In this research, the concept of piggybacking has been extended to concatenate Transmission Control Protocol (TCP) and User Datagram Protocol (UDP) packets. In any given network scenario, voice (UDP) is given priority over data (TCP) packet. During high traffic load, a UDP packet is processed at a higher priority, thus accumulating the TCP packets and leading to congestion and retransmission of TCP packets. Because it is challenging to integrate UDP and TCP packets an efficient queuing model has been proposed to concatenate the packets without causing a negative impact on UDP or voice traffic. In this paper, we propose the algorithm and model to concatenate UDP and TCP packets into a single packet and obtain better throughput for TCP traffic, efficient utilization of network bandwidth. The concatenation is performed based on parameters such as priority, destination and MTU size. The concept of discrete-time Markov chain has been leveraged to analyze the router utilization and efficiently handle the concatenated packets. The PCATTCP tool has been used to study the performances of UDP and TCP packets traversing a LAN between two end hosts. These values have been used for the simulation of the problem. Discrete Event Simulation has also been performed to determine the optimal values and associated system parameters.