NDLI: On the uniqueness of solutions to the Poisson equations for average cost Markov chains with unbounded cost functions

Content Provider	Springer Nature Link
Author	Bhulai, Sandjai Spieksma, Flora M.
Copyright Year	2003
Abstract	We consider the Poisson equations for denumerable Markov chains with unbounded cost functions. Solutions to the Poisson equations exist in the Banach space of bounded real-valued functions with respect to a weighted supremum norm such that the Markov chain is geometrically ergodic. Under minor additional assumptions the solution is also unique. We give a novel probabilistic proof of this fact using relations between ergodicity and recurrence. The expressions involved in the Poisson equations have many solutions in general. However, the solution that has a finite norm with respect to the weighted supremum norm is the unique solution to the Poisson equations. We illustrate how to determine this solution by considering three queueing examples: a multi-server queue, two independent single server queues, and a priority queue with dependence between the queues.
Starting Page	221
Ending Page	236
Page Count	16
File Format	PDF
ISSN	14322994
Journal	Mathematical Methods of Operations Research
Volume Number	58
Issue Number	2
e-ISSN	14325217
Language	English
Publisher	Springer-Verlag
Publisher Date	2003-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometric ergodicity Poisson equations Lyapunov functions Multi-server queue Priority queue
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research Mathematics Software

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On the uniqueness of solutions to the Poisson equations for average cost Markov chains with unbounded cost functions