Package jline.api.cache

Class CacheSojourn

java.lang.Object

jline.api.cache.CacheSojourn

public final class CacheSojourn
extends Object

The average of a cache mean-field trajectory against a phase-type clock, integrated WITH the drift. Java twin of MATLAB cache_sojourn_ode.m.

For a drift dx/dt = f(x) and a clock with row phase vector phi, dphi/dt = phi A, density g(t) = phi(t) c, it returns xbar = int_0^T x g dt / int_0^T g dt and wtot = int_0^T g dt, by augmenting the state with phi, int g x and int g. The value is accurate to the ODE tolerance and does NOT depend on any output grid: a Riemann sum over the grid did, and that is what made the adaptive (MATLAB) and fixed-grid (JAR/Python/C++) ENV cache mean fields differ in the third digit.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	CacheSojourn.Clock	A phase-type clock: dphi/dt = phi A, phi(0) = phi0, density phi c.
static interface	CacheSojourn.Drift	The drift of the cache mean field.
static final class	CacheSojourn.OdeResult	Output of cache_sojourn_ode(jline.api.cache.CacheSojourn.Drift, double[], double[], jline.api.cache.CacheSojourn.Clock): the time grid tout (nt), the occupancy trajectory xtraj (dim x nt) and the clock-weighted average sj (null when no clock was given), as MATLAB [tout, xtraj, sj] = cache_sojourn_ode(...).
static final class	CacheSojourn.Result	A sojourn average: occupancy xbar (null when wtot is 0), clock mass, per-user miss rate.

Method Summary

Modifier and Type	Method	Description
static CacheSojourn.Result	average(CacheSojourn.Drift f, double[] x0, double t1, CacheSojourn.Clock clk)	Integrates the augmented system over [0, t1] from x0 and returns the clock-weighted average, with the MATLAB cache_miss_rmf tolerances (AbsTol 1e-10, RelTol 1e-8).
static CacheSojourn.OdeResult	cache_sojourn_ode(CacheSojourn.Drift f, double[] tspan, double[] x0, CacheSojourn.Clock clk)	Java twin of MATLAB cache_sojourn_ode(drift, tspan, x0, wgen, odeopt) with the ode15s default tolerances (RelTol 1e-3, AbsTol 1e-6).
static CacheSojourn.OdeResult	cache_sojourn_ode(CacheSojourn.Drift f, double[] tspan, double[] x0, CacheSojourn.Clock clk, double relTol, double absTol)	Integrates dx/dt = f(x) over tspan from x0 and, when clk is given, the clock-weighted average of the trajectory carried as extra state (phi, int g x, int g), so that it is accurate to the ODE tolerance and independent of the output grid.
static CacheSojourn.Clock	holdingClock(Matrix D0in, Matrix D1in, double lam)	The holding-time clock of a random-environment stage whose holding time is the MAP {D0,D1}, in a drift time unit that is lam times real time: A = D0/lam, c = -D0 1/lam, phi0 = map_pie, so that int_0^T g = F(T/lam) with F the holding-time CDF.
static double[]	missRate(Matrix[] lambdaCache, double[] pi0)	Per-user miss rate MU(v) = sum_i lambda_v(i) pi0(i) of a per-item out-of-cache probability pi0, the same functional as the transient MU_t, which is affine in the occupancy.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

holdingClock

public static CacheSojourn.Clock holdingClock(Matrix D0in,
 Matrix D1in,
 double lam)

The holding-time clock of a random-environment stage whose holding time is the MAP {D0,D1}, in a drift time unit that is lam times real time: A = D0/lam, c = -D0 1/lam, phi0 = map_pie, so that int_0^T g = F(T/lam) with F the holding-time CDF.

cache_sojourn_ode

public static CacheSojourn.OdeResult cache_sojourn_ode(CacheSojourn.Drift f,
 double[] tspan,
 double[] x0,
 CacheSojourn.Clock clk)

Java twin of MATLAB cache_sojourn_ode(drift, tspan, x0, wgen, odeopt) with the ode15s default tolerances (RelTol 1e-3, AbsTol 1e-6). With clk == null the integration is the plain drift and sj is null.

cache_sojourn_ode

public static CacheSojourn.OdeResult cache_sojourn_ode(CacheSojourn.Drift f,
 double[] tspan,
 double[] x0,
 CacheSojourn.Clock clk,
 double relTol,
 double absTol)

Integrates dx/dt = f(x) over tspan from x0 and, when clk is given, the clock-weighted average of the trajectory carried as extra state (phi, int g x, int g), so that it is accurate to the ODE tolerance and independent of the output grid. A two-element tspan = [t0, t1] returns the integrator's own (adaptive) steps, as MATLAB ode15s; a longer tspan returns the solution at exactly those instants. relTol/absTol play the role of odeopt (RelTol/AbsTol).

average

public static CacheSojourn.Result average(CacheSojourn.Drift f,
 double[] x0,
 double t1,
 CacheSojourn.Clock clk)

Integrates the augmented system over [0, t1] from x0 and returns the clock-weighted average, with the MATLAB cache_miss_rmf tolerances (AbsTol 1e-10, RelTol 1e-8). Shorthand for cache_sojourn_ode(jline.api.cache.CacheSojourn.Drift, double[], double[], jline.api.cache.CacheSojourn.Clock).

missRate

public static double[] missRate(Matrix[] lambdaCache,
 double[] pi0)

Per-user miss rate MU(v) = sum_i lambda_v(i) pi0(i) of a per-item out-of-cache probability pi0, the same functional as the transient MU_t, which is affine in the occupancy.