Computing cumulative measures of stiff Markov chains using aggregation

Author

Bobbio, Andrea ; Trivedi, Kishor

Author_Institution

Dept. of Comput. Sci., Duke Univ., Durham, NC, USA

Volume

39

Issue

10

fYear

1990

fDate

10/1/1990 12:00:00 AM

Firstpage

1291

Lastpage

1298

Abstract

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

Keywords

Markov processes; fault tolerant computing; linear differential equations; queueing theory; reliability theory; aggregation; approximate value; cumulative measure; fast-current states; fast-transient states; linear differential equations; nonstiff set; queueing models; reliability models; slow states; stiff Markov chains; stiff Markov models; stiffness; time-dependent system behavior; transient cumulative measures; Algorithm design and analysis; Circuit testing; Computer network reliability; Computer science; Cyclic redundancy check; Digital systems; Fault detection; Fault tolerance; Notice of Violation; Time measurement;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.59859

Filename

59859