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LINE Solver (C++)
Templated C++ port of the LINE queueing solver
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LINE Solver (C++)
Templated C++ port of the LINE queueing solver
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MAPs, marked MAPs, MMPPs and phase-type distributions: moments, transformations, superposition, fitting (KPC-Toolbox, M3A, BuTools), and the QBD machinery for the rate matrices R and G. More...
Files | |
| file | include/line/api/mam/amap2_adjust_gamma.h |
| Nearest AMAP(2)-feasible (M2, M3, GAMMA) (matlab/lib/m3a/m3a/amap2/amap2_adjust_gamma.m). | |
| file | include/line/api/mam/amap2_assemble.h |
| Assemble an AMAP(2) in one of the two canonical forms (matlab/lib/m3a/m3a/amap2/amap2_assemble.m). | |
| file | include/line/api/mam/amap2_fit_gamma.h |
| AMAP(2) fit of three moments and the autocorrelation decay rate (matlab/lib/m3a/m3a/amap2/amap2_fit_gamma.m). | |
| file | include/line/api/mam/amap2_fitall_gamma.h |
| All AMAP(2) representations matching three moments and the autocorrelation decay rate (matlab/lib/m3a/m3a/amap2/amap2_fitall_gamma.m). | |
| file | include/line/api/mam/aph2_adjust.h |
| Nearest APH(2)-feasible values of the second and third moments (matlab/lib/m3a/m3a/aph2/aph2_adjust.m, method 'simple'). | |
| file | include/line/api/mam/aph2_adjust_opt.h |
| Optimization-based APH(2) moment adjustment: the 'opt_param' and 'opt_char' methods of matlab/lib/m3a/m3a/aph2/aph2_adjust.m. | |
| file | include/line/api/mam/aph2_assemble.h |
| Assemble an APH(2) from its canonical parameters (matlab/lib/m3a/m3a/aph2/aph2_assemble.m). | |
| file | include/line/api/mam/aph2_fit.h |
| APH(2) fit of three moments, with a fallback to adjusted moments (matlab/lib/m3a/m3a/aph2/aph2_fit.m). | |
| file | include/line/api/mam/aph2_fitall.h |
| All APH(2) representations matching three moments (matlab/lib/m3a/m3a/aph2/aph2_fitall.m). | |
| file | include/line/api/mam/aph_convseq.h |
| Convolution of a sequence of matrix-exponential laws. | |
| file | include/line/api/mam/aph_fit.h |
| Minimal-order acyclic phase-type fit of the first three moments (matlab/lib/kpctoolbox/aph/aph_fit.m). | |
| file | include/line/api/mam/aph_fit_moments.h |
| Acyclic phase-type fitters from the first two moments. | |
| file | include/line/api/mam/aph_simplify.h |
| Composition of two matrix-exponential distributions given in (alpha, T) form. | |
| file | include/line/api/mam/cme.h |
| Concentrated matrix exponentials, and the two-moment fit built on them. | |
| file | include/line/api/mam/dmap.h |
| Discrete-time Markovian arrival processes (D-MAPs). | |
| file | include/line/api/mam/dmap_optim_dist.h |
| The DISCRETE twins of map_optim_dist / map_optim_dist_acf: fit a D-MAP's D1 by minimizing a distance to a reference, with D0 held fixed. | |
| file | include/line/api/mam/dtime.h |
| Discrete-time (slotted) matrix-analytic primitives and queues. | |
| file | include/line/api/mam/hyperexp_fit_longtail.h |
| Fitting a hyperexponential to a long-tail distribution. | |
| file | include/line/api/mam/iltcme_table.h |
| The vendored concentrated-matrix-exponential (CME) coefficient table that matlab_ilt reads from iltcme.json. | |
| file | include/line/api/mam/ldqbd.h |
| Level-dependent QBD processes with finitely many levels: the rate matrices R^(n) by the backward matrix continued fraction, and the stationary distribution. | |
| file | include/line/api/mam/ldqbd_mphc.h |
| Port of ldqbd_mphc.m and ph_multisets.m: the exact level-dependent QBD blocks of an M/PH/c queue. | |
| file | include/line/api/mam/libqbd_taylor.h |
| Transient distribution of a level-independent-in-the-tail QBD by an adaptive Taylor series (libQBD QBD + TaylorSeriesAdaptive). | |
| file | include/line/api/mam/m3a_fit_from.h |
| The m3a fitters driven from a process or from a trace rather than from moments. | |
| file | include/line/api/mam/m3pp22_fitc_cov.h |
| M3PP(2, 2) fitted to the count COVARIANCE between its two classes (matlab/lib/m3a/m3a/m3pp/m3pp22_fitc_approx_cov_multiclass.m and matlab/lib/m3a/m3a/m3pp/m3pp22_fitc_approx_cov.m). | |
| file | include/line/api/mam/m3pp2m_fitc.h |
