Estimating waiting time in double auction

Hi guys!

I am currently researching on double auction in the case when bidders and sellers would like to sell/obtain the good as soon as possible.
For that, I would like to estimate the expected waiting time that a bidder has to wait after posting a bid.

Imagine that:

Each bidder bids a price based on its valuation of the good, drawn from U(0,1) and oppositely, each seller asks a price based on the opportunity cost of the good drawn from U(0,1). Bidders and sellers arrive following Poisson distribution with known arrival rate lambda_b and lambda_s for each time period.

At that time period, bidders that have bid the n highest bids are matched with the n sellers having offered the lowest asks.

How many time periods am I expected to wait, knowing my value bid b as well as the arrival rate of lambda_b and lambda_s?

Thank you all very much for your feedback.
seems like the action of the sellers is irrelevant to your waiting times if you are a bidder with bid 'b'? I mean, ur done waiting when the clock hits 0 and you are among the n highest bids right? Or is there some other condition?