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otherwise, it is distributed as the time needed to reduce the number of service requests present from M + 1 to M The semi-Markov decision formulation with an embedded state space makes sense only when it is feasible to calculate the one-step expected transition times (M,t) (s) and the one-step expected costs c(M,t) (s) The calculation of these quantities is easy, since service completions occur according to a Poisson process with rate s as long as all of the s channels are occupied In other words, whenever M or more requests are in the system, we can equivalently imagine that a single superchannel is servicing requests one at a time at an exponential rate of s This analogy enables us to invoke the formulas (262) and (263) Taking n = 1 and replacing the mean by 1/(s ) in these formulas, we nd that the expected time needed to reduce the number of requests present from M + 1 to M, given that all channels are on, is 1 1/(s ) = 1 /(s ) s and the expected holding and operating costs incurred during the time needed to reduce the number of requests present from M + 1 to M, given that all channels are on, is hs 1 rs h(M +1) + rs h hM + + + = + s s s s (s ) s s (s )2 Here the term hM/(s ) represents the expected holding costs for the M service requests which are continuously present during the time needed to reduceRead QR Code In .NETUsing Barcode reader for .NET framework Control to read, scan read, scan image in Visual Studio .NET applications.OPTIMIZATION OF QUEUES Print Bar Code In .NETUsing Barcode generation for Visual Studio .NET Control to generate, create barcode image in .NET framework applications.the number in system from M + 1 to M If all of the s channels are busy, then the time until the next event (service completion or new arrival) is exponentially distributed with mean 1/( + s ) and the next event is generated by an arrival with probability /( + s ) Putting the pieces together, we nd (M,t) (s) = and c(M,t) (s) = K(t, s) + hM + rs + + s + s s + s h(M + 1) + rs h + s (s )2 + s 1 + + s + s 1 s = s ( + s )(s )Recognize Bar Code In VS .NETUsing Barcode scanner for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications.Also, by the last argument above, p(M,t)(M 1,s) (s) = and p(M,t)(M,s) (s) =QR Code 2d Barcode Generator In Visual C#.NETUsing Barcode encoder for Visual Studio .NET Control to generate, create Quick Response Code image in Visual Studio .NET applications.For the other states of the embedded state space I , the basic elements of the semi-Markov decision model are easily speci ed We have (i,t) (a) = and c(i,t) (a) = K(t, a) + hi + ra , + min(i, a) 0 i M 1, 0 a s 1 , + min(i, a) 0 i M 1, 0 a s,QR Code 2d Barcode Creation In Visual Studio .NETUsing Barcode creation for ASP.NET Control to generate, create QR image in ASP.NET applications.The one-step transition probabilities are left to the reader Next we formulate the value-iteration algorithm In the data transformation we take = 1/( + s ) Then the recurrence relation (723) becomes Vn ((i, t)) = min +Make QR Code 2d Barcode In Visual Basic .NETUsing Barcode encoder for VS .NET Control to generate, create QR Code image in Visual Studio .NET applications.Create USS Code 128 In .NETUsing Barcode encoder for .NET Control to generate, create Code 128B image in .NET framework applications.ECC200 Drawer In .NET FrameworkUsing Barcode encoder for VS .NET Control to generate, create DataMatrix image in .NET applications.Making UPC A In VS .NETUsing Barcode maker for ASP.NET Control to generate, create UPCA image in ASP.NET applications.Draw Bar Code In JavaUsing Barcode generator for Java Control to generate, create bar code image in Java applications.Bar Code Generator In JavaUsing Barcode creation for Java Control to generate, create barcode image in Java applications.Print Code 39 In VB.NETUsing Barcode creation for VS .NET Control to generate, create Code-39 image in Visual Studio .NET applications.