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Use Soda PDF OCR to turn any PDF, image, or scanned document into a fully editable file with the help of Optical Character Recognition ( OCR ) software . In this section we discuss a generally applicable up- and downcrossing technique that, in onjunction with the PASTA property, can be used to establish relations between customer-average and time-average probabilities in queueing systems To illustrate this, we consider the so-called GI /M/1 queue In this single-server system, customers arrive according to a renewal process and the service times of the customers have a common exponential distribution The single server can handle only one customer at a time and there is ample waiting room for customers who nd the server busy upon arrival The service times of the customers are independent of each other and are also independent of the arrival process Denoting by the average arrival rate (1/ = the mean interarrival time) and by the service rate (1/ = the mean service time), it is assumed that < The continuous-time stochastic process {X(t), t 0} and the discrete-time stochastic process {Xn , n = 1, 2, } are de ned by X(t) = the number of customers present at time t, and Xn = the number of customers present just prior to the nth arrival epoch The stochastic processes {X(t)} and {Xn } are both regenerative The regeneration epochs are the epochs at which an arriving customer nds the system empty It is stated without proof that the assumption of / < 1 implies that the processes have a nite mean cycle length Thus we can de ne the time-average and the customer-average probabilities pj and j by pj = the long-run fraction of time that j customers are present and j = the long-run fraction of customers who nd j other customers present upon arrival for j = 0, 1, Time averages are averages over time, and customer averages t are averages over customers To be precise, pj = limt (1/t) 0 Ij (u) du and j = limn (1/n) n Ik (j ), where Ij (t) = 1 if j customers are present at k=1 time t and Ij (t) = 0 otherwise, and In (j ) = 1 if j other customers are present just before the nth arrival epoch and In (j ) = 0 otherwise The probabilities pj and j are related to each other by j 1 = pj , j = 1, 2, (271). gocr online: Mar 23, 2019 · You have surely seen my other article about OCR, here. It uses Microsoft OneNote, which is an app that ... best arabic ocr online Free Online OCR - Convert JPEG, PNG, GIF, BMP, TIFF, PDF, DjVu ...
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