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<p>An aggregation method for computing transient cumulative measures of large, stiff Markov models is presented. The method is based on classifying the states of the original problem into slow, fast-transient, and fast-current states. The authors aggregate fast-transient states and fast-recurrent states so that an approximate value to the desired cumulative measure can be obtained by solving a nonstiff set of linear differential equations defined over a reduced subset of slow states only. Several examples are included to illustrate how stiffness arises naturally in actual queuing and reliability models, and to show that cumulative measures provide a better characterization of the time-dependent system behavior.</p>
queueing models; stiff Markov chains; aggregation; transient cumulative measures; stiff Markov models; fast-current states; fast-transient states; approximate value; cumulative measure; nonstiff set; linear differential equations; slow states; stiffness; reliability models; time-dependent system behavior; fault tolerant computing; linear differential equations; Markov processes; queueing theory; reliability theory.
A. Bobbio, K. Trivedi, "Computing Cumulative Measures of Stiff Markov Chains Using Aggregation", IEEE Transactions on Computers, vol. 39, no. , pp. 1291-1298, October 1990, doi:10.1109/12.59859
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