Analysis of steady-state and transient delay in discrete-time single-arrival and batch-arrival systems

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• 作者：J. Walraevens ; ^{jw@telin.UGent.be" class="auth_mail} ; D. Claeys ^{dclaeys@telin.UGent.be" class="auth_mail} ; H. Bruneel ^{hb@telin.UGent.be" class="auth_mail}
• 关键词：Queueing theory ; Generating functions ; Transient analysis ; Virtual delay
• 刊名：Applied Mathematics and Computation
• 出版年：1 August 2014
• 年：2014
• 卷：240
• 期：Complete
• 页码：62-71
• 全文大小：396 K

文摘

We perform an analysis of the transient delay in a discrete-time FIFO buffer with batch arrivals. As transient delay is an ambiguous concept, we first discuss different possible definitions of the term (delay of the kth customer, delay of a customer arriving at time t, etc.). In this paper, we focus on the analysis of the delay of a customer arriving in slot t, also sometimes called virtual delay in single-arrival systems. It turns out that the modeling in batch-arrival systems is more intricate. In analysis, we relate transient delay to transient unfinished work and characterize the latter. Some time-dependent as well as limiting steady-state delay measures are calculated. We also study a variation that is related to active probing measurements. A substantial part of the article finally focuses on some fundamental differences between alternative definitions of transient delay.