Self-averaging property of queuing systems
  We establish the averaging property for a queuing process with one server, M(t)/GI/1. It is a new relation between the output flow rate and the input flow rate, crucial in the study of the Poisson Hypothesis. Its implications include the statement that the output flow always possesses more regularity than the input flow. 
Alexandre Rybko, Senya Shlosman and Alexandre Vladimirov