cache_rrm_meanfield.h File Reference

Steady state of the RANDOM(m) multi-list mean field. More...

#include <cstddef>
#include <vector>
#include "line/api/cache/cache_rrm_meanfield_ode.h"
#include "line/num/number.h"
#include "line/util/error.h"
#include "line/util/ode.h"

Include dependency graph for cache_rrm_meanfield.h:

Go to the source code of this file.

Classes
struct	line::cache::CacheRrmMeanfieldResult< T >
	Return value of cache_rrm_meanfield. More...

Namespaces
namespace	line
namespace	line::cache

Functions
template<class T>
CacheRrmMeanfieldResult< T >	line::cache::cache_rrm_meanfield (const std::vector< T > &lambda, const std::vector< int > &m, const T &tmax)
	Steady state of the RANDOM(m) multi-list mean field.
template<class T>
CacheRrmMeanfieldResult< T >	line::cache::cache_rrm_meanfield (const std::vector< T > &lambda, const std::vector< int > &m)
	cache_rrm_meanfield with the reference horizon tmax = 1e4.

Detailed Description

Steady state of the RANDOM(m) multi-list mean field.

Port of matlab/src/api/cache/cache_rrm_meanfield.m, which is a SCRIPT rather than a function: it fixes n = 7 items, m = [1 1 3], a fixed popularity vector and a fixed initial condition, integrates the drift of cache_rrm_meanfield_ode.m with ode23s over [0,10000] and prints the terminal occupancy, the miss rate lambda*x(:,1) and the miss ratio. This header is that computation with the data as arguments.

The right-hand side was already ported (cache_rrm_meanfield_ode.h) and noted there that the steady state needed a stiff integrator that the port did not have. It now does: line/util/ode.h. The Jacobian is not written out here – the drift is bilinear, so a numeric central-difference Jacobian is accurate to about eps^(2/3) and the integrator forms it itself; that is the deliberate choice, since unlike cache_miss_rmf nothing downstream needs an exact Jacobian and an analytic one would be a second expression of the same formula to keep in step with the first.

The initial condition is the reference's: every item outside the cache, x(k,0) = 1. Integrating from there to t = 1e4 is exactly what cache_rrm_meanfield.m does.

ARITHMETIC. Gated: the answer is the limit of a tolerance-driven integration.

Definition in file cache_rrm_meanfield.h.