Abstract: This paper studies the M/G/1 repairable queueing system with D-policy and two types of failure modes. The first type of failure is the failure of the service desk during the service of a customer, the second type of failure is the failure of the service desk during the idle period, and the failure efficiency of the two types of failure modes is different. By using the total probability decomposition, L-transform, generating function and other tools, the transient distribution and equilibrium distribution of the system queue-length are discussed from any initial state. The recursive expression of the steady-state queue length distribution and the random decomposition results of the steady-state queue length are obtained. Furthermore, on the basis of establishing the cost model, the optimal control strategy D^* is discussed, which makes the system reach the minimum value in a long-term unit time by numerical examples. The optimal control strategy under the same set of parameters is compared with the optimal control strategy when the service desk does not fail.

Key words: repairable queueing system, failure in warm standby, D-policy, queuelength distribution, optimal control strategy