qsys_mapm1.h File Reference

The MAP/M/1 FCFS queue, the single-server case of MAP/M/c. More...

#include <cstddef>
#include <vector>
#include "line/api/mam/map_moment.h"
#include "line/api/qsys/qsys_mapmc.h"
#include "line/num/number.h"

Include dependency graph for qsys_mapm1.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
MapMcResult< T >	line::qsys::qsys_mapm1 (const mam::Map< T > &arrival, const T &mu, std::size_t dist_size)
	MAP/M/1 by the matrix-geometric solution, i.e.
template<class T>
MapMcResult< T >	line::qsys::qsys_mapm1 (const mam::Map< T > &arrival, const T &mu)
	qsys_mapm1 with 100 materialized levels.

Detailed Description

The MAP/M/1 FCFS queue, the single-server case of MAP/M/c.

ALGORITHM, AND HOW IT DIFFERS FROM THE MATLAB REFERENCE. matlab/src/api/qsys/qsys_mapm1.m is a one-line wrapper for qsys_mapmc with c = 1, which in turn calls Q-MAM's Q_CT_MAP_M_C, which is not transcribed here. This port keeps the same delegation and calls this port's own qsys_mapmc (see qsys_mapmc.h), which builds the quasi-birth-death process directly: at c = 1 the level blocks are A0 = D1, A1 = D0 - mu I, A2 = mu I with a single boundary level, and R comes from cyclic reduction. Different algorithm, same quantity.

At c = 1 this is also exactly a MAP/MAP/1 queue with an exponential service MAP, so qsys_mapmap1(arrival, {[-mu], [mu]}) must return the same numbers by a completely different route (cyclic reduction on the Kronecker-product QBD rather than cyclic reduction on the arrival-phase QBD). That cross-check is one of the assertions in the test file, and holds to 1e-13.

MEASURED AGREEMENT (MATLAB R2025a, T = double). Metric order is meanQueueLength / meanWaitingTime / meanSojournTime / utilization.

• M/M/1 collapse, qsys_mapm1(D0 = [-2], D1 = [2], mu = 3): MATLAB 1.999999994584355 / 0.6666666665442794 / 0.9999999998776128 / 0.6666666666666666. This port returns the textbook 2 / 0.666666666666667 / 1 / 0.666666666666667 to 1e-15, so the relative differences against MATLAB are 2.7e-9, 1.7e-10 and 1.2e-10. The residual is the reference's maxNumComp = 500 level truncation; the port sums the geometric tail in closed form and matches the exact formulas.
• Correlated MMPP2 arrivals D0 = [-2.5 0.2; 0.1 -0.7], D1 = diag(2.3, 0.6) (lambda = 7/6), mu = 2: MATLAB 2.795385119831413 / 1.896044396731732 / 2.396044396731732 / 0.5833333333333333; port 2.79538513100956 / 1.89604439800819 / 2.39604439800819 / 0.583333333333333. Relative differences 4.0e-9, 6.7e-10, 5.3e-10.
• Erlang-2 arrivals D0 = [-4 4; 0 -4], D1 = [0 0; 4 0] (lambda = 2), mu = 3: MATLAB 1.568729300352212 / 0.4510313188166638 / 0.7843646521499972 / 0.6666666666666666; port 1.56872930440884 / 0.451031318871088 / 0.784364652204421 / 0.666666666666667. Relative differences 2.6e-9, 1.2e-10, 6.9e-11.

The cross-check against qsys_mapmap1 mentioned above was run on both non-Poisson instances and agrees to 5e-16 on meanQueueLength and meanWaitingTime, which identifies the 1e-9 residuals above as the reference's truncation rather than this port's error.

ARITHMETIC. Gated on num_traits<T>::has_transcendental, inherited from qsys_mapmc: cyclic reduction drives R to a tolerance and never terminates in a finite number of field operations. See qbd_r.h.

Definition in file qsys_mapm1.h.