eprintid: 1779
rev_number: 4
eprint_status: archive
userid: 46
dir: disk0/00/00/17/79
datestamp: 2013-09-17 13:05:26
lastmod: 2013-09-17 13:05:26
status_changed: 2013-09-17 13:05:26
type: conference_item
succeeds: 1673
metadata_visibility: show
creators_name: Cello, Marco
creators_name: Gnecco, Giorgio
creators_name: Marchese, Mario
creators_name: Sanguineti, Marcello
creators_id: 
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
creators_id: 
title: A Stochastic Knapsack Problem with Nonlinear Capacity Constraint
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
pres_type: paper
keywords: Knapsack Problem, Stochastic Inter-Arrival Times, Nonlinear
Capacity Constraint, Coordinate-Convex Policies, Greedy Algorithms.
abstract: There exist various generalizations and stochastic variants of the NP-hard 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 inter-arrival times are exponentially-distributed 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 class-dependent 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. A-priori knowledge
of structural properties of the (unknown) optimal policies is useful to find satisfactorily accurate suboptimal policies. The family of coordinate-convex
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 coordinate-convex 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.
date: 2011
date_type: published
pagerange: 147
event_title: AIRO 2011
event_location: Brescia, Italy
event_dates: September 6th-9th, 2011
event_type: conference
refereed: TRUE
related_url_url: http://airo2011.eco.unibs.it/
related_url_type: org
citation:   Cello, Marco and Gnecco, Giorgio and Marchese, Mario and Sanguineti, Marcello  A Stochastic Knapsack Problem with Nonlinear Capacity Constraint.  In: AIRO 2011, September 6th-9th, 2011, Brescia, Italy p. 147.        (2011)