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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - General notions of indexability for queueing control and asset management
AU - Glazebrook, K D
AU - Hodge, D J
AU - Kirkbride, C
PY - 2011
Y1 - 2011
N2 - We develop appropriately generalized notions of indexability for problems of dynamic resource allocation where the resource concerned may be assigned more flexibility than is allowed, for example, in classical multi-armed bandits. Most especially we have in mind the allocation of a divisible resource (manpower, money, equipment) to a collection of objects (projects) requiring it in cases where its over-concentration would usually be far from optimal. The resulting project indices are functions of both a resource level and a state. They have a simple interpretation as a fair charge for increasing the resource available to the project from the specified resource level when in the specified state. We illustrate ideas by reference to two model classes which are of independent interest. In the first, a pool of servers is assigned dynamically to a collection of service teams, each of which mans a service station. We demonstrate indexability under a natural assumption that the service rate delivered is increasing and concave in the team size. The second model class is a generalization of the spinning plates model for the optimal deployment of a divisible investment resource to a collection of reward generating assets. Asset indexability is established under appropriately drawn laws of diminishing returns for resource deployment. For both model classes numerical studies provide evidence that the proposed greedy index heuristic performs strongly.
AB - We develop appropriately generalized notions of indexability for problems of dynamic resource allocation where the resource concerned may be assigned more flexibility than is allowed, for example, in classical multi-armed bandits. Most especially we have in mind the allocation of a divisible resource (manpower, money, equipment) to a collection of objects (projects) requiring it in cases where its over-concentration would usually be far from optimal. The resulting project indices are functions of both a resource level and a state. They have a simple interpretation as a fair charge for increasing the resource available to the project from the specified resource level when in the specified state. We illustrate ideas by reference to two model classes which are of independent interest. In the first, a pool of servers is assigned dynamically to a collection of service teams, each of which mans a service station. We demonstrate indexability under a natural assumption that the service rate delivered is increasing and concave in the team size. The second model class is a generalization of the spinning plates model for the optimal deployment of a divisible investment resource to a collection of reward generating assets. Asset indexability is established under appropriately drawn laws of diminishing returns for resource deployment. For both model classes numerical studies provide evidence that the proposed greedy index heuristic performs strongly.
KW - Asset management
KW - dynamic programming
KW - dynamic resource allocation
KW - full indexability
KW - index policy
KW - Lagrangian relaxation
KW - monotone policy
KW - queueing control
U2 - 10.1214/10-AAP705
DO - 10.1214/10-AAP705
M3 - Journal article
VL - 21
SP - 876
EP - 907
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 3
ER -