Waiter Vacation M/g/1 Repairable Queuing System Analysis

In this paper, we introduced the theoretical and practical situation about the queue system with repairable server station and queue with server vacations. Based on this, we mainly researched the repairable M/G/I queue with server vacations in two aspects: 1. We discussed the system from queue theory. (1) Using imbedded Markov chain of queueing length, we obtained the generated function of equilibrium queueing length (2) We also discussed the waiting time of the customers and got the LS transform of its equilibrium distribution w(s)= (3) We got the recursion expressions of the equilibrium queueing length given N(O) (4) Furthermore, we researched the departure process of the system. 2. We researched the system from reliability theory. (1) We offered the L transform of the transient unavailability and equilibrium unavailability 1im,(t) pp(2) We got the L transform of failure treqLlcncy of the system.