Load-balancing for Multi-skilled Servers with Bernoulli Routing

Fernando Miguelez (1) , Josu Doncel (2) , Balakrishna Prabhu (3)

1 UPV / EHU - University of the Basque Country = Euskal Herriko Unibertsitatea
2 UPV/EHU - Universidad del Pais Vasco / Euskal Herriko Unibertsitatea [Espagne]
3 LAAS-SARA - Équipe Services et Architectures pour Réseaux Avancés

We study the optimal Bernoulli routing in a multiclass queueing sys-tem with a dedicated server for each class as well as a common (or multi-skilled) server that can serve jobs of all classes. Jobs of each class arriveaccording to a Poisson process. Each server have a holding cost per cus-tomer and use the processor sharing discipline for service. The objectiveis to minimize the weighted mean holding cost.First, we provide conditions under which classes send their traffic onlyto their dedicated server, only to the common server, or to both. Afixed point algorithm is given for the computation of the optimal solution.We then specialize to two classes and give explicit expressions for theoptimal loads. Finally, we compare the cost of multiskilled server withthat of only dedicated or all common servers. The theoretical results arecomplemented by numerical examples that illustrate the various structuralresults as well as the convergence of the fixed point algorithm.

Domaines: Modélisation et simulation; Recherche opérationnelle [math.OC]; Calcul [stat.CO]

Fernando Miguelez, Josu Doncel, Balakrishna Prabhu. Load-balancing for Multi-skilled Servers with Bernoulli Routing. Annals of Operations Research, 2022, 312 (2), pp.949-971. ⟨10.1007/s10479-022-04532-7⟩. ⟨hal-03084240⟩