Computing Cumulative Measures of Stiff Markov Chains Using Aggregation

We present an aggregation method for the computation of transient cumulative measures of large, stiff Markov models. The method is based on the classification of the states of the original problem into slow, fast transient, and fast recurrent states. We 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 queueing and reliability models, and to show that cumulative measures provide a better characterization of the time dependent system behavior.