Monte Carlo Summation for Product-Form Loss Networks

1995 ◽  
pp. 229-248
Author(s):  
Keith W. Ross
Keyword(s):  
Monte Carlo ◽  
Product Form ◽  
Loss Networks

Monte Carlo Summation Applied to Product-Form Loss Networks

1992 ◽  
Vol 6 (3) ◽  
pp. 323-348 ◽  
Author(s):  
Keith W. Ross ◽  
Jie Wang
Keyword(s):  
Monte Carlo ◽  
Sampling Technique ◽  
Computational Effort ◽  
Form Solution ◽  
Product Form ◽  
Normalization Constant ◽  
Star Network ◽  
Loss Networks ◽  
Blocking Probabilities ◽  
Little's Formula

Loss networks with direct routing have a product-form solution for their equilibrium probabilities. The product-form solution typically involves a normalization constant calling for a multidimensional summation over an astronomical number of states. We propose the application of Monte Carlo summation in order to determine the normalization constant, the blocking probabilities, and the revenue sensitivities. We show that if the proper sampling technique is employed, then the computational effort of Monte Carlo summation is independent of link capacities. We also discuss the application of importance sampling, antithetic variates, and indirect estimation via Little's formula. The method is illustrated with a four-leaf star network supporting multirate traffic.

On critically loaded loss networks

1989 ◽  
Vol 21 (04) ◽  
pp. 831-841 ◽  
Author(s):  
P. J. Hunt ◽  
F. P. Kelly
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Stationary Distribution ◽  
Product Form ◽  
Large Loss ◽  
Loss Networks ◽  
Critical Loading

This paper studies the behaviour of large loss networks, paying particular attention to links at a certain critical loading where the load offered very nearly matches capacity. We correct and extend an earlier central limit theorem for the stationary distribution of a loss network with critically loaded links. We then use this result to show that acceptance probabilities have a limiting product-form decomposition, despite marked dependencies between the occupancies of critically loaded links.

scholarly journals Product form approximations for highly linear loss networks with trunk reservation

2003 ◽  
Vol 38 (11-13) ◽  
pp. 1147-1156 ◽  
Author(s):  
M. Bebbington ◽  
P. Pollett ◽  
I. Ziedins
Keyword(s):  
Product Form ◽  
Loss Networks ◽  
Trunk Reservation ◽  
Linear Loss
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