Simulation Methods for Estimation of Blocking Probabilities in Cellular Telecommunication Networks

Blocking probabilities in FDMA/TDMA cellular mobile communication networks using dynamic channel assignment are hard to compute for realistic sized systems. This computational dif"culty is due to the structure of the state space, which imposes strong coupling constraints amongst components of the occupancy vector. Tractable models for dynamically recon"gurable networks have been proposed, and for those, the stationary distribution of the occupancy vector is a product of truncated Poisson random variables. Nonetheless, even in such cases realistic network sizes prevent computation of the closed form within reasonable time and the only viable way to estimate blocking seems to be through simulation. Alas! Simulation as a means for estimating blocking probability suffers from the fact that the relative error of the estimates can grow without bound for the same number of samples, as the blocking probability diminishes. Small blocking probabilities thus typically require an enormous amount of CPU time for the estimates to be meaningful. Advanced simulation approaches use importance sampling (IS) to overcome this problem. This is known in the simulation literature as “rare event simulation”. Two simulation approaches can be identi"ed. The "rst one attempts to use simulation as a means for generating the stationary distribution directly. We review the Acceptance/Rejection (A/R) method and a fast simulation approach applied to it. While it does give a remarkable variance reduction, this method requires solving a complex optimisation problem before IS can be applied. Next we describe a Markov Chain Monte Carlo method that we have call the Filtered Gibbs Sampler (FGS), which dramatically outperforms A/R and does not need any set-up to perform the simulations. The second simulation method is to simulate the actual occupancy process and estimate blocking from the measurements. This method can in principle be more robust than estimation of the product form probabilities, because realistic channel assignments can be dealt with, and not just models that satisfy the product form. In this paper we study two regimes under which blocking is a rare event: low utilisation and high capacity. Our simulations use the Standard Clock (SC) method that generates directly the birth and death process and we propose a change of measure that we call static ISSCwhich has bounded relative error: as the traf"c intensity decreases, the relative ef"ciency of this method becomes in"nitely better than the FGS method. For high capacity, we use a change of measure that depends on the current state of the network occupancy. This is the dynamic ISSCmethod, for which we can prove optimality in single clique models and we empirically show the advantages of this method over na1̈ve simulation for networks of moderate size and traf"c loads.