# Expected shares filled from a limit order

If I place a limit order to buy a stock at the bid, what is the expected number of shares that will be filled by the close? I think it depends on

1. The time until the close. More time until the close increases the number of shares filled.
2. The size of the bid and the ask. More shares offered than bid suggests that there are more sellers to hit my bid, increasing the number of shares filled.
3. The volatility of the stock. The higher it is, the more likely the stock will trade through my bid, getting me a fill.
4. The average daily volume of the stock. Higher volume should mean more shares filled.

Is there a theory for how the expected shares filled for a limit order depends on these variables?