A three-server queueing system has a controlled arrival process that provides customers in time to keep the servers continuously busy. Service times have an exponential distribution with mean 0.5.
You observe the queueing system starting up with all three servers beginning service at time t = 0. You then note that the first completion occurs at time t = 1. Given this information, determine the expected amount of time after t = 1 until the next service completion occurs.