Queuing system with state-dependent controlled batch arrivals and server under maintenance (Q1939051)

The paper under review considers \(M/M/1\) queueing systems. The service discipline is first-come-first-served. As the system becomes empty, the server immediately starts preventive maintenance for an exponentially distributed random duration. The customers arriving during a maintenance period are not allowed to join the system and lost. The paper also assumes that a random batch of customers arrives in the system during an exponentially distributed service time. Upon arrival, each individual customer in the batch is subject to control admission policy. The paper provides explicit expressions for the queue-length in time \(t\) in terms of the modified Bessel functions. The steady state behaviour and key performance measures are studied.