The MAP/PH/1 FCFS queue. More...

#include <cstddef>
#include <vector>
#include "line/api/mam/map_moment.h"
#include "line/api/qsys/qsys_mapmap1.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/matrix.h"

Include dependency graph for qsys_mapph1.h:

Namespaces
namespace	line
namespace	line::qsys

Functions
template<class T>
MapMap1Result< T >	line::qsys::qsys_mapph1 (const mam::Map< T > &arrival, const std::vector< T > &sigma, const Matrix< T > &S, std::size_t dist_size)
	MAP/PH/1 by the exact QBD solution of the equivalent MAP/MAP/1 queue.
template<class T>
MapMap1Result< T >	line::qsys::qsys_mapph1 (const mam::Map< T > &arrival, const std::vector< T > &sigma, const Matrix< T > &S)
	qsys_mapph1 with 100 materialized levels, the reference's numQLProbs.

Detailed Description

The MAP/PH/1 FCFS queue.

ALGORITHM, AND HOW IT DIFFERS FROM THE MATLAB REFERENCE. matlab/src/api/qsys/qsys_mapph1.m computes these quantities by calling BUTools' MMAPPH1FCFS, which is not transcribed here. This port computes the SAME quantities from the port's own QBD machinery: a PH service (sigma, S) is the renewal MAP

D0 = S,    D1 = (-S e) sigma,

so MAP/PH/1 is literally a MAP/MAP/1 queue with a renewal service process, and the problem is handed to qsys_mapmap1 (see qsys_mapmap1.h for the QBD construction). Different algorithm, same quantity. Because the service MAP built this way IS a renewal process, none of the caveats about discarded service correlation in qsys_mapmap1.h apply to this function: the reference and the port model the identical stochastic system here.

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

M/M/1 collapse, qsys_mapph1(D0 = [-2], D1 = [2], sigma = [1], S = [-3]): MATLAB 1.999999999999999 / 0.6666666666666656 / 0.9999999999999989 / 0.6666666666666666; the port returns the textbook 2 / 0.666666666666668 / 1 / 0.666666666666667. Relative differences 5e-16, 1.8e-15, 1.1e-15, 1e-16.
Correlated MMPP2 arrival D0 = [-2.5 0.2; 0.1 -0.7], D1 = diag(2.3, 0.6) (lambda = 7/6) with Erlang-2 service sigma = [1 0], S = [-6 6; 0 -6]: MATLAB 0.8364637529649164 / 0.3836355977794533 / 0.7169689311127866 / 0.3888888888888888; port 0.836463752964917 / 0.383635597779453 / 0.716968931112786 / 0.388888888888889. Relative differences below 1e-15 on every metric.
Erlang-2 arrival D0 = [-4 4; 0 -4], D1 = [0 0; 4 0] (lambda = 2) with hyperexponential service sigma = [0.6 0.4], S = diag(-8, -1.6): MATLAB 2.133647429543165 / 0.7418237147715814 / 1.066823714771581 / 0.65; port 2.13364742954318 / 0.741823714771588 / 1.06682371477159 / 0.65. Relative differences below 1e-15 on every metric.

The port therefore reproduces the BUTools reference to machine precision on this family. It deliberately does NOT reproduce LINE's own MATLAB qbd_mapmap1 on the equivalent MAP pair, which returns 0.8364637492083693 and 2.133647423495968 for the second and third cases: those are 4.5e-9 and 2.8e-9 BELOW the values above because MATLAB's qbd_mapmap1 sums the level distribution until the accumulated mass reaches 1 - 1e-10 and discards the remaining tail times its level index, while this port sums the whole geometric tail in closed form (see qbd_mapmap1.h).

ARITHMETIC. Gated on num_traits<T>::has_transcendental, inherited from qsys_mapmap1 and ultimately from the cyclic reduction that produces R; see qbd_r.h. The PH-to-MAP conversion itself is exact matrix algebra.

Definition in file qsys_mapph1.h.

Namespaces

Functions

Detailed Description