 |
LINE Solver (C++)
Templated C++ port of the LINE queueing solver
|
|
LINE Solver (C++)
Templated C++ port of the LINE queueing solver
|
One station in isolation, from M/M/1 to MAP/G/1/K: exact results, two-moment approximations, bounds, robust queueing, diffusion and fluid limits, and the scheduling variants. More...
Files | |
| file | include/line/api/qsys/qsys_bmapm1.h |
| BMAP/M/1 by the matrix-analytic (M/G/1-type) method. | |
| file | include/line/api/qsys/qsys_bmapphnn_retrial.h |
| The BMAP/PH/N/N bufferless retrial queue with flexible retrial admission control. | |
| file | include/line/api/qsys/qsys_dmc.h |
| D/M/c: deterministic interarrival times, exponential service. | |
| file | include/line/api/qsys/qsys_gg1.h |
| G/G/1 dispatcher: exact where a two-moment description determines the answer, Allen-Cunneen otherwise. | |
| file | include/line/api/qsys/qsys_ggingi_tga.h |
| Truncated Gaussian approximation (TGA-G) for the G/GI/n+GI queue. | |
| file | include/line/api/qsys/qsys_ggisgi_fluid.h |
| Steady state of the G/GI/s+GI fluid model. | |
| file | include/line/api/qsys/qsys_ggnm_diffusion.h |
| Diffusion approximation for the G/GI/n/m queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_allencunneen.h |
| Allen-Cunneen approximation of the mean response time of a G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_gelenbe.h |
| Gelenbe diffusion approximation with instantaneous-return boundary. | |
| file | include/line/api/qsys/qsys_gig1_approx_heyman.h |
| Heyman approximation of the mean response time of a G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_kimura.h |
| Kimura diffusion-interpolation approximation for the G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_klb.h |
| Kraemer and Langenbach-Belz approximation for the G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_kobayashi.h |
| Kobayashi diffusion approximation for the G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_marchal.h |
| Marchal approximation of the mean response time of a G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_myskja.h |
| Myskja's third-moment approximation of the mean response time of a G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_myskja2.h |
| Myskja's enhanced third-moment approximation of the mean response time of a G/I/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_approx_whitt.h |
| Whitt's approximation of the G/G/1 mean response time. | |
| file | include/line/api/qsys/qsys_gig1_bnds_extremal.h |
| Extremal two-moment bounds for the GI/GI/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_lbnd.h |
| Fundamental lower bound on the mean response time of a G/G/1 queue. | |
| file | include/line/api/qsys/qsys_gig1_rq.h |
| Robust Queueing (RQ) approximation of a G/GI/1 queue characterized by its arrival index of dispersion and the first two service moments. | |
| file | include/line/api/qsys/qsys_gig1_rqt.h |
| Robust Queueing Theory (RQT) worst-case system time of a G/G/1 FCFS queue, the single-server case of qsys_gigk_rqt (Theorem 2 and eq. | |
| file | include/line/api/qsys/qsys_gig1_ubnd_kingman.h |
| Kingman upper bound on the mean waiting time of a G/G/1 queue. | |
| file | include/line/api/qsys/qsys_gigk_approx.h |
| Default G/I/G/k approximation of the mean response time. | |
| file | include/line/api/qsys/qsys_gigk_approx_cosmetatos.h |
| Cosmetatos / Page interpolation approximation for the GI/G/k queue. | |
| file | include/line/api/qsys/qsys_gigk_approx_kingman.h |
| Kingman (Lee-Longton) scaling of the exact M/M/k waiting time. | |