| Marked MMPP(2) with m classes, fitted to counting-process characteristics (matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc.m). | |
| file | include/line/api/mam/m3pp2m_fitc_approx.h |
| M3PP(2, m) fitted to counting-process characteristics with an optimized per-class split (matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx.m, matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx_ag.m, matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_approx_ag_multiclass.m). | |
| file | include/line/api/mam/m3pp2m_fitc_trace.h |
| M3PP(2, m) fitted to the counting process of a multi-class TRACE (matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_trace.m), and the analogous MMPP(2) entry point for a given MAP (matlab/lib/kpctoolbox/mmpp/mmpp2_fitc_theoretical.m). | |
| file | include/line/api/mam/m3pp2m_interleave.h |
| LUMPED interleaving of several M3PP(2, m), and the two fitters built on it (matlab/lib/m3a/m3a/m3pp/m3pp2m_interleave.m, matlab/lib/m3a/m3a/m3pp/m3pp2m_fitc_theoretical.m, matlab/lib/m3a/m3a/m3pp/m3pp22_interleave_fitc.m). | |
| file | include/line/api/mam/m3pp_superpos_fitc.h |
| M3PP obtained by SUPERPOSING one second-order process per class (matlab/lib/m3a/m3a/m3pp/m3pp_superpos_fitc.m and its two entry points m3pp_superpos_fitc_theoretical.m and m3pp_superpos_fitc_trace.m). | |
| file | include/line/api/mam/mam_transient2.h |
| Laplace-domain transient level-to-level transform V(s,n,m) of a piecewise level-dependent QBD, the port of matlab/src/solvers/MAM/mam_transient2.m (finite, closed at a top level) and mam_transient2_open.m (the last regime repeating to infinity). | |
| file | include/line/api/mam/mamap22_fit_bs.h |
| Fit a MAMAP(2,2) matching the BACKWARD moment and the class TRANSITION probability sigma. | |
| file | include/line/api/mam/mamap22_fit_fs.h |
| Fit a MAMAP(2,2) matching the FORWARD moment and the class TRANSITION probability sigma. | |
| file | include/line/api/mam/mamap2m_coefficients.h |
| The marking coefficients of a canonical AMAP(2), for the sigma fitters. | |
| file | include/line/api/mam/mamap2m_fit.h |
| Fit a MAMAP(2,m): a second-order acyclic MAP marked with m classes, matching the forward and backward per-class moments. | |
| file | include/line/api/mam/mamap_marked_poisson.h |
| The marked Poisson process every MAMAP fitter falls back to. | |
| file | include/line/api/mam/map2_fit.h |
| Explicit inverse characterization of a second-order acyclic MAP (matlab/lib/kpctoolbox/map/map2_fit.m). | |
| file | include/line/api/mam/map2_fit_idc.h |
| Fit a MAP(2) to three moments and an asymptotic index of dispersion. | |
| file | include/line/api/mam/map2mmpp.h |
| Read a MAP as an MMPP (matlab/lib/kpctoolbox/map/map2mmpp.m). | |
| file | include/line/api/mam/map_acfc.h |
| Autocorrelation of the counting process of a MAP at a given timescale. | |
| file | include/line/api/mam/map_algebra.h |
| MAP algebra missing from the moment and transform headers: time reversal, the Kronecker product composition, the subdominant eigenvalue of the embedded chain and the large-order threshold. | |
| file | include/line/api/mam/map_anfit.h |
| Fit a superposition of interrupted Poisson processes to a Hurst parameter. | |
| file | include/line/api/mam/map_bernstein.h |
| Acyclic phase-type approximation of an arbitrary density by Bernstein exponentials. | |
| file | include/line/api/mam/map_block.h |
| Fit a MAP(2) to three moments and an autocorrelation decay rate. | |
| file | include/line/api/mam/map_cdf.h |
| Cumulative distribution of the inter-arrival time of a MAP. | |
| file | include/line/api/mam/map_count_idc.h |
| Index of dispersion for counts (IDC) of a MAP at resolution t. | |
| file | include/line/api/mam/map_count_mean.h |
| Mean of the counting process of a MAP at resolution t. | |
| file | include/line/api/mam/map_count_moment.h |
| Power moments of the counts of a MAP in a window of length t. | |
| file | include/line/api/mam/map_count_var.h |
| Variance of the counting process of a MAP at resolution t. | |
| file | include/line/api/mam/map_dist.h |
| Analytic distances between continuous-time MAPs. | |
| file | include/line/api/mam/map_fit_detail.h |
