A network can have diverse packets generated dependent on the kind of events. A large portion of these may be regular packets. But it also produce emergency packets whenever some emergency event occurs, which need to reach destination faster. We propose a backpressure-based queue model where an emergency packet will be given preference and send forward using backpressure method. The end-to-end delay is calculated for different kind of packets. The resultant graph demonstrate that the emergency packets are conveyed faster than ordinary packets and the delay is essentially reduced.