The problem of obtaining maximum likelihood estimates for the parameters involved in a stationary single-channel, Markovian queuing process is considered. A method of taking observations is presented which simplifies this problem to that of determining a root of a certain quadratic equation. A useful and even simpler rational approximation is also studied.
"Maximum Likelihood Estimates in a Simple Queue." Ann. Math. Statist. 28 (4) 1036 - 1040, December, 1957. https://doi.org/10.1214/aoms/1177706808