- 期刊
A Set of Efficient Formulae for Buffer Size Allocation of Real-Time Systems Using M/G/1 Queueing Models
使用M/G/1佇列模型做即時系統緩衝器大小配置用之一組有效之計算公式
摘要
A set of new, efficient and compact formulae for buffer size analysis of real-time systems using M/G/1 queueing model has been developed. For Poisson random arrival and general service time distribution of a single-server system, or an M/G/1 system, and for a certain probability of overflow as the confidence level, the needed size of buffer can be estimated. Two subsets of M/G/1 systems, namely the M/D/1 and M/E_k /1 systems, are investigated in detail to illustrate the practicality of this approach. The formulae are derived analytically and are validated using term-by-term evaluation. The size of buffer needed for M/D/1 and M/E_k /1 systems are tabulated for design and validation purposes. The newly derived formulae are more efficient than currently known computation methods.
並列摘要
本文介紹一組新而有效的公式，可供使用M/G/1佇列模型做即時系統緩衝器大小配置之用。對於以Poisson分佈之隨機事件到達及一般的服務時間分佈的單一處理器之系統而言(又稱M/G/1系統)，在某一作為信心水準的過載機率值之下，該系統所需的緩衝器大小值，可以估算出來。為展現此分析方法之可行性，乃針對M/G/1系統之兩種子系統，即M/D/1及M/E_k/1系統，來進行細部分析。本公式乃以解析方式所導出，並且用逐項估算的方式，來確認其正確性。使用M/D/1及M/E_k/1系統時，在各種信心水準值之下，所需配置的緩衝器大小，列在表格中，作為系統設計及確認之用。本論文所導出之公式，比目前所知的計算方式更為有效。