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the piece by a new one and letting the piece operate for the present day A preventive replacement takes one day A new piece has working condition i = 1 A piece whose present working condition is i has the next day working condition j with known probability qij where qij = 0 for j < i The following replacement rule is used The current piece is only replaced by a new one when ts working condition is greater than the critical value m, where m is a given integer with 1 m < N (a) De ne an appropriate Markov chain and specify its one-step transition probabilities (b) Explain how to calculate the long-run fraction of days the equipment is inoperative and the fraction of replacements occurring in the failure state N 315 Consider a stochastically failing piece of equipment with two identical components that operate independently of each other The lifetime in days of each component has a discrete probability distribution {pj , j = 1, , M} A component in the failure state at the beginning of a day is replaced instantaneously It may be economical to preventively replace the other working component at the same time the failed component has to be replaced The cost of replacing only one component is K1 , while the cost of replacing simultaneously both components equals K2 with 0 < K2 < 2K1 The control rule is as follows Replace a component upon failure or upon reaching the age of R days, whichever occurs rst If a component is replaced and the other component is still working, the other component is preventively replaced when it has been in use for r or more days The parameters r and R are given integers with 1 r < R (a) De ne an appropriate Markov chain and specify its one-step transition probabilities (b) How can you calculate the long-run average cost per day 316 A transmission channel transmits messages one at a time, and transmission of a message can only start at the beginning of a time slot The time slots have unit length and the transmission time of a message is one time slot However, each transmission can fail with some probability f A failed transmission is tried again at the beginning of the next time slot The numbers of new messages arriving during the time slots are independent random variables with a common discrete distribution {ak , k = 0, 1, } Newly arriving messages are temporarily stored in a buffer of ample capacity It is assumed that the average arrival rate of new messages is smaller than the average number of attempts needed to transmit a message successfully, that is, k kak < 1/f The goal is to nd the long-run average throughput per time unit (a) De ne an appropriate Markov chain with a one-dimensional state space and specify its one-step transition probabilities (b) Can you give a recursive algorithm for the computation of the state probabilities Express the average throughput in terms of the state probabilities 317 Messages arrive at a transmission channel according to a Poisson process with rate The channel can transmit only one message at a time and a new transmission can only start at the beginnings of the time slots t = 1, 2, The transmission time of a message is one time slot The following access-control rule is used The gate is closed for newly arriving messages when the number of messages awaiting transmission has reached the level R and is opened again when the number of messages awaiting transmission has dropped to the level r, where the parameters r and R are given integers with 0 r < R The goal is to study the long-run fraction of lost messages as function of r and R (a) De ne an appropriate Markov chain and specify its one-step transition probabilities (b) Show how to calculate the long-run fraction of lost messages 318 In Example 351 we have determined for the GI /M/1 queue the customer-average probability j denoting the long-run fraction of customers who nd j other customers present upon arrival Denote by the time-average probability pj the long-run fraction of time that j customers are present for j = 0, 1, Use Theorem 333 and Lemma 114.



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The State pattern allows you to have an object represent the state of your application and to switch application states by switching objects For example, you can have an enclosing class switch between a number of related contained classes and pass method calls on to the current contained class Design Patterns suggests that the State pattern switches between internal classes in such a way that the enclosing object appears to change its class In Java, at least, this is a bit of an exaggeration, but the actual purpose to which the classes are put can change significantly

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Click "OK" on the Add Reference dialog . this value can be decreased to obtain a higher density barcode. . Encode an ASCII character: The format ~ddd may be used to .Related: ASP.NET Code 128 Generation , Creating ISBN .NET WinForms , Make UPC-E Excel

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else if (miText == "Center") { valign = StringAlignmentCenter; m_cxAdjust = (int)(sizeWidth / 2); } else if (miText == "Far") { valign = StringAlignmentFar; m_cxAdjust = (int)sizeWidth; } // Force a redraw Invalidate(); } private void formMain_Paint(object sender, PaintEventArgs e) { Graphics g = eGraphics; // Calculate reference point for text drawing float xDraw = (float)(ClientRectangleRight / 2); float yDraw = (float)(ClientRectangleBottom / 2); // Create drawing objects Brush brBlack = new SolidBrush(ColorBlack); Pen penBlack = new Pen(ColorBlack); // Create StringFormat for text drawing details var sf = new StringFormat(); sfFormatFlags = StringFormatFlagsNoClip; sfAlignment = valign; sfLineAlignment = halign; // Calculate size of string bounding box SizeF size = gMeasureString(thisText, Font); int cxWidth = (int)sizeWidth; int cyHeight = (int)sizeHeight; // Adjust values to accommodate alignment request float sinTextX = (float)(xDraw - m_cxAdjust); float sinTextY = (float)(yDraw - m_cyAdjust); // Draw text bounding box Brush hbrFill = new SolidBrush(ColorGray); Rectangle rc = new Rectangle((int inTextX, (int)sinTextY, cxWidth, cyHeight); gFillRectangle(hbrFill, rc);. Code 39 Extended Printer In VS .NET Using Barcode maker for ASP .Related: .NET WinForms PDF417 Generation , VB.NET Code 39 Generating , Excel UPC-A Generator

