Service is often provided in contexts where tasks or customers are impatient or perishable in that they have natural lifetimes of availability for useful service. Moreover, these lifetimes are usually unknown to the service provider. The question of how service might best be allocated to the currently waiting tasks or customers in such a context has been neglected and we propose three simple models. For each model, an index heuristic is developed and is assessed numerically. In all cases studied the heuristic comes close to optimality.
Service is often provided in contexts where tasks or customers are impatient or perishable in that they have natural lifetimes of availability for useful service. Moreover, these lifetimes are usually unknown to the service provider. The question of how service might best be allocated to the currently waiting tasks or customers in such a context has been neglected and we propose three simple models. For each model, an index heuristic is developed and is assessed numerically. In all cases studied the heuristic comes close to optimality.
This paper is the first to consider general multiarmed bandit problems on parallel machines working at different speeds. Block allocation policies make a once-for-all allocation of bandits to machines at time zero. In this class we describe how to achieve Blackwell optimality under given conditions. The block allocation policy identified allocates the bandits with the largest guaranteed reward rates to the machines operating at greatest speed. This policy is shown to be average-reward optimal in the class of general (nonanticipative, nonidling) policies.
We consider generalisations of two classical stochastic scheduling models, namely the discounted branching bandit and the discounted multi-armed bandit, to the case where the collection of machines available for processing is itself a stochastic process. Under rather mild conditions on the machine availability process we obtain performance guarantees for a range of controls based on Gittins indices. Various forms of asymptotic optimality are established for index-based limit policies as the discount rate approaches 0.
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