Sanguineti, Marcello and Cello, Marco and Gnecco, Giorgio and Marchese, Mario
A Stochastic Knapsack Problem with Nonlinear Capacity Constraint.
In: AIRO 2011, September 6th9th, 2011, Brescia, Italy
p. 147.
(2011)
Full text not available from this repository.
Abstract
There exist various generalizations and stochastic variants of the NPhard 0/1 knapsack problem [1,2]. The following model is considered here. A knapsack of capacity C is given, together with K classes of objects. The stochastic
nature come into play since, in contrast to the classical knapsack, the objects belonging to each class become available randomly. The interarrival times are exponentiallydistributed with means depending on the class and on the state of the knapsack. Each object has a sojourn time independent from the sojourn times of the other objects and described by a classdependent distribution.
The other difference with respect to the classical model consists is the following generalization. For k = 1;K, let nk be the number of objects of class k that are currently inside the knapsack; then, the portion of knapsack
occupied by them is given by a nonlinear function bk(nk). When included in the knapsack, an object from class k generates revenue at a positive rate rk. The objects can be placed into the knapsack as long as the sum of their
sizes does not exceed the capacity C. The problem consists in finding a policy that maximizes the average revenue, by accepting or rejecting the arriving objects in dependence of the current state of the knapsack. Apriori knowledge
of structural properties of the (unknown) optimal policies is useful to find satisfactorily accurate suboptimal policies. The family of coordinateconvex
policies is considered here. In this context, structural properties of the optimal policies are investigated. New insights into a criterion proposed in [3] to improve coordinateconvex policies are discussed and the greedy presented in [5] is further developed. Applications in Call Admission Control (CAC) for telecommunication networks are discussed. In this case, the objects are requests of connections coming from K different classes of users, each with an associated bandwidth requirement and a distribution of its duration.
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