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

M. Larrañaga, U. Ayesta, I.M. Verloop
2013 Performance evaluation (Print)  
OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 12576 To link to this article : a b s t r a c t 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
more » ... 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 thecµ/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 thecµ-rule and when the number of customers is sufficiently large the optimal policy follows thecµ/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. (I.M. Verloop).
doi:10.1016/j.peva.2013.08.009 fatcat:is4mzjilmjaxhgdkduboys7sje