Queueing analysis of a discrete closed-loop conveyor with service facilities

We consider a discrete closed-loop conveyor system consisting of a loading station, an unloading station, and a number of carriers which move with constant speed along a closed track. At the loading station units arrive in batches while the arrival of batches is governed by a Poisson process. The units queue at the loading station and await there the arrival of an empty carrier. Each unit requires some amount of service which is provided while the unit is on a carrier. After completion of service a unit leaves the system as soon as it reaches the unloading station. Our interest focuses on the steady-state queue length at the loading station. We obtain explicit results for the case where units leave their carriers on passing the unloading station for the second time. We were motivated to study this case by a slotted ring protocol for local area networks.