Probabilistic Models of Database Locking: Solutions, Computational Algorithms, and Asymptotics
Journal of the ACM (JACM)
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
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
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
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
Optimal capacity planning in stochastic loss networks
ACM SIGMETRICS Performance Evaluation Review
On throughput in linear wireless networks
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Revisiting stochastic loss networks: structures and algorithms
SIGMETRICS '08 Proceedings of the 2008 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Improved Approximations for Stochastic Loss Networks
ACM SIGMETRICS Performance Evaluation Review
Performance management of IT services delivery
ACM SIGMETRICS Performance Evaluation Review
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Stochastic loss networks are often very effective models for studying the random dynamics of systems requiring simultaneous resource possession. Given a stochastic network and a multi-class customer workload, the classical Erlang model renders the stationary probability that a customer will be lost due to insufficient capacity for at least one required resource type. Recently a novel family of slice methods has been proposed by Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407---418, 2008) to approximate the stationary loss probabilities in the Erlang model, and has been shown to provide better performance than the classical Erlang fixed point approximation in many regimes of interest. In this paper, we propose some new methods for loss probability calculation. We propose a refinement of the 3-point slice method of Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407---418, 2008) which exhibits improved accuracy, especially when heavily loaded networks are considered, at comparable computational cost. Next we exploit the structure of the stationary distribution to propose randomized algorithms to approximate both the stationary distribution and the loss probabilities. Whereas our refined slice method is exact in a certain scaling regime and is therefore ideally suited to the asymptotic analysis of large networks, the latter algorithms borrow from volume computation methods for convex polytopes to provide approximations for the unscaled network with error bounds as a function of the computational costs.