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Real-time systems are those systems in which the correctness of the system depends not only on the logical results of computation but also on time at which these results are produced. Real-time systems are gaining importance rapidly nowadays. It is widely used in many real-time applications such as power stations, nuclear reactors, space vehicles and airplanes. Real-time systems scheduling is a set of rules that determine which task should be executed at a particular time such that the time constraints of the tasks are satisfied. Scheduling multiprocessor real-time system is an active field of research .Its objective is to assign a set of n tasks to m processors while still meeting all deadlines. In almost cases, the optimal allocation of tasks to processors is NP-hard problem. This book Explain MMUF algorithm , apply it in multiprocessor systems and improve MMUF scheduling algorithm to use it for scheduling uniprocessor and multiprocessor real-time systems in order to get betterprocessors utilization, reduce the number of failed tasks and reduce the number of context switches.