snc_mean_backlog.h File Reference

Upper bound on the mean backlog, from integrating the backlog tail bound. More...

#include <cmath>
#include "line/api/snc/snc_thetaopt.h"
#include "line/api/snc/snc_types.h"
#include "line/util/error.h"

Include dependency graph for snc_mean_backlog.h:

Go to the source code of this file.

Namespaces
namespace	line
namespace	line::snc

Functions
SncResult	line::snc::snc_mean_backlog (const Envelope &arv, const Envelope &srv, double thetamax=1e3)
	Upper bound on the mean backlog, from integrating the backlog tail bound.

Detailed Description

Upper bound on the mean backlog, from integrating the backlog tail bound.

The counterpart of snc_mean_delay with a = theta: the clipped integral of K*exp(-theta*b) is (log(K)+1)/theta when K >= 1 and K/theta otherwise. The unit of the answer is the unit of the envelopes: jobs when the pair is snc_env_poisson with snc_srv_exp, units of work when it is snc_env_cpoisson with snc_srv_rate.

SolverBA does NOT use this for its queue-length column: it applies Little's law to the response-time bound instead, so that Q and R stay consistent with the exact open-network throughput. The two are close but not identical, since each optimizes its own theta.

Port of matlab/src/api/snc/snc_mean_backlog.m.

Definition in file snc_mean_backlog.h.