Probabilistic Models of Database Locking: Solutions, Computational Algorithms, and Asymptotics
Journal of the ACM (JACM)
On the linear convergence of descent methods for convex essentially smooth minimization
SIAM Journal on Control and Optimization
Computational complexity of loss networks
Theoretical Computer Science - Special issue on probabilistic modelling
ATM network design and optimization: a multirate loss network framework
IEEE/ACM Transactions on Networking (TON)
Multiservice Loss Models for Broadband Telecommunication Networks
Multiservice Loss Models for Broadband Telecommunication Networks
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
The Erlang model with non-poisson call arrivals
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Optimal capacity planning in stochastic loss networks with time-varying workloads
Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Scalability of wireless networks
IEEE/ACM Transactions on Networking (TON)
Optimal capacity planning in stochastic loss networks
ACM SIGMETRICS Performance Evaluation Review
Improved Approximations for Stochastic Loss Networks
ACM SIGMETRICS Performance Evaluation Review
Improved approximations for the Erlang loss model
Queueing Systems: Theory and Applications
Performance management of IT services delivery
ACM SIGMETRICS Performance Evaluation Review
Fine-grain diagnosis of overlay performance anomalies using end-point network experiences
Proceedings of the 8th International Conference on Network and Service Management
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This paper considers structural and algorithmic problems in stochastic loss networks. The very popular Erlang approximation can be shown to provide relatively poor performance estimates, especially for loss networks in the critically loaded regime. This paper proposes a novel algorithm for estimating the stationary loss probabilities in stochastic loss networks based on structural properties of the exact stationary distribution, which is shown to always converge, exponentially fast, to the asymptotically exact results. Using a variational characterization of the stationary distribution, an alternative proof is provided for an important result due to Kelly, which is simpler and may be of interest in its own right. This paper also determines structural properties of the inverse Erlang function characterizing the region of capacities that ensures offered traffic is served within a set of loss probabilities. Numerical experiments investigate various issues of both theoretical and practical interest.