Abstract
We use semi-regenerative, fluctuations methods, and sequential games to examine a queueing system with server performing a secondary maintenance work. When the buffer becomes empty, the server leaves the system to service packets of jobs at a maintenance facility where his time there is restricted by T (a random time). He returns to the system when his sojourn time expires and if the last packet is fully processed. If the buffer contents is below N, the server departs from the system again to continue with maintenance; this time rendering just one packet at a time until the buffer is replenished. We obtain compact and explicit functionals for the queueing process in equilibrium for both discrete and continuous time parameter processes.