MX/M/1可變服務速率等候模型之解析

Abstract

本研究乃在解析可變服務速率之等候模型。研究中探討了三個等候模型，分別為M[X] /M/1等候模型之兩階段服務速率控制，M/M/1等候模型之三階段服務速率控制及M[X]/M/1 等候模型之三階段服務速率控制。研究中推導出系統在狀態零與期望系統人數之方程式。 研究中也提出計算系統人數機率的計算程序，以及模式所一般化的特例與範例之探討。

In this paper, we consider a class of Markovian queues with state-dependent service rates. The models under consideration are M[X]/M/1 queue with bilevel hysteretic service rate control, M/M/1 queue with tri-level hysteretic service rate control and M[X]/M/1 queue with tri-level hysteretic service rate control. We derive the equations of steady-state probability of empty state and expected number of customers in system. Computational procedures are presented to compute the probabilities of number of customers in system. Special cases and numerical examples are also presented.