In this paper

a continuous time queueing model with multiple vacation and set-up time with second optional service is considered.Using imbedded Markov chain and the broad sense service time method

the generating function of the steady state queue length

the LST of waiting time and their stochastic decompositions are derived.Meanwhile

two particular cases of the model are obtained.Finally

using some numerical examples

we verify that this model can simulate some practical problems reasonably well.