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Queuing Theory with Applications to Computer Science

Finally, we comment on the amazing fact that the proof of Little’s law turns out to be independent of • specific assumptions regarding the arrival distribution A(t) • specific assumptions regarding the service time distribution B(t) • number of servers • particular queueing discipline Little’s law is important for three reasons: • because it is so widely applicable (it requires only very weak assumptions), it will be valuable to us in checking the consistency of measurement data • for example, in studying computer systems we frequently will find that we know two of the quantities related by Little’s law (say, the average number of requests in a system and the throughput of that system) and desire to know the third (the average system residence time, in this case) • it is central to the algorithms for evaluating several queueing network models Given a computer system, Little’s law can be applied at many different levels: to a single resource, to a subsystem, or to the system as a whole. The key to success is consistency: the definitions of population, throughput, and residence time must be compatible with one another. Over the past few years, it has become increasingly important in many fields of applications.