Airline passengers must pass through a security check point consisting of a metal detector and carry on luggage X Ray machine. Suppose that passengers arrive according to a Poisson process with a rate ω = 20 passengers per minute. The Security check point clears customers at a rate of ¥ = 22. I am asked to find the number of customers waiting in line to be checked. I know for Poisson process the mean is lambda( which I think in the question is given by ω= 20) i am thinking the expected number to be same as 20, but will this be correct.
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Oct 25 '18 at 08:47
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The number of customers waiting is a random variable, likely you are asked to find the (steady state) expected number of customers in an M/M/1 queue with parameters $\lambda$ and $\mu$ with $\lambda = 20, \mu=22$. – Michael Oct 25 '18 at 08:48