On the “pasta” property and a further relationship between customer and time averages in stationary queueing systems

We consider queueing systems in statistical equilibrium and discuss a property which is known as PASTA (Poisson Arrivals See Time Averages). We give examples showing that for this property as well as for a related property called Conditional PASTA to be valid the independence assumption usually made in this connection is not necessary. Furthermore, we extend to queueing systems with preemptive service discipline a formula of Brumelle's relating the time-average workload to the delay in queue and the service time of a customer.