Cello, Marco and Gnecco, Giorgio and Marchese, Mario and Sanguineti, Marcello A Stochastic Knapsack Problem with Nonlinear Capacity Constraint. In: AIRO 2011, September 6th9th, 2011, Brescia, Italy p. 147. (2011)
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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.
Item Type:  Conference or Workshop Item (Paper) 

Uncontrolled Keywords:  Knapsack Problem, Stochastic InterArrival Times, Nonlinear Capacity Constraint, CoordinateConvex Policies, Greedy Algorithms. 
Subjects:  Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
Research Area:  Computer Science and Applications 
Depositing User:  Giorgio Gnecco 
Date Deposited:  17 Sep 2013 13:05 
Last Modified:  17 Sep 2013 13:05 
URI:  http://eprints.imtlucca.it/id/eprint/1779 
Available Versions of this Item

A Stochastic Knapsack Problem with Nonlinear Capacity Constraint. (deposited 11 Sep 2013 09:59)
 A Stochastic Knapsack Problem with Nonlinear Capacity Constraint. (deposited 17 Sep 2013 13:05) [Currently Displayed]
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