Individuals enter the system in accordance with a Poisson process having rate Each arrival independently makes its way through the states of the system Let a,(s) denote the probability that an individual is in state i a time s after it arrived Let N,(t) denote the number of individuals in state i at time t. Show that the N,(t), i 1, are independent and N,(r) is Poisson with mean equal to AE [amount of time an individual is in state i during its first t units in the system]