Load-balancing for multi-skilled servers with Bernoulli routing

Abstract We study the optimal Bernoulli routing in a multiclass queueing system with dedicated server for each class as well common (or multi-skilled) that can serve jobs of all classes. Jobs arrive according to Poisson process. Each has holding cost per customer and use processor sharing discipline service. The objective is minimize weighted mean cost. First, we provide conditions under which classes send their traffic only server, or both. A fixed point algorithm given computation solution. then specialize two give explicit expressions loads. Finally, compare multi-skilled servers. theoretical results are complemented by numerical examples illustrate various structural convergence algorithm.