Geo/Geo/1 Queue with N-limited Working Repairs and State-dependent Arrival and Service Rates

Incorporating N-Limited working repairs ensures the uninterrupted forwarding of packets for some time in the event of a processor failure. This mechanism is applied to Geo/Geo/1 queueing systems characterized by state-dependent arrival and service rates. Employing matrix geometric analysis, we delve into the exploration of the steady-state distribution, accounting for state-dependent service times. The server may encounter breakdowns, yet, during repairs, the system maintains packet forwarding for the subsequent N customers. We derive equilibrium conditions and scrutinize the steady-state distribution of the system state and the number of customers in the system. This study contributes to understanding the implications of N-limited working repairs on the average number of customers in Geo/Geo/1 queues governed by state-dependent characteristics.