| Scalar helpers shared by the MAP/PH moment-matching headers. | |
| file | include/line/api/mam/map_gamma.h |
| Autocorrelation decay rate of a MAP: the gamma of the geometric model rho(k) = rho0 * gamma^k with rho0 = (1 - 1/scv)/2. | |
| file | include/line/api/mam/map_joint_derivative.h |
| Derivatives at the origin of a MAP's complementary CDF and of its joint inter-arrival density. | |
| file | include/line/api/mam/map_m1ps.h |
| Sojourn time distribution in a MAP/M/1 processor-sharing queue. | |
| file | include/line/api/mam/map_mark.h |
| Mark the arrivals of a MAP with class probabilities (matlab/lib/kpctoolbox/map/map_mark.m). | |
| file | include/line/api/mam/map_max.h |
| Maximum of two independent MAPs, and its marked k-stage generalization. | |
| file | include/line/api/mam/map_mmpp2.h |
| Fit an MMPP(2) to a mean, an SCV, a skewness and a lag-1 autocorrelation. | |
| file | include/line/api/mam/map_moment.h |
| Markovian arrival process descriptors: stationary vectors, rate, moments, autocorrelation and the index of dispersion. | |
| file | include/line/api/mam/map_moment_extra.h |
| Three small MAP quantities the C++ tree had not carried: the factorial and joint moments, and the MMAP generator. | |
| file | include/line/api/mam/map_optim_dist.h |
| Fit the D1 of a MAP by MINIMIZING a distance to a reference MAP. | |
| file | include/line/api/mam/map_pdf.h |
| Probability density of the inter-arrival time of a MAP. | |
| file | include/line/api/mam/map_pnt.h |
| Counting probabilities of a MAP: P_n(t), the matrix whose (i,j) entry is the probability of n arrivals in [0,t) ending in phase j, given phase i at 0. | |
| file | include/line/api/mam/map_rand.h |
| Random MAP, MMPP, MMAP, acyclic-PH and hyperexponential generators, plus the hyperexponential reader. | |
| file | include/line/api/mam/map_sample.h |
| Sample the inter-arrival times of a MAP, a RAP or a matrix exponential. | |
| file | include/line/api/mam/map_transform.h |
| MAP constructors and structural transformations. | |
| file | include/line/api/mam/map_varcount.h |
| Variance of the counts of a MAP over windows of length t, in the spelling of matlab/lib/kpctoolbox/map/map_varcount.m. | |
| file | include/line/api/mam/maph2m_fit.h |
| Fit a MAPH(2,m): a second-order acyclic phase-type marked with m classes. | |
| file | include/line/api/mam/matlab_ilt.h |
| Numerical inverse Laplace transform in the Abate-Whitt framework, the port of matlab/lib/thirdparty/iltcme/matlab_ilt.m. | |
| file | include/line/api/mam/me_sample.h |
| Sample a matrix exponential by numerical inversion of its exact CDF. | |
| file | include/line/api/mam/mfq_fluflu_sojourn.h |
| Sojourn-time distribution of a fluid queue whose SERVICE is itself a Markov-modulated fluid flow, as an ME or PH representation (alpha, A). | |
| file | include/line/api/mam/mfq_ld_distr.h |
| Stationary density and distribution of a first- or second-order level-dependent (multi-regime) Markovian fluid queue, evaluated at requested fluid levels. | |
| file | include/line/api/mam/mfq_ld_mean.h |
| Stationary mean fluid level E[X] of a first- or second-order level-dependent (multi-regime) Markovian fluid queue, in closed form from the matrix-exponential building blocks. | |
| file | include/line/api/mam/mfq_ld_solve.h |
| First- and second-order level-dependent (multi-regime) Markovian fluid queues: the matrix-exponential building blocks of the stationary law. | |
| file | include/line/api/mam/mfq_multiregime.h |
| Multi-regime FEEDBACK Markovian fluid queue: density, density derivative and distribution of the fluid level. | |
| file | include/line/api/mam/mfq_prio_queue.h |
| Fluid priority queue: per-class fluid level and sojourn time of an MMAP[K]/PH[K]/1-type continuous fluid queue served in priority order. | |
| file | include/line/api/mam/mfq_sojourn.h |
| Sojourn-time distribution of a Markov-modulated fluid queue, as a matrix-exponential or phase-type representation (alpha, A). | |
| file | include/line/api/mam/mfq_solve.h |
| Core of the Markovian fluid queue: the fundamental matrices Psi, K, U and the matrix-exponential stationary solution of a general fluid model. | |
