This paper presents the derivation of an analytical model for a multi-queue nodes network router, which is referred to as the multi-queue nodes (mQN) model. In this model, expressions are derived to calculate two performance metrics, namely, the queue node and system utilization factors. In order to demonstrate the flexibility and effectiveness of the mQN model in analyzing the performance of an mQN network router, two scenarios are performed. These scenarios investigated the variation of queue nodes and system utilization factors against queue nodes dropping probability for various system sizes and packets arrival routing probabilities. The performed scenarios demonstrated that the mQN analytical model is more flexible and effective when compared with experimental tests and computer simulations in assessing the performance of an mQN network router. This paper presents the derivation of an analytical model for a multi-queue nodes network router, which is referred to as the multi-queue nodes (mQN) model. In this model, expressions are derived to calculate two performance metrics, namely, the queue node and system utilization factors. In order to demonstrate the flexibility and effectiveness of the mQN model in analyzing the performance of an mQN network router, two scenarios are performed. These scenarios investigated the variation of queue nodes and system utilization factors against queue nodes dropping probability for various system sizes and packets arrival routing probabilities. The facilitation of the mQN analytical model is more flexible and effective when compared with experimental tests and computer simulations in assessing the performance of an mQN network router.