The time available for network elements to process packets with Quality of Service (QoS) requirements decreases with higher network speed. Packet processing functions such as queuing and scheduling need to be performed at high speed to ensure QoS. The two basic queuing strategies in routers are Output Queuing (OQ) and Input Queuing (IQ). OQ guarantees QoS and gives optimal throughput but it is not scalable. Although IQ has been identified as the most scalable its maximum throughput is 58.6% due to Head Of Line (HOL) blocking. The Virtual Output Queuing (VOQ), a proffered solution to the HOL blocking achieves 100% throughput with an effective scheduling algorithm. This paper proposes a Multistage Queuing and Scheduling strategy in which VOQ is implemented at the input ports and OQ at the output ports of the router. The scheduling algorithm for the VOQ presented in this paper is an Iterative Probabilistic Scheduling.