Achieving an even distribution of orders in the queue

Question

Baron Law, Frederi Viens: Market Making under a Weakly Consistent Limit Order Book Model contains the following paragraph

"The market maker may achieve her target execution profile by continuously adjusting her limit orders in the LOB to be roughly the proportion ρ of the queue length at each price level, but the detailed mechanism is outside the scope of this paper."

Does anyone have any references for how this is achieved in practice given the presence of both trades and cancels removing depth at the best prices?

Answer 1

Suppose your target participation rate is 1/11 ~ 9%. At each price level, whenever someone puts a limit order of size 10, you put a limit order of size 1 right after him. Whenever someone cancel an order of size 10, you cancel 1 share from your limit order with the lowest priority. When a market order arrives, you adjust your limit orders depending on whether your limit orders are executed or not.

However, I would like to stress that the uniform distribution assumption is more like a simplifying assumption, rather than the goal, in deriving the optimal risk limit in my paper. As a market-maker, you always want your limit orders to be at the top of the queue.