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  • 1
    Electronic Resource
    Electronic Resource
    Optimal control of single-server fluid networks (2000)
    Springer
    Queueing systems 35 (2000), S. 185-200 
    Details
    ISSN: 1572-9443
    Keywords: stochastic fluid model ; index policy ; Klimov index ; largest remaining index algorithm ; maximum principle ; sample path argument ; reentrant fluid lines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a stochastic single-server fluid network with both a discounted reward and a cost structure. It can be shown that the optimal policy is a priority index policy. The indices coincide with the optimal indices in a semi-Markovian Klimov problem. Several special cases like single-server reentrant fluid lines are considered. The approach we use is based on sample path arguments and Pontryagins maximum principle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019146111903
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Structured policies in the sequential design of experiments (1991)
    Springer
    Annals of operations research 32 (1991), S. 165-188 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A general control model under uncertainty is considered. Using a Bayesian approach and dynamic programming, we investigate structural properties of optimal decision rules. In particular, we show the monotonicity of the total expected reward and of the so-called Gittins-Index. We extend the stopping rule and the stay-on-a-winner rule, which are well-known in bandit problems. Our approach is based on the multivariate likelihood ratio order andTP 2 functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02204833
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    On Bayesian group sequential sampling procedures (1991)
    Springer
    Annals of operations research 32 (1991), S. 189-203 
    Details
    ISSN: 1572-9338
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A general group sequential statistical decision model is investigated. Using a Bayesian approach and Bayesian dynamic programming, we examine structural properties of the cost functions and of optimal sampling procedures. In particular, we consider variable-sample-size-sequential probability ratio tests and show that the so-called onion-skins conjecture is false.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02204834
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Measurable selection theorems for optimization problems (1978)
    Springer
    Manuscripta mathematica 24 (1978), S. 115-131 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we attempt a unification of several selection theorems in the literature by introducing the notion of a selection class and give sufficient conditions for the existence of measurable ε-maximizers. Various special cases are discussed. Finally, as an application of the selection theorem of Kuratowski and Ryll-Nardzewski [12] a Baire classification of ε-maximizers is determined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01168566
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Markov games with incomplete information (1997)
    Springer
    Mathematical methods of operations research 46 (1997), S. 263-279 
    Details
    ISSN: 1432-5217
    Keywords: Markov games with incomplete information ; Repeated games ; Optimal strategies ; Algorithms ; Linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider zero-sum Markov games with incomplete information. Here, the second player is never informed about the current state of the underlying Markov chain. The existence of a value and of optimal strategies for both players is shown. In particular, we present finite algorithms for computing optimal strategies for the informed and uninformed player. The algorithms are based on linear programming results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217695
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Optimal greedy policies for stochastic control models (1996)
    Springer
    Mathematical methods of operations research 44 (1996), S. 115-133 
    Details
    ISSN: 1432-5217
    Keywords: Stochastic control models ; greedy policies ; error bounds ; MDP with an absorbing set ; deterministic dynamic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We introduce the notion of a greedy policy for general stochastic control models. Sufficient conditions for the optimality of the greedy policy for finite and infinite horizon are given. Moreover, we derive error bounds if the greedy policy is not optimal. The main results are illustrated by Bayesian information models, discounted Bayesian search problems, stochastic scheduling problems, single-server queueing networks and deterministic dynamic programs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01246332
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  • 7
    Electronic Resource
    Electronic Resource
    Optimal scheduling in heterogeneous two-station queueing networks (1998)
    Springer
    Mathematical methods of operations research 48 (1998), S. 337-347 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Multiclass queueing networks ; dynamic scheduling ; stochastic control ; switching-curve policy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We consider a two-station network with two types of jobs: type 0 jobs require service at station 1 only and type 1 jobs require service both at station 1 and 2 in sequence. Each station has a single server. The problem is to schedule the server at station 1 between the two types of jobs in order to minimize the linear holding cost of the system. We will treat the discounted as well as the average cost criterion. In both cases we can prove that the optimal policy is a switching-curve policy. A numerical sensitivity analysis is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050031
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Monotonicity and bounds for convex stochastic control models (1994)
    Springer
    Mathematical methods of operations research 39 (1994), S. 187-207 
    Details
    ISSN: 1432-5217
    Keywords: Convex stochastic control models ; Monotonicity results ; Bounds ; Convex stochastic orderings and Blackwell ordering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider a general convex stochastic control model. Our main interest concerns monotonicity results and bounds for the value functions and for optimal policies. In particular, we show how the value functions depend on the transition kernels and we present conditions for a lower bound of an optimal policy. Our approach is based on convex stochastic orderings of probability measures. We derive several interesting sufficient conditions of these ordering concepts, where we make also use of the Blackwell ordering. The structural results are illustrated by partially observed control models and Bayesian information models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01415581
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Optimal control of single-server queueing networks (1993)
    Springer
    Mathematical methods of operations research 37 (1993), S. 187-205 
    Details
    ISSN: 1432-5217
    Keywords: single-server queueing networks ; open bandit processes ; discounted dynamic programming ; largest-index policies ; bounds ; largest-remaining-index method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract A general single-server queueing network model is considered. It is well-known that an optimal policy is determined by the largest-index policy. There is an index for each given queue and one allocates the server to a queue with largest current index. Using discounted dynamic programming we give a new and short proof of this result and derive some characterizations and bounds of the indices. Moreover, it is shown that an approximate largest-index policy yields an approximately optimal policy. These results lead to efficient methods for computing the indices. In particular, we present a general largest-remaining-index method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01414156
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    Paper (German National Licenses)
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