Effective bandwidth and fast simulation of ATM intree networks
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Analysis of an importance sampling estimator for tandem queues
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient simulation of a tandem Jackson network
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Efficient simulation of buffer overflow probabilities in jackson networks with feedback
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for Jackson networks
Queueing Systems: Theory and Applications
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This note describes an importance sampling (IS) algorithm to estimate buffer overflows of stable Jackson networks with a tree topology. Three new measures of service capacity and traffic in Jackson networks are introduced and the algorithm is defined in their terms. These measures are effective service rate, effective utilization and effective service-to-arrival ratio of a node. They depend on the nonempty/empty states of the queues of the network. For a node with a nonempty queue, the effective service rate equals the node's nominal service rate. For a node i with an empty queue, it is either a weighted sum of the effective service rates of the nodes receiving traffic directly from node i, or the nominal service rate, whichever smaller. The effective utilization is the ratio of arrival rate to the effective service rate and the effective service-to-arrival ratio is its reciprocal. The rare overflow event of interest is the following: 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 shared by all nodes, and (2) each node has its own fixed size buffer. The constructed IS algorithm is asymptotically optimal, i.e., the variance of the associated estimator decays exponentially in the buffer size at the maximum possible rate. This is proved using methods from (Dupuis et al. in Ann. Appl. Probab. 17(4):1306---1346, 2007), which are based on a limit Hamilton---Jacobi---Bellman equation and its boundary conditions and their smooth subsolutions. Numerical examples involving networks with as many as eight nodes are provided.