In this paper, we study an M/M/2 queueing system with multiple
vacations where the service rates of the servers are not identical.
This queuing system has been analyzed as a quasi-birth and death
process by Kumar and Madheswari (2005). However, by expressing the rate
matrix explicitly, we have obtained a explicit expression of the
stationary distribution of the queue length. The conditional
stochastic decomposition properties of the queue length and the
waiting time have been also established for such a system.