EXERCISES in .NET Making QR Code 2d barcode in .NET EXERCISES EXERCISESQR Scanner In VS .NETUsing Barcode Control SDK for VS .NET Control to generate, create, read, scan barcode image in VS .NET applications.probability that a repair involves the high repair cost Rc Give the long-run average cost per time unit (c) Verify that the average cost is minimal for the unique solution z to the equation z exp[ (L z)] = Rp /(Rc Rp ) when L > Rp /(Rc Rp ) 223 A group of N identical machines is maintained by a single repairman The machines operate independently of each other and each machine has a constant failure rate Repair is done only if the number of failed machines has reached a given critical level R with 1 R N Then all failed machines are repaired simultaneously Any repair takes a negligible time and a repaired machine is again as good as new The cost of the simultaneous repair of R machines is K + cR, where K, c > 0 Also there is an idle-time cost of > 0 per time unit for each failed machine (a) De ne a regenerative process and identify its regeneration epochs (b) Determine the long-run average cost per time unit 224 The following control rule is used for a slow-moving expensive product No more than one unit of the product is kept in stock Each time the stock drops to zero a replenishment order for one unit is placed The replenishment lead time is a positive constant L Customers asking for the product arrive according to a renewal process in which the interarrival times are Erlang (r, ) distributed Each customer asks for one unit of the product Each demand occurring while the system is out of stock is lost (a) De ne a regenerative process and identify its regeneration epochs (b) Determine the long-run fraction of demand that is lost (c) Determine the long-run fraction of time the system is out of stock (Hint: use part (b) of Exercise 25) 225 Jobs arrive at a station according to a renewal process The station can handle only one job at a time, but has no buffer to store other jobs An arriving job that nds the station busy is lost The handling time of a job has a given probability density h(x) Use renewal-reward theory to verify for this loss system that the long-run fraction of jobs that are rejected is given by 0 M(x)h(x) dx divided by 1 + 0 M(x)h(x) dx, where M(x) is the renewal function in the renewal process describing the arrival of jobs What is the long-run fraction of time that the station is busy Simplify the formulas for the cases of deterministic and Poisson arrivals 226 Use the renewal-reward theorem to prove relation (233) when customers arrive according to a renewal process and the stochastic processes {L(t)} and {Un } regenerate themselves each time an arriving customer nds the system empty, where the cycle lengths have nite expectations For ease assume the case of an in nite-capacity queue Use the following relations: (i) the long-run average reward earned per time unit = (the expected reward earned in one cycle)/(expected length of one cycle), (ii) the long-run average amount paid per customer = (the expected amount earned in one cycle)/(expected number of arrivals in one cycle), (iii) the long-run average arrival rate = (expected number of arrivals in one cycle)/(expected length of one cycle) 227 Let {X(t), t 0} be a continuous-time regenerative stochastic process whose state space is a subset of the non-negative reals The cycle length is assumed to have a nite expectation Denote by P (y) the long-run fraction of time that the process {X(t)} takes on a value larger than y Use the renewal-reward theorem to prove thatQR-Code Encoder In VS .NETUsing Barcode creation for VS .NET Control to generate, create QR Code image in .NET framework applications.Reading QR In VS .NETUsing Barcode scanner for VS .NET Control to read, scan read, scan image in VS .NET applications.Barcode Reader In .NET FrameworkUsing Barcode decoder for VS .NET Control to read, scan read, scan image in .NET framework applications.Denso QR Bar Code Creator In .NET FrameworkUsing Barcode drawer for ASP.NET Control to generate, create QR image in ASP.NET applications.EAN 13 Maker In Visual Studio .NETUsing Barcode generator for Visual Studio .NET Control to generate, create EAN13 image in .NET applications.Bar Code Maker In VS .NETUsing Barcode maker for .NET framework Control to generate, create barcode image in .NET framework applications.Code 128A Creation In Visual C#Using Barcode generation for .NET Control to generate, create Code 128C image in Visual Studio .NET applications.Barcode Creator In JavaUsing Barcode maker for Java Control to generate, create bar code image in Java applications.Code 39 Generator In VS .NETUsing Barcode encoder for ASP.NET Control to generate, create Code 39 Extended image in ASP.NET applications.Painting Barcode In VB.NETUsing Barcode generation for .NET framework Control to generate, create bar code image in .NET framework applications.