| file | include/line/api/qsys/qsys_gigk_approx_whitt.h |
| Whitt (1993) approximation for the GI/G/k queue, eqs. | |
| file | include/line/api/qsys/qsys_gigk_rqt.h |
| Robust Queueing Theory (RQT) worst-case system time of a G/G/k FCFS queue. | |
| file | include/line/api/qsys/qsys_gigk_rqt_gamma.h |
| Service variability parameter of the Robust Queueing Theory (RQT) framework. | |
| file | include/line/api/qsys/qsys_gm1.h |
| Exact mean response time of the G/M/1 queue. | |
| file | include/line/api/qsys/qsys_gtmtst_fluid.h |
| The Gt/Mt/st+GI many-server fluid queue, and the network of them. | |
| file | include/line/api/qsys/qsys_hh1_lindley.h |
| Conditional waiting-time moments of the Hl/Hn/1 Lindley recursion. | |
| file | include/line/api/qsys/qsys_ldps_workload.h |
| Stationary distribution of the unfinished work in a single-stage load-dependent generalized-processor-sharing station with Poisson arrivals and blocking. | |
| file | include/line/api/qsys/qsys_lindley_moment.h |
| One conditional Lindley moment for exponential primitives. | |
| file | include/line/api/qsys/qsys_mapd1.h |
| The MAP/D/1 FCFS queue: deterministic service of length s fed by a Markovian arrival process. | |
| file | include/line/api/qsys/qsys_mapdc.h |
| The MAP/D/c FCFS queue: c servers, deterministic service of length s, fed by a Markovian arrival process. | |
| file | include/line/api/qsys/qsys_mapg1.h |
| The MAP/G/1 FCFS queue, by moment-matching the general service time to a phase-type distribution. | |
| file | include/line/api/qsys/qsys_mapg1k.h |
| The MAP/G/1/K queue with tail drop: Markovian arrivals, an arbitrary service law F, and a buffer of K packets counting the one in transmission. | |
| file | include/line/api/qsys/qsys_mapg1k_perflow.h |
| Per-flow throughput and loss ratio of a tail-drop FIFO buffer fed by N flows of mutually different statistical character. | |
| file | include/line/api/qsys/qsys_mapm1.h |
| The MAP/M/1 FCFS queue, the single-server case of MAP/M/c. | |
| file | include/line/api/qsys/qsys_mapmap1.h |
| The MAP/MAP/1 FCFS queue: mean number in system, waiting time, sojourn time, utilization and the queue-length distribution. | |
| file | include/line/api/qsys/qsys_mapmc.h |
| The MAP/M/c FCFS queue: c identical exponential servers of rate mu fed by a Markovian arrival process. | |
| file | include/line/api/qsys/qsys_mapph1.h |
| The MAP/PH/1 FCFS queue. | |
| file | include/line/api/qsys/qsys_mapphc.h |
| The MAP/PH/c FCFS queue, solved exactly. | |
| file | include/line/api/qsys/qsys_maxima_twomoment.h |
| Two-moment approximation for the maximum of n iid non-negative variables. | |
| file | include/line/api/qsys/qsys_mdc_crommelin.h |
| M/D/c by Crommelin's embedded chain. | |
| file | include/line/api/qsys/qsys_mg1.h |
| Exact mean response time of the M/G/1 queue (Pollaczek-Khinchine). | |
| file | include/line/api/qsys/qsys_mg1_fb.h |
| M/G/1 under FB (feedback), also called LAS (least attained service). | |
| file | include/line/api/qsys/qsys_mg1_lrpt.h |
| M/G/1 under LRPT (longest remaining processing time). | |
| file | include/line/api/qsys/qsys_mg1_prio.h |
| M/G/1 with non-preemptive head-of-line priorities: per-class mean response times from the Cobham/Kleinrock formula. | |
| file | include/line/api/qsys/qsys_mg1_ps.h |
| Sojourn-time distribution of the M/G/1 processor-sharing queue. | |
| file | include/line/api/qsys/qsys_mg1_psjf.h |
| M/G/1 under PSJF (preemptive shortest job first). | |
| file | include/line/api/qsys/qsys_mg1_setf.h |
| M/G/1 under SETF (shortest elapsed time first), the non-preemptive counterpart of FB/LAS. | |
