Analyzing Effectiveness of Warm-up Detection Methods

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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