Abstract:

By leading into broad sense service time and using the method of imbedded Markov chains, the Geom／G／1 queue with second optional service and multiple vacation was studied. The PGF(probability generating function) of the steady state queue length and waiting time were derived. And then two particular models were given to further verify the correctness of the model. Final, the numerical examples proved that our model could represent some practical problems reasonably.

Key words: discrete-time queues; multiple vacation; second optional service; broad sense service time