Analyzing Effectiveness of Warm-up Detection Methods

Yıl 2017, Cilt: 32 Sayı: 4, 201 - 210, 15.12.2017

Nuşin Uncu

https://doi.org/10.21605/cukurovaummfd.383428

Öz

In discrete event system simulation, it is necessary
to purify the system from effects of its initial conditions for unbiased
estimation of performance outputs. Particularly in non-terminating models, the
period during which the system reaches the steady state, that is, the warm-up
period statistics, should not be included in the calculations to remove the
biased effects on the performance output values. In problems which simulation
and optimization methods are used together, the update of simulation parameters
before each run results in variation of warm-up periods.  In order to decrease this variation, the
online warm-up determination methods are used. In this study, Welch’s Graphical
method and two online warm-up detection methods: Exponential Variation Rate
Rule and Euclidean Distance methods are applied for M/M/1 queueing systems
simulation. The effectiveness of these methods based on convergence to the
analytic solutions and CPU times are compared.

Anahtar Kelimeler

Simulation, Warm-up detection, Welch’s graphical method, Euclidean distance, Exponential variation rate, Lyapunov exponent

Isınma Periyodu Belirleme Yöntemlerinin Etkinliklerinin Analizi

Öz

Kesikli
olay simülasyonunda, performans çıktı değerlerinin yansız tahmini için sistemi
başlangıç durumu etkilerinden arındırmak gerekmektedir. Özellikle sonlanmayan
modellerde, sistemin durağan duruma ulaşana kadar geçirdiği süre yani ısınma
periyodu istatistikleri, performans çıktı değerlerinin üzerindeki yanlı etkilerinin
ortadan kaldırılması için hesaplamalara dâhil edilmemelidir. Simülasyon ve
optimizasyon yöntemlerinin birlikte kullanıldığı problemlerde ise simülasyon
parametrelerinin her koşum öncesi güncellenmesi ısınma periyodunda da
değişimlere sebep olmaktadır. Bu değişimi azaltmak için, anlık ısınma periyodu
belirleme yöntemleri kullanılmaktadır. Bu çalışmada, Welch Grafik yöntemi ve
anlık ısınma periyodu belirleme yöntemlerinden Üstel Değişim Oranı Kuralı ve
Öklid Uzaklığı yöntemleri M/M/1 kuyruk modeli için uygulanmıştır. Yöntemler
etkinlikleri analitik sonuçlara yakınsama başarımları ve CPU zamanları bazında
etkinlikleri karşılaştırılmıştır.

Anahtar Kelimeler

Simülasyon, Isınma periyodu, Welch grafiği, Öklid uzaklığı, Üstel değişim oranı kuralı, Lyapunov üssü

Kaynakça

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