Consider a three-station series queueing system (single server at each station) with Poisson input (parameter ) and exponential service (parameters 1, 2, 3). There is

Consider a three-station series queueing system (single server at each station) with Poisson input (parameter λ) and exponential service (parameters

µ1, µ2, µ3). There is no capacity limit on the queue in front of the first two stations, but at the third there is a limit of K allowed (including service). If K are in the third station, then any subsequent arrivals are shunted out of the system. Find the expected number in the system (all three stations) and the expected time spent in the system by a customer that completes all three stages of service.