Dynamic fluid-based scheduling in a multi-class abandonment queue - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Performance Evaluation Année : 2013

Dynamic fluid-based scheduling in a multi-class abandonment queue

Résumé

We investigate how to share a common resource among multiple classes of customers in the presence of abandonments. We consider two different models: (1) customers can abandon both while waiting in the queue and while being served, (2) only customers that are in the queue can abandon. Given the complexity of the stochastic optimization problem we propose a fluid model as a deterministic approximation. For the overload case we directly obtain that the c˜µ/θ rule is optimal. For the underload case we use Pontryagin’s Maximum Principle to obtain the optimal solution for two classes of customers; there exists a switching curve that splits the two-dimensional state-space into two regions such that when the number of customers in both classes is sufficiently small the optimal policy follows the c˜µ-rule and when the number of customers is sufficiently large the optimal policy follows the c˜µ/θ-rule. The same structure is observed in the optimal policy of the stochastic model for an arbitrary number of classes. Based on this we develop a heuristic and by numerical experiments we evaluate its performance and compare it to several index policies. We observe that the suboptimality gap of our solution is small.
Fichier principal
Vignette du fichier
Larranaga_12576.pdf (1.6 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01130331 , version 1 (11-03-2015)

Identifiants

Citer

Maialen Larrañaga, Urtzi Ayesta, Ina Maria Maaike Verloop. Dynamic fluid-based scheduling in a multi-class abandonment queue. Performance Evaluation, 2013, vol. 70 (n° 10), pp. 841-858. ⟨10.1016/j.peva.2013.08.009⟩. ⟨hal-01130331⟩
182 Consultations
214 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More