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The API of ABBYY Cloud OCR SDK uses HTTP POST and HTTP GET methods for sending data to an HTTP server. The parameters of requests are specified in ... long-run average cost per time unit Using the embedding idea from Section 74, develop a value-iteration algorithm for the control problem Solve for the numerical data = 3, 1 = 28, 2 = 22, h = 2, r = 4 and K = 10 Try other numerical examples and verify experimentally that the optimal control rule is a so-called hysteretic (m, M) rule under which the slower server is turned on when the number of customers present is M or more and the slower server is switched off when this server completes a service and the number of customers left behind in the system is below m This problem is based on Nobel and Tijms (2000), who developed a tailor-made policy-iteration algorithm for this problem 711 Consider again the heterogeneous server problem from Exercise 710 Assume now that there are two slower servers in addition to the faster server, where the two slower servers may have different speeds The faster server is always available for service, while the slower servers are activated for service when too many customers are present The service time of a customer is exponentially distributed with mean 1/ i when service is provided by server i Server 1 is the faster server and servers 2 and 3 are the slower servers It is assumed that /( 1 + 2 + 3 ) < 1 and 1 > max( 2 , 3 ) There is an operating cost of ri > 0 per time unit when the slower server i is on for i = 2, 3 A holding cost of h > 0 per time unit is incurred for each customer in the system There is no switching cost for turning either of the slower servers on Develop a value-iteration algorithm for this problem Assuming that the slower servers are numbered such that r2 / 2 < r3 / 3 , verify experimentally that the optimal control rule is characterized by critical numbers 1 m1 < m2 and prescribes using the slower server 2 when the number of customers present is more than m1 , and using both slow servers when the number of customers present is more than m2 712 Messages arrive at a transmission channel according to a Poisson process with a controllable arrival rate The two possible arrival rates are 1 and 2 with 0 2 < 1 The buffer at the transmission channel has ample space for temporarily storing arriving messages The channel can only transmit one message at a time The transmission time of each message is exponentially distributed with mean 1/ It is assumed that 2 / < 1 At any point in time it can be decided to change the arrival intensity from one rate to the other There is a xed cost of K 0 for changing the arrival rate An operating cost of ri > 0 per time unit is incurred when the prevailing arrival rate is i , i = 1, 2 Also, there is a holding cost of h > 0 per time unit for each message awaiting service The goal is to nd a control rule that minimizes the long-run average cost per time unit Using the embedding idea from Example 741, develop a value-iteration algorithm for this control problem Solve for the numerical data 1 = 4, 2 = 2, = 5, K = 5, r1 = 1, r2 = 10 and h = 2 Try other numerical examples and investigate whether the optimal control rule has a speci c structure 713 Customers of types 1 and 2 arrive at a shared resource according to independent Poisson processes with respective rates 1 and 2 The resource has c service units An arriving customer of type i requires bi service units The customer is rejected when less than bi units are available upon arrival An accepted customer of type i immediately nters service and has an exponentially distributed residency time with mean 1/ i During this residency time the customer keeps all of the bi assigned service units occupied These units are released simultaneously when the customer departs Develop a value-iteration algorithm for the computation of a control rule that minimizes the total average rejection rate Solve for the numerical data c = 30, b1 = 2, b2 = 5, 1 = 6, 2 = 8, 1 = 1 and 2 = 05 Try other numerical examples and verify experimentally that the optimal control rule can (r) (r) be characterized by two monotone sequences {a1 } and {a2 } Under this control rule an arriving customer of type i nding r customers of the other type present upon arrival is (r) accepted only when less than ai customers of the same type i are present and at least bi service units are free. ocr library: OCR Sdk Free - CVISION Technologies abbyy ocr sdk documentation OCR Sdk Free - CVISION Technologies
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