Load-balancing for multi-skilled servers with Bernoulli routing
研究多类排队系统中，每类有专用服务器和一个多技能公共服务器时的最优伯努利路由策略，以最小化加权平均持有成本，并给出固定点算法和两类的显式解。
Abstract We study the optimal Bernoulli routing in a multiclass queueing system 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 arrive according to a Poisson process. Each server has a holding cost per customer and use the processor sharing discipline for service. The objective is to minimize the weighted mean holding cost. First, we provide conditions under which classes send their traffic only to their dedicated server, only to the common server, or to both. A fixed point algorithm is given for the computation of the optimal solution. We then specialize to two classes and give explicit expressions for the optimal loads. Finally, we compare the cost of multi-skilled server with that of only dedicated or all common servers. The theoretical results are complemented by numerical examples that illustrate the various structural results as well as the convergence of the fixed point algorithm.