26. In a queue with unlimited waiting space, arrivals are Poisson (parameter ) and service times are

26. In a queue with unlimited waiting space, arrivals are Poisson (parameter λ)

and service times are exponentially distributed (parameter μ). However, the server waits until K people are present before beginning service on the first customer;

thereafter, he services one at a time until all K units, and all subsequent arrivals, are serviced. The server is then “idle” until K new arrivals have occurred.

(a) Define an appropriate state space, draw the transition diagram, and set up the balance equations.