Enhancement of network performance is a big challenge today for the emerging technology based on IEEE 802.16. Wireless technology is an alternate solution to wired technology. Network availability all the way is an important challenge in day-to-day life. Due to the huge population, the availability of the network is again a big challenge. Also, it becomes more difficult to capture the network if considering rural areas, hilly, lakes, and seashores today. This work proposed relay stations in WiMAX (Worldwide Interoperability for Microwave Access) networks along with various bandwidth allocation algorithms to increase the signal strength over the long distance using retransmission of the original signal by relay station and extend the coverage with a higher data rate and higher user capacity. The availability of WiMAX networks for the channel bandwidth assignment to users for data and service is very important in today's scenario. This paper focuses on evaluating the performance of bandwidth allocation algorithms in light WiMAX networks with and without relay stations. The performance evaluation is done by increasing the number of nodes with various bandwidth allocation techniques with and without relay stations. In this work the round robin and strict priority algorithms are used for channel bandwidth allocation in a light WiMAX network and performance is analyzed through throughput, goodput, and packet drop rate, which will help to implement and configure the suggested optimal parameters in the production environment. This work enhanced the throughput and goodput and reduce the dropout rate, and the user capacity also increased.