Consider a sampled-time M/D/m/m queueing system. The arrival process is Bernoulli with probability λ That is, the new customer receives one unit of service by the next state time, and all the old...

Consider a sampled-time M/D/m/m queueing system. The arrival process is Bernoulli with probability λ <>

That is, the new customer receives one unit of service by the next state time, and all the old customers receive one additional unit of service. If the oldest customer has received d units of service, then it leaves the system by the next state time. Note that it is possible for a customer with d units of service at the present time to leave the system and be replaced by an arrival at the present time (i.e., (7.100) with n = m, x_n
= d). Let B(n, x) denote the next state if either no arrival occurs or if a new arrival is discarded.