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11 Oct 2014 ... Hello, I have been searching Google for some time but cannot find an answer to my question. I have unwanted layers of OCR in a docu... 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). captcha ocr online: Convertio OCR - Easy tool to convert scanned documents into editable Word, Pdf, Excel and Text output formats. No downl ... pdf ocr converter mac free Convert JPG to TXT ( OCR ) online - Convert PDF Online
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In this article, I will introduce you 3 top OCR programs for Mac and show you the benefits of each product. other customers present The process {X(t)} makes a downcrossing from state j to state j 1 if the service of a customer is completed and j 1 other customers are left behind Observation 1 Since customers arrive singly and are served singly, the long-run average number of upcrossings from j 1 to j per time unit equals the long-run average number of downcrossings from j to j 1 per time unit This follows by noting that in any nite time interval the number of upcrossings from j 1 to j and the number of downcrossings from j to j 1 can differ at most by 1 Observation 2 The long-run fraction of customers seeing j 1 other customers upon arrival is equal to the long-run average number of upcrossings from j 1 to j per time unit the long-run average number of arrivals per time unit for j = 1, 2, In other words, the long-run average number of upcrossings from j 1 to j per time unit equals j 1 The latter relation for xed j is in fact a special case of the Little relation (241) by assuming that each customer nding j 1 other customers present upon arrival pays $1 (using this reward structure observation 2 can also be obtained directly from the renewal-reward theorem) Observations 1 and 2 do not use the assumption of exponential services and apply in fact to any regenerative queueing process in which customers arrive singly and are served singly Observation 3 For exponential services, the long-run average number of downcrossings from j to j 1 per time unit equals pj with probability 1 for each j 1 The proof of this result relies heavily on the PASTA property To make this clear, x j and note that service completions occur according to a Poisson process with rate as long as the server is busy Equivalently, we can assume that an exogenous Poisson process generates events at a rate of , where a Poisson event results in a service completion only hen there are j customers present Thus, by part (a) of Theorem 241, E[Ij (t)] = E[Dj (t)] for t > 0 (272). When the object is at position 0, it is within the sensing radius of nodes 1, 3, and 4 and is detected by the sampling tasks at those three nodes Now, each node sends a TargetAlert to all nodes in its neighborhood Hence, node 1 will receive alerts from nodes 3 and 4 Depending on the precise moment when the alerts are generated and the delays in transmitting the alerts over the network, node 1 could receive the reading from node 3 before it receives the reading from node 4 The Leader task on node 1 will be invoked when its own sampling task detects the object, and when the alerts are received from nodes 3 and 4Hence, in its first invocation, the node s own reading is nonzero but it hasn t received any readings from neighbors. any splits), the initial download size, and more data on each split. 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