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Discrete-Time Markov Chains - Two-Time-Scale Methods and Applications (Paperback, Softcover reprint of hardcover 1st ed. 2005)
Loot Price: R2,870
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Discrete-Time Markov Chains - Two-Time-Scale Methods and Applications (Paperback, Softcover reprint of hardcover 1st ed. 2005)
Series: Stochastic Modelling and Applied Probability, 55
Expected to ship within 10 - 15 working days
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This book focuses on two-time-scale Markov chains in discrete time.
Our motivation stems from existing and emerging applications in
optimization and control of complex systems in manufacturing,
wireless communication, and ?nancial engineering. Much of our e?ort
in this book is devoted to designing system models arising from
various applications, analyzing them via analytic and probabilistic
techniques, and developing feasible compu- tionalschemes.
Ourmainconcernistoreducetheinherentsystemcompl- ity. Although each
of the applications has its own distinct characteristics, all of
them are closely related through the modeling of uncertainty due to
jump or switching random processes.
Oneofthesalientfeaturesofthisbookistheuseofmulti-timescalesin
Markovprocessesandtheirapplications. Intuitively,notallpartsorcom-
nents of a large-scale system evolve at the same rate. Some of them
change rapidly and others vary slowly. The di?erent rates of
variations allow us to reduce complexity via decomposition and
aggregation. It would be ideal if we could divide a large system
into its smallest irreducible subsystems completely separable from
one another and treat each subsystem indep- dently. However, this
is often infeasible in reality due to various physical constraints
and other considerations. Thus, we have to deal with situations in
which the systems are only nearly decomposable in the sense that
there are weak links among the irreducible subsystems, which
dictate the oc- sional regime changes of the system. An e?ective
way to treat such near decomposability is time-scale separation.
That is, we set up the systems as if there were two time scales,
fast vs. slow. xii Preface
Followingthetime-scaleseparation,weusesingularperturbationmeth-
ology to treat the underlying systems.
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