I trade closed-end funds, which have limited liquidity. Is there a mathematical model for how many shares of a limit buy order are expected to be filled? For example, at 1:10pm EST I think the market for DSL was 19.93-19.94, 500 shares bid and 700 offered. I placed a buy order for 10,000 shares at 19.94 limit. I was immediately filled on 700 shares, after which my order was filled in various pieces and was completely filled at 2:28 PM. I think the expected number of shares filled by the close depends positively on (1) expected volume until the close (2) realized volatility until the close but I wonder how exactly. Of course one's buy orders are more likely to be filled in a falling market, but I don't want to make an assumption about the near-term direction of the market. Probably this question has been studied in the "market microstructure" literature.