Optimal order flow routing, exchange competition, and the effect of make/take fees

In modern equity markets, traders have a choice of many exchanges, each operating as an electronic limit order book that can be modeled as a pair of multi-class queues operating under the "time/price" priority rule. The dynamics of the exchanges are coupled via price protection mechanisms. We present mathematical models to study the order routing problem, characterize market equilibria, and derive insights about the queue, delay and adverse selection measures for different exchanges. We present some empirical data that supports our findings.