On Large Queue Lengths in Generalised Jackson Networks

Key Points

• This research aims to establish a large deviation principle for queue lengths in subcritical generalized Jackson networks.
• Proved the large deviation principle (LDP) for the stationary distribution of queue lengths.
• Assumed the Cramèr condition on interarrival and service times.
• Characterized the deviation function using the quasipotential.
• Confirmed that the stationary distribution follows the large deviation principle.
• Established that the quasipotential effectively describes the deviation function.