qsys_md1.h File Reference

Exact analysis of the M/D/1 queue: the M/G/1 moments with deterministic service plus the queue-length distribution. More...

#include <cmath>
#include <vector>
#include "line/api/qsys/qsys_mg1.h"
#include "line/api/qsys/qsys_res.h"
#include "line/util/error.h"

Include dependency graph for qsys_md1.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
QsysRes	line::qsys::qsys_md1 (double lambda, double mu, long nmax=-1)
	Exact M/D/1 queue.

Detailed Description

Exact analysis of the M/D/1 queue: the M/G/1 moments with deterministic service plus the queue-length distribution.

Port of matlab/src/api/qsys/qsys_md1.m. The mean measures are qsys_mg1's with cs = 0 and E[S^3] = 1/mu^3. The distribution follows from the embedded-chain recursion with a_0 = exp(-rho) and the Poisson tails Abar_k = P(N > k):

p_0 = 1 - rho, p_n = (p_0 Abar_{n-1} + sum_{j=1}^{n-1} p_j Abar_{n-j}) / a_0,

run until the mass left is below 1e-14 (or to nmax when given).

ARITHMETIC: double, as the reference.

Definition in file qsys_md1.h.