Virtual output queueing (VOQ) is a widely deployed buffering scheme in high-performance input-queued switches and routers. While there has been extensive investigation of the performance of switch architectures employing VOQ, the majority of the work addresses traffic that is uncorrelated and uniformly distributed among the outputs. The paper presents analysis for discrete-time virtual output queued switches with incoming traffic governed by a Markov modulated ON/OFF process, whereby bursts are non-uniformly distributed among the various destinations. Under the assumption of geometrically distributed interservice times, we utilize the probability generating functions of the interarrival times to obtain per-queue closed-form expressions for the mean queue occupancy and mean delay. The validity of the analytical inference is established through simulation results.