隊伍系統顧客平均極限分配與時間平均極限分配之間的關係

Abstract

本文目的在於找出顧客平均極限分配和時間平均極限分配之間的關係式。我們的方法利用到了隨機觀察者和逆向過程的觀念，證明出顧客平均極限分配與時間平均極限分配之間的函數關係式，接著舉了M/G/k/k和M/M/k二個排隊模型的範例。本文最後推導出初步估計值，模擬了各種的排隊模型，來分析初步估計值和模擬值的估計結果，並說明初步估計值何時會高估或是低估。

This paper is to find the relationship between customer-average distribution and time-average distribution. Our method includes random observers and reversed process, and in steady-state we prove the relationship, and then give two examples in M/G/k/k and M/M/k models. Finally we derive the preliminary estimation to analyze when it will overestimate or underestimate in various queue models.