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In probability theory, the Lindley equation, Lindley recursion or Lindley processes is a discrete-time stochastic process ''A''''n'' where ''n'' takes integer values and ::''A''''n'' + 1 = max(0, ''A''''n'' + ''B''''n''). Processes of this form can be used to describe the waiting time of customers in a queue or evolution of a queue length over time. The idea was first proposed in the discussion following Kendall's 1951 paper. ==Waiting times== In Dennis Lindley's first paper on the subject the equation is used to describe waiting times experienced by customers in a queue with the First-In First-Out (FIFO) discipline. ::''W''''n'' + 1 = max(0,''W''''n'' + ''U''''n'') where * ''T''''n'' is the time between the ''n''th and (''n''+1)th arrivals, * ''S''''n'' is the service time of the ''n''th customer, and * ''U''''n'' = ''S''''n'' − ''T''''n'' * ''W''''n'' is the waiting time of the ''n''th customer. The first customer does not need to wait so ''W''1 = 0. Subsequent customers will have to wait if they arrive at a time before the previous customer has been served. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lindley equation」の詳細全文を読む スポンサード リンク
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