Encode Data using the Online Encoder; Using the Barcode Recognition . up an environment for using the .NET Barcode Font Encoder . Create a reference to the assembly .Related: Print ITF-14 Word , Creating ISBN .NET , Word Code 128 Generation

Configuration. Code128 Printer In VS .NET Using Barcode generator for ASP . ControlsAdd(_result); Validation ControlsAdd(new LiteralControl("<br/>")) Button .Related: Generate ISBN Excel , Generate ISBN ASP.NET , EAN-8 Generating Java

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Class Add Inherits Calculation Protected Overrides Function Calculate() As Double eturn Number1 + Number2 End Function End Class Class Subtract Inherits Calculation Protected Overrides Function Calculate() As Double Return Number1 Number2 End Function End Class Class Multiply Inherits Calculation Protected Overrides Function Calculate() As Double Return Number1 * Number2 End Function End Class Listing 712: Three classes that inherit from the abstract Calculation class. In Visual Studio .NET Using Barcode printer for .NET . The three new classes shown in Listing 712 ene t from inheriting from their abstract base class since they do not have to individually supply member variables for storing the two numbers to be calculated on or a method for displaying the result of a calculation; these are available through the inheritance They also have the bene t of all being types of Calculation class, and so could be used interchangeably We could now actually use a reference variable of the Calculation class (see Listing 713).Related: Java PDF417 Generation , EAN-8 Generating Word , QR Code Generating C#

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Case 2 C = New Subtract() Case 3 C = New Multiply() Case 4 C = New Divide() End elect CNumber1 = 10 CNumber2 = 5 CDisplayResult() End Sub Listing 728: Being unaware of the class in use Bar Code Encoder In NET Framework Using Barcode printer for ASP .

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In Listing 728, the statement i = CInt(Int((4 * Rnd()) + 1)) generates a random integer number in the range 1 to 4 (look up Microsoft s example in the Help page for the Rnd() function) Since we are using a random number to determine what class of calculate object is nstantiated, we have no way of knowing what type of object will do the calculation However, since all of the Calculation classes conform to the same interface, Visual Basic allows us to do this The scenario given above is not a very realistic situation, and apart from games programming, you would be unlikely to encounter the need for such code However, as programmers, we often need to work with objects where their type is uncertain We may need to process a Deposit into a BankAccount, without knowing the precise type of account (Deposit, Investment, SpecialInvestment, etc), or we might wish to change the font of every control on a Windows form, no matter what type of control it is Polymorphism is the object-oriented way of allowing us to deal with these situations and many others The only requirement of any object for it to receive a message is that it conforms to a given set of interface methods As we ve seen in this chapter, we have two ways of making that happen: we can either use code inheritance to provide a new class with an interface that has already been fully coded, or we can use interface inheritance, and implement a required interface In either case, the result is to allow us to create classes that are type-compatible This in turn allows us to substitute one class for another in a section of code without having to change the code at all If you think back to the strongly typed collection class example used earlier, this is an example in which we deliberately limited the range of classes whose objects could be added to an instance of the collection All of the built-in collections in NET are widely polymorphic, since they allow us to add objects of any class to them That can have its advantages, if we need to be able to deal with objects of any type, but that would be an unusual requirement Instead, we typically wish to create and use a small range of types of object (such as different styles of bank account, or different types of calculation) and use them as exibly as possible By creating a strongly typed collection, we are enabling polymorphism by stipulating that any objects added to it must conform to a minimum interface (every type of BankAccount provides Deposit() and Withdraw() methods, and Name and Balance properties) That allows us to do things like iterating through an entire collection of items of different (but related) classes (Listing 729).

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