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(8.1) we have     m 1 P 1 1 m m i r i \$ 2c1 s2 m2 b m2 Var Y0 s2 m 2 1 b 2 b i 1 c2 m2 b ; as m 3 I; 8:27 Printing Code 39 In VS .NETUsing Barcode maker for .NET Control to generate, create Code 39 image in VS .NET applications.I P i 0 Decoding Code 39 In Visual Studio .NETUsing Barcode reader for Visual Studio .NET Control to read, scan read, scan image in .NET applications.E c0;1 i c0;1 i k I ft0;1 > i kg \$ const k b Encode Bar Code In .NETUsing Barcode creator for VS .NET Control to generate, create bar code image in Visual Studio .NET applications. 8:26 Barcode Scanner In .NETUsing Barcode decoder for .NET Control to read, scan read, scan image in .NET applications.where c1 and c2 are some positive constants and 0 < b < 1. Substituting Eq. (8.27) into (8.3) we get r m k \$ 1 c m k 1 2 b 2c2 mk 2 b c2 m k 1 2 b 2c2 m2 b 2 as m 3 I:Code-39 Maker In Visual C#.NETUsing Barcode maker for .NET framework Control to generate, create Code-39 image in .NET framework applications. 1 k 1 2 b 2k 2 b k 1 2 b ; 2Encoding Code 39 Full ASCII In .NETUsing Barcode maker for ASP.NET Control to generate, create USS Code 39 image in ASP.NET applications.It means, according to the de nition (8.10), that process Y is asymptotically secondorder self-similar with parameter 0 < b < 1. j Corollary 8.3.5. If a random process ck;j i is a constant one, ck;j i  ck;j for all i 0; 1; 2; . . . , then a process Y . . . ; Y 1 ; Y0 ; Y1 ; . . . de ned by Eq. (8.11), with nite mean m EYt < I and variance s2 Var Yt < I, will be asymptotically second-order self-similar with parameter 0 < b < 1, if Prft0;1 > kgE c2 jt0;1 > k \$ const k 1 b ; 0;1 or Prft0;1 kgE c2 jt0;1 k \$ const k 2 b ; 0;1 as k 3 I: 8:29 as k 3 I; 8:28 ANSI/AIM Code 39 Generation In Visual Basic .NETUsing Barcode drawer for .NET Control to generate, create Code 39 Extended image in .NET applications.BOUNDS ON THE BUFFER OCCUPANCY PROBABILITY Generate Data Matrix In .NETUsing Barcode printer for .NET Control to generate, create DataMatrix image in VS .NET applications.Proof. Since c0;1 i does not depend on i, from Eq. (8.19) we have r k UPC Code Encoder In .NETUsing Barcode creation for VS .NET Control to generate, create UPC-A Supplement 2 image in VS .NET applications.I l P Prft0;1 > kgE c2 jt0;1 > k : 0;1 s2 i 0 Encoding Code 128 Code Set B In .NET FrameworkUsing Barcode printer for VS .NET Control to generate, create USS Code 128 image in VS .NET applications.Substituting Eq. (8.28) in the above equation, we obtain r k \$ const Drawing Identcode In Visual Studio .NETUsing Barcode drawer for Visual Studio .NET Control to generate, create Identcode image in Visual Studio .NET applications.I P i 0 UCC - 12 Generation In Visual Studio .NETUsing Barcode maker for ASP.NET Control to generate, create UCC-128 image in ASP.NET applications. i k 1 b \$ const k b ;ECC200 Encoder In JavaUsing Barcode generation for Java Control to generate, create ECC200 image in Java applications.as k 3 I:Code 128 Code Set C Creation In Visual Studio .NETUsing Barcode generation for ASP.NET Control to generate, create Code 128 image in ASP.NET applications.Then from Theorem 8.3.4 it immediately follows that Y is an asymptotically secondorder self-similar process. Statement (8.29) can be proved in the same way. jUPC Symbol Printer In VB.NETUsing Barcode printer for .NET Control to generate, create UPC Symbol image in .NET applications.8.4 ASYMPTOTICAL BOUNDS FOR BUFFER OVERFLOW PROBABILITY In this section we consider the process Y de ned by Eq. (8.11) as the input traf c of a single server queueing system with constant server rate equal to C and in nite buffer size. Suppose process Y has nite mean m EYt < C < I and nite variance s2 Var Yt < I. We will consider the particular form of the process Y . Namely, we consider the case when the random process ci;j t  1. Let Prft0;1 ig \$ c0 i 2 b 8:30 Make EAN 13 In Visual Basic .NETUsing Barcode maker for .NET Control to generate, create UPC - 13 image in VS .NET applications.as i 3 I, with 0 < b < 1. Then, according to Eq. (8.29) with c0;1  1, process Y will be asymptotically second-order self-similar with Hurst parameter H 1 b=2. Now we are interested in the queue length behavior. 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