| file | include/line/api/mam/mmap_assemble.h |
| The MMAP assembly primitives solver_mam_basic.m builds its per-station arrival stream from: mmap_exponential, the probabilistic mmap_mark, the per-class mmap_scale, and mmap_super_safe. | |
| file | include/line/api/mam/mmap_compress.h |
| Compression of a marked MAP into a smaller representation, and the two M3A primitives it is built from: the class-conditional backward moments and the probabilistic mixture of MAPs. | |
| file | include/line/api/mam/mmap_count_var.h |
| Per-class variance of the counting process of a marked MAP. | |
| file | include/line/api/mam/mmap_k_fit.h |
| EXACT inverses of the class-marking map: solve for the split directly instead of optimizing it. | |
| file | include/line/api/mam/mmap_lambda.h |
| Marked MAP (MMAP) algebra: per-class rates, class probabilities, superposition, normalization and scaling. | |
| file | include/line/api/mam/mmap_modulate.h |
| Modulate a family of marked MAPs by an environment chain. | |
| file | include/line/api/mam/mmap_stats.h |
| Marked MAP statistics: embedded chains, class-transition probabilities, forward and cross moments, counting means and covariances. | |
| file | include/line/api/mam/mmapph1fcfs.h |
| The MMAP[K]/PH[K]/1 FCFS queue: per-class mean number in system and per-class queue-length distribution. | |
| file | include/line/api/mam/mmdp_isfeasible.h |
| Feasibility predicate for a Markov-modulated deterministic process. | |
| file | include/line/api/mam/mmpp2_fit.h |
| MMPP(2) matching three moments and the lag-1 autocorrelation (matlab/lib/kpctoolbox/mmpp/mmpp2_fit.m). | |
| file | include/line/api/mam/mmpp2_fit1.h |
| MAP(2) matching mean, SCV, skewness and the index of dispersion for counts (matlab/lib/kpctoolbox/mmpp/mmpp2_fit1.m). | |
| file | include/line/api/mam/mmpp2_fit2.h |
| MMPP(2) matching mean, SCV, skewness and the autocorrelation decay rate (matlab/lib/kpctoolbox/mmpp/mmpp2_fit2.m). | |
| file | include/line/api/mam/mmpp2_fit3.h |
| MMPP(2) matching three moments and the autocorrelation decay rate (matlab/lib/kpctoolbox/mmpp/mmpp2_fit3.m). | |
| file | include/line/api/mam/mmpp2_fit4.h |
| MMPP(2) matching mean, SCV, skewness and the lag-1 autocorrelation (matlab/lib/kpctoolbox/mmpp/mmpp2_fit4.m). | |
| file | include/line/api/mam/mmpp2_fitc.h |
| MMPP(2) matching counting-process characteristics (matlab/lib/kpctoolbox/mmpp/mmpp2_fitc.m). | |
| file | include/line/api/mam/mmpp2_fitc_approx.h |
| MMPP(2) fitted to counting-process characteristics by optimization (matlab/lib/kpctoolbox/mmpp/mmpp2_fitc_approx.m). | |
| file | include/line/api/mam/qbd_bmapbmap1.h |
| Level blocks of a BMAP/MAP/1 queue: batch Markovian arrivals against a single-departure MAP service process. | |
| file | include/line/api/mam/qbd_depproc.h |
| Departure process of a MAP/MAP/1 queue: the ETAQA-truncated MAP descriptor under FCFS and under PS, and the joint moments of consecutive inter-departure times. | |
| file | include/line/api/mam/qbd_mapmap1.h |
| The MAP/MAP/1 queue solved as a quasi-birth-death process. | |
| file | include/line/api/mam/qbd_r.h |
| Quasi-birth-death processes: the rate matrix R, the fundamental matrix G, the caudal characteristic, and the stationary distribution. | |
| file | include/line/api/mam/qbd_rap.h |
| Quasi-birth-death processes with rational arrival process components, and the RAP/RAP/1 queue built on top of them. | |
| file | include/line/api/mam/qbd_setupdelayoff.h |
| Mean queue length of an M/M/1 queue with a setup delay and a delayed-off period, solved as a QBD. | |
| file | include/line/lib/smc/etaqa.h |
| ETAQA: the aggregated stationary vector and the queue-length moments of an M/G/1-type and of a GI/M/1-type Markov chain. | |
| file | include/line/lib/smc/mg1.h |
| The M/G/1-type and GI/M/1-type fundamental-matrix solvers of MAMSolver / SMCSolver, ported from matlab/lib/thirdparty/MG1files: stat.m, MG1_EG.m, MG1_Decay.m, GIM1_Caudal.m, MG1_Shifts.m, MG1_CR.m, MG1_FI.m and GIM1_R.m. | |
MAPs, marked MAPs, MMPPs and phase-type distributions: moments, transformations, superposition, fitting (KPC-Toolbox, M3A, BuTools), and the QBD machinery for the rate matrices R and G.
1.18.0