Optimal quantum of a priority queue

We consider a single server priority queuing system with a FIFO high priority queue (HPQ) and a round-robin low priority queue (LPQ). Such systems are encountered in data communication systems with high priority command packets and low priority data packets. We analyze this system with general service time at the HPQ and exponential service time at the LPQ. We present response time expressions for the two types of packets and use those expressions to find the optimal quantum at the LPQ for a given threshold response time for the command packets.