| file | include/line/api/qsys/qsys_mg1_srpt.h |
| M/G/1 under SRPT (shortest remaining processing time), by the Schrage-Miller formula. | |
| file | include/line/api/qsys/qsys_mg1k_loss.h |
| Exact M/G/1/K loss probability, via the chain embedded at service-start epochs. | |
| file | include/line/api/qsys/qsys_mg1k_loss_mgs.h |
| MacGregor Smith's closed-form approximation of the M/G/1/K loss probability. | |
| file | include/line/api/qsys/qsys_mginf.h |
| Exact solution of the M/G/infinity queue. | |
| file | include/line/api/qsys/qsys_mgisrgi_whitt.h |
| Engineering solution of the call-center model M/GI/s/r+GI. | |
| file | include/line/api/qsys/qsys_mm1.h |
| Exact mean response time of the M/M/1 queue. | |
| file | include/line/api/qsys/qsys_mm1_dps.h |
| Multiclass M/M/1 under DPS (discriminatory processor sharing), solved numerically on the truncated population chain. | |
| file | include/line/api/qsys/qsys_mm1_lindley.h |
| Conditional waiting-time moments of the M/M/1 Lindley recursion. | |
| file | include/line/api/qsys/qsys_mm1_ps.h |
| Exact sojourn-time moments of the multiclass M/M/1-PS queue. | |
| file | include/line/api/qsys/qsys_mm1_tandem_lindley.h |
| Conditional waiting time at the SECOND station of an M/M/1 -> /M/1 tandem. | |
| file | include/line/api/qsys/qsys_mm1k_loss.h |
| Blocking probability of the M/M/1/K queue. | |
| file | include/line/api/qsys/qsys_mmapg1k.h |
| Exact per-class throughput and loss ratio of an MMAP[K]/G/1/K tail-drop queue. | |
| file | include/line/api/qsys/qsys_mmapgk1.h |
| The MMAP[K]/G[K]/1 FCFS queue: K customer types with class-dependent GENERAL service, fed by a marked Markovian arrival process. | |
| file | include/line/api/qsys/qsys_mmcc_retrial_fp.h |
| Fixed-point approximation for the M/M/c/c retrial queue. | |
| file | include/line/api/qsys/qsys_mmck.h |
| Exact analysis of the M/M/c/K queue (truncated Erlang form). | |
| file | include/line/api/qsys/qsys_mmk.h |
| Exact mean response time of the M/M/k queue (Erlang-C). | |
| file | include/line/api/qsys/qsys_mmk_qed.h |
| Halfin-Whitt QED approximation for the M/M/s queue, and the square-root staffing rule that inverts it. | |
| file | include/line/api/qsys/qsys_mtginf.h |
| Exact time-varying analysis of the Mt/G/infinity queue. | |
| file | include/line/api/qsys/qsys_mtgs0_mol.h |
| Modified-offered-load and pointwise-stationary approximations for a time-varying multiserver system. | |
| file | include/line/api/qsys/qsys_mxm1.h |
| M^X/M/1: the batch-arrival queue with exponential service. | |
| file | include/line/api/qsys/qsys_phm1.h |
| Exact PH/M/1, the GI/M/1 queue with phase-type interarrival times. | |
| file | include/line/api/qsys/qsys_phmc.h |
| Exact PH/M/c by Neuts' matrix-geometric method. | |
| file | include/line/api/qsys/qsys_phph1.h |
| The PH/PH/1 FCFS queue. | |
| file | include/line/api/qsys/qsys_quadrature.h |
| Adaptive quadrature for the qsys functions whose MATLAB originals call integral(), and the cumulative trapezoid rule for the one that calls cumtrapz(). | |
| file | include/line/api/qsys/qsys_tandem_lindley.h |
| Sample-path Lindley recursion along a tandem of single-server FCFS queues. | |
| file | include/line/api/qsys/qsys_tandem_ub_ciucu.h |
| Tail bounds for a GI/Hn/1 -> . | |
| file | include/line/api/qsys/qsys_types.h |
| Shared return type and arithmetic helpers for the templated qsys port. | |
One station in isolation, from M/M/1 to MAP/G/1/K: exact results, two-moment approximations, bounds, robust queueing, diffusion and fluid limits, and the scheduling variants.
1.18.0