A Simple Proof of the Equivalence of the Limiting Distributions of the Continuous-Time and the Embedded Process of the Queue Size in the M/G/1 Queue*

This paper presents an extremely simple proof of the known remarkable fact that for the M/G/1 queue the continuous-time process describing the number of customers in the system has the same limiting distribution as the embedded process describing the number of customers in the system just after service completion epochs.