We consider a general queueing model with a Poisson arrival process whose rate is random, and realized once for the entire process. We show that the distribution of the arrival rate at arrival instants is the size-biased counterpart of the original distribution. In particular, the ASTA (arrivals...

Consider a single-server service system with uncertain quality level (which is assumed to be binary). Both the server and the customers know the distribution of quality levels and are engaged in the following two-stage game. In the first stage, the server commits to a strategy (possibly mixed)...