Interest of Boundary Kernel Density Techniques in Evaluating an Approximation Error of Queueing Systems Characteristics

Algorithm 2

Approximation error with the weight norm.

(0) Begin

(1) Generate a sample of size of general probability distribution with

theoretical density ;

(2) Estimate the theoretical density by a nonparametric density noted

in general ;

(3) Introduce the mean service rate of the system;

(4) Determine the mean arrival rate of the system: ;

(5) Verify the stability: if then “the system is not stable” go to (9);

else the system is -strongly stable for go to (6);

(6) Determine the proximity of and :

;

(7) Determine the approximation domain ( of the system:

;

;

if then “the proximity is not sufficient”, go to (9);

else the approximation is valid go to (8);

(8) Determine the minimal error on the stationary distribution:

;

(9) End.