplicities.Joint moments of the queue-length vector of a closed product-form network, obtained from normalizing constants.Result of the RGF recursion: the whole log-normalizing-constant sequence.Harrison and Coury, "On the asymptotic behaviour of closed multiclass queueing networks", Perf.Normalizing constant and its logarithm.Density, distribution and moments of a passage time along an overtake-free path.PFQN mom algorithms (documentation marker).PFQN nc algorithms (documentation marker).PFQN procomom algorithms (documentation marker).