In this paper, an M^[x]/(G₁(a,b),G₂(a,b))/1 queueing model with closedown, multiple vacation and state dependent arrival rate is considered. The single server provides two modes of service. The server provides mode 1 service with probability a₁ or mode 2 service with probability a₂ where a₂=1-a₁. It is considered that the arrival rate depends on the state of server. Using supplementary variable technique, the steady-state probability generating function of the system size at an arbitrary time is obtained. The performance measures and cost model are also derived. Numerical illustrations are presented to visualize the effect of system parameters.