Virtual Output Queuing (VOQ) is an architecture widely employed in modern networking products. Traffic from every ingress port is stored in a set of queues mirroring the structure of the egress ports. This architecture allows congestion on one egress port to be isolated from the other ports. A request-grant protocol is used to route packets from ingress to egress. When a packet is received, a request signal is issued. After the request reaches the egress side, a grant signal is generated based on some fixed threshold indicating there is space in the egress buffer to absorb the largest packet size dispatched from ingress. The buffer must be sized deep enough to accommodate in-flight traffic associated with a scenario where heavy congestion is found after the grant is issued. Awaiting a grant signal to arrive before dispatching packets incurs significant end-to-end latency. To alleviate this problem, a speculative packet dispatch approach (SPD) is proposed in which the request grant protocol is completely eliminated. Packets are dispatched speculatively from ingress to egress based on predictions that there is enough space in the egress buffer. This is achieved by incorporating an LSTM recurrent neural network as part of the VOQ controller. The LSTM is trained by time-series data sets generated from past observations on the queue occupancy. The experimental results show that SPD delivers excellent improvement on the system performance, reduces buffering requirements and preserves the property of VOQ.