Asymptotically optimal importance sampling for Jackson networks with a tree topology

Consider a stable open Jackson Network with a tree topology. Customers arrive at the single root of the tree. The system is stable in the sense that the average service rate at each node is faster than the average arrival rate to that node. This paper develops efficient and asymptotically optimal Importance Sampling algorithms to compute the probability of the following overflow event: given that initially the network is empty the system experiences a buffer overflow before returning to the empty state. Two types of buffer structures are considered: 1) A single system-wide buffer of size n shared by all nodes 2) each node i has its own buffer of size βin, βi ∈ (0, 1). The algorithms developed here are based on the game approach of [3, 2, 4, 9].

• Type: Journal
• Year: 2010
• Where: QUESTA
• Authors: Ali Devin Sezer
• Keywords: Average Arrival Rate, Node, QUESTA 2010, Stable Open Jackson