The Computation of Average Optimal Policies in Denumerable State Markov Decision Chains

1997 ◽  
Vol 29 (01) ◽  
pp. 114-137
Author(s):  
Linn I. Sennott
Keyword(s):  
Discrete Time ◽  
Average Cost ◽  
Queueing Systems ◽  
State Spaces ◽  
Original Process ◽  
Optimal Policies ◽  
Finite State ◽  
Markov Decision ◽  
Optimal Average ◽  
Infinite State

This paper studies the expected average cost control problem for discrete-time Markov decision processes with denumerably infinite state spaces. A sequence of finite state space truncations is defined such that the average costs and average optimal policies in the sequence converge to the optimal average cost and an optimal policy in the original process. The theory is illustrated with several examples from the control of discrete-time queueing systems. Numerical results are discussed.

The Computation of Average Optimal Policies in Denumerable State Markov Decision Chains

1997 ◽  
Vol 29 (1) ◽  
pp. 114-137 ◽  
Author(s):  
Linn I. Sennott
Keyword(s):  
Discrete Time ◽  
Average Cost ◽  
Queueing Systems ◽  
State Spaces ◽  
Original Process ◽  
Optimal Policies ◽  
Finite State ◽  
Markov Decision ◽  
Optimal Average ◽  
Infinite State

This paper studies the expected average cost control problem for discrete-time Markov decision processes with denumerably infinite state spaces. A sequence of finite state space truncations is defined such that the average costs and average optimal policies in the sequence converge to the optimal average cost and an optimal policy in the original process. The theory is illustrated with several examples from the control of discrete-time queueing systems. Numerical results are discussed.

scholarly journals Local model checking for infinite state spaces

1992 ◽  
Vol 96 (1) ◽  
pp. 157-174 ◽  
Author(s):  
Julian Bradfield ◽  
Colin Stirling
Keyword(s):  
Model Checking ◽  
Local Model ◽  
State Spaces ◽  
Infinite State ◽  
Local Model Checking

Examples for the Theory of Strong Stationary Duality with Countable State Spaces

1990 ◽  
Vol 4 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Persi Diaconis ◽  
James Allen Fill
Keyword(s):  
Stopping Time ◽  
Renewal Theory ◽  
Hitting Times ◽  
State Spaces ◽  
Ergodic Markov Chain ◽  
Countable State Space ◽  
Strong Stationary Duality ◽  
Countable State ◽  
Infinite State ◽  
First Hitting Times

Let X1,X2,… be an ergodic Markov chain on the countable state space. We construct a strong stationary dual chain X* whose first hitting times give sharp bounds on the convergence to stationarity for X. Examples include birth and death chains, queueing models, and the excess life process of renewal theory. This paper gives the first extension of the stopping time arguments of Aldous and Diaconis [1,2] to infinite state spaces.

scholarly journals Well (and Better) Quasi-Ordered Transition Systems

2010 ◽  
Vol 16 (4) ◽  
pp. 457-515 ◽  
Author(s):  
Parosh Aziz Abdulla
Keyword(s):  
Petri Nets ◽  
Timed Automata ◽  
Timed Petri Nets ◽  
Transition Systems ◽  
State Spaces ◽  
Rewriting Systems ◽  
Symbolic Representations ◽  
Infinite State ◽  
Lossy Channel ◽  
Quasi Ordering

AbstractIn this paper, we give a step by step introduction to the theory ofwell quasi-orderedtransition systems. The framework combines two concepts, namely (i) transition systems which aremonotonicwrt. awell-quasi ordering; and (ii) a scheme for symbolicbackwardreachability analysis. We describe several models with infinite-state spaces, which can be analyzed within the framework, e.g., Petri nets, lossy channel systems, timed automata, timed Petri nets, and multiset rewriting systems. We will also presentbetter quasi-orderedtransition systems which allow the design of efficient symbolic representations of infinite sets of states.

INDEXABILITY OF BANDIT PROBLEMS WITH RESPONSE DELAYS

2010 ◽  
Vol 24 (3) ◽  
pp. 349-374 ◽  
Author(s):  
Felipe Caro ◽  
Onesun Steve Yoo
Keyword(s):  
Discrete Time ◽  
Bayesian Learning ◽  
The Other ◽  
Independent Random Variables ◽  
Important Class ◽  
Marginal Productivity ◽  
Bandit Problems ◽  
Theoretical Justification ◽  
State Spaces ◽  
Infinite State

This article considers an important class of discrete time restless bandits, given by the discounted multiarmed bandit problems with response delays. The delays in each period are independent random variables, in which the delayed responses do not cross over. For a bandit arm in this class, we use a coupling argument to show that in each state there is a unique subsidy that equates the pulling and nonpulling actions (i.e., the bandit satisfies the indexibility criterion introduced by Whittle (1988). The result allows for infinite or finite horizon and holds for arbitrary delay lengths and infinite state spaces. We compute the resulting marginal productivity indexes (MPI) for the Beta-Bernoulli Bayesian learning model, formulate and compute a tractable upper bound, and compare the suboptimality gap of the MPI policy to those of other heuristics derived from different closed-form indexes. The MPI policy performs near optimally and provides a theoretical justification for the use of the other heuristics.

scholarly journals Computing Stationary Expectations in Level-Dependent QBD Processes

2013 ◽  
Vol 50 (1) ◽  
pp. 151-165 ◽  
Author(s):  
Hendrik Baumann ◽  
Werner Sandmann
Keyword(s):  
Performance Measures ◽  
Network Performance ◽  
Queueing Network ◽  
Birth And Death Processes ◽  
State Spaces ◽  
Additive Functionals ◽  
Long Run ◽  
Qbd Processes ◽  
Special Cases ◽  
Infinite State

Stationary expectations corresponding to long-run averages of additive functionals on level-dependent quasi-birth-and-death processes are considered. Special cases include long-run average costs or rewards, moments and cumulants of steady-state queueing network performance measures, and many others. We provide a matrix-analytic scheme for numerically computing such stationary expectations without explicitly computing the stationary distribution of the process, which yields an algorithm that is as quick as its counterparts for stationary distributions but requires far less computer storage. Specific problems arising in the case of infinite state spaces are discussed and the application of the algorithm is demonstrated by a queueing network example.

Sign in / Sign up

Export Citation Format

Share Document