Advanced Mathematical Models & Applications

This paper investigates a single-server retrial queueing model incorporating the behavior of burst traffic under a modified J-maintenance mechanism in Optical Burst Switching Networks (OBS). Upon arrival, if the server is available, the server processes each burst through two stages: a mandatory hop and an optional hop. Otherwise, the burst may be buffered or balk. Likewise, a buffered burst may renege, if its retrial attempt is unsuccessful. After each hop, if a transmission error is detected, the burst is directed to the buffer for retransmission. Otherwise, it proceeds to its destination. The server initiates maintenance activities whenever the buffer is empty. After completing a maintenance activity, if a burst is found in the buffer, the server waits in the network. Otherwise, it proceeds to the next maintenance activity. This loop continues for a maximum of J maintenance activities. After completing the Jth maintenance, the server remains in the network regardless of the buffer state. The proposed system is mathematically analyzed using the Supplementary Variable Technique to derive key performance metrics. The impact of various parameters on system characteristics is illustrated through numerical results. Additionally, cost optimization is performed using the Particle Swarm Optimization (PSO) technique.