Load-balancing for multi-skilled servers with Bernoulli routing

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.

Queueing Dynamics and State Space Collapse in Fragmented Limit Order Book Markets

In modern equity markets, participants have a choice of many exchanges at which to trade, each of which typically operates as an electronic limit order book. This paper analyzes this setting as a multiclass queueing system. Taking into account the effect of investors’ order-routing decisions across exchanges, they find that the equilibrium of this decentralized market exhibits a state space collapse property, whereby the queues at different exchanges are coupled, and the overall behavior of the market is captured through a one-dimensional process that can be viewed as a weighted aggregate queue length across all exchanges. The key driver of this coupling phenomenon is anticipated delay as opposed to the queue lengths themselves.