The Repairable Batch Arrival Queueing Systems With Variable Service Rate

The paper researches the repairable batch arrival queueing system with variable service rate, we study several kind of different models according to the variant of different service. The M^X /G/1 queueing system has been studied by many researchers and many results have been obtained. On the other hand the queueing system with variable service rate has also been studied by some researcher, but the queueing system combining batch arrival , variable service rate and the repairable model has not been studied. Under this circumstance, we study the repairable batch arrival queueing systems with variable service rate. Firstly, we study a repairable M^X /(G₁ + G₂)(M/M)/1 queueing system with two phase heterogeneous service; secondly, we study the repairable M^X /G(M/M)/1 queueing system with variable service speed under an N-policy; thirdly, we study a repairable batch arrival queueing system with priority custom and the second optional service; at last we study a repairable M^X /(G₁+G₂)I(M/ M)/1 queueing system with two phase heterogeneous service and multiple delay vacations on the basis of the repairable M^X /(G₁ + G₂)(M / M)/1 queueing system. By the method of supplementary variable we derive the queue-length and some reliability indexes of these models.