Yingdong Lu, Jing-Sheng Song, et al.
IIE Transactions
We consider fundamental properties of stochastic loss networks, seeking to improve on the so-called Erlang fixed-point approximation. We propose a family of mathematical approximations for estimating the stationary loss probabilities and show that they always converge exponentially fast, provide asymptotically exact results, and yield greater accuracy than the Erlang fixed-point approximation. We further derive structural properties of the inverse of the classical Erlang loss function that characterize the region of capacities that ensures a workload is served within a set of loss probabilities. We then exploit these results to efficiently solve a general class of stochastic optimization problems involving loss networks. Computational experiments investigate various issues of both theoretical and practical interest, and demonstrate the benefits of our approach.
Yingdong Lu, Jing-Sheng Song, et al.
IIE Transactions
David A. Goldberg, Dmitriy Katz-Rogozhnikov, et al.
Mathematics of Operations Research
Arnab Bhattacharyya, Elena Grigorescu, et al.
SODA 2009
Soumyadip Ghosh, Yingdong Lu, et al.
Journal of Applied Analysis