![]() ![]() These are called Jackson queueing networks in honor of the pioneer researcher who first studied their behavior. We focus on a class of Markovian mathematical models where knowing only the present or current state of the system, not the entire history of the system operations, its future statistical behavior is determined. This demands additional assumptions concerning the job arrival and execution time statistics, as well as the scheduling policy. The figure below plots the number in system process J(t) versus time t for one possible scenario.ĬHAPTER 6: JACKSON NETWORK ANALYSIS Our goal in this section is to extend the previous performance analysis (based only on mean execution times) to include both fluctuations about mean values as well as ordering constraints or correlations between different steps and different jobs. All jobs are ready for processing at time t =0. In order to motivate the result, we return to a static model of a computer system. 4.1 Little's Law In the technical literature, a key result is attributed to Little. Once we understand that case, we will generalize to systems where multiple types of jobs take multiple steps and demand multiple resources at each step. Our program here is to first analyze systems where there is only one type of job that takes only one step and one resource. ![]() In our experience with operational systems and field experience, this is possibly the single most important fundamental result in analyzing computer communication system performance. We now focus on mean value analysis, long term time averaged behavior of mean throughput rate and mean delay. ![]() Much of the complexity in analysis seemingly disappears when the long term time averaged behavior of these types of computer system models is analyzed. 1-CHAPTER 4: MEAN VALUE ANALYSIS Up to this point we have examined detailed operational descriptions of models of computer communication systems. ![]()
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