On the average idle time and average queue length estimates in a M/M/1 queue

The paper studies the bias in the means of average idle time and average queue length estimates, over the interval [0,t], in a transient M/M/1 queue. It develops some formulas, in terms of the busy period distribution, that show that the bias is O(1/t). These formulas yield simple bounds for the means of the transient estimates. The bound for the bias in the mean of the average idle time estimate is also shown to be an excellent approximation.