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.
The formula is all asks at or below your bid. In your case, the price moved away from your bid, so the rest wasn't filled until the price drifted back down. If the price had kept moving away, you would only have the 700 shares. If a security is illiquid, and you want to move large relative amounts, it's best to call and make a block trade. The market is probably more liquid than you think anyways. I experimented with a large market order once against a large company, and yes, the order took some time to fill, was broken up, and filled at higher and higher prices although the increments were small.