International Journal of Mathematics and Mathematical Sciences / 2014 / Article / Alg 2

Research Article

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.

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