qsys_mapmapc.h File Reference

The MAP/MAP/c FCFS queue whose service MAP is CARRIED in service-start order. More...

#include <cstddef>
#include <vector>
#include "line/api/mam/ldqbd_mphc.h"
#include "line/api/mam/map_moment.h"
#include "line/api/mam/qbd_r.h"
#include "line/api/qsys/qsys_mapphc.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/linalg.h"
#include "line/util/lu.h"
#include "line/util/matrix.h"

Include dependency graph for qsys_mapmapc.h:

Go to the source code of this file.

Namespaces
namespace	line
	Conservation laws of a layered queueing network, enumerated from its structure.
namespace	line::qsys

Functions
template<class T>
MapPhcResult< T >	line::qsys::qsys_mapmapc (const mam::Map< T > &arrival, const mam::Map< T > &service, unsigned c, std::size_t dist_size=500, std::size_t num_w_moms=3)
	MAP/MAP/c FCFS with the service phase carried in start order, exactly.

Detailed Description

The MAP/MAP/c FCFS queue whose service MAP is CARRIED in service-start order.

THE SERVICE LAW. The service MAP is one station-level process whose successive draws are chained in service-START order, idle periods included: each job starts in the phase the previous draw ENDED in, which is how JMT and both LDES engines sample a MAP service and the law SolverCTMC follows through its pair form. A renewal reading of the marginal (qsys_mapphc, or the single-fast-server surrogate) discards the autocorrelation of the service times.

THE STATE SPACE. With V = (-S0)^-1 S1, a draw started in h lands in j with probability V(h,j); a busy server is a PAIR (i,j) of current phase i and landing j, run under S0 conditioned on ending in j. A level holds the MULTISET of busy pairs and the landing phase of the draw started last. ldqbd_mphc(..., carry) builds those blocks; this header lifts them to a MAP arrival stream and solves the level-independent QBD above level c matrix-geometrically, exactly as qsys_mapphc does for a renewal service. At c = 1 it is the frozen-phase MAP/MAP/1 queue.

References: S. Asmussen and J.R. Moller, "Calculation of the steady state waiting time distribution in GI/PH/c and MAP/PH/c queues", Queueing Systems 37(1):9-29, 2001. M.F. Neuts, "Matrix-geometric solutions in stochastic models", Johns Hopkins University Press, 1981.

Definition in file qsys_mapmapc.h.