Estimation of blocking probabilities in cellular networks with dynamic channel assignment

Blocking probabilities in cellular mobile communication networks using dynamic channel assignment are hard to compute for realistic sized systems. This computational difficulty is due to the structure of the state space, which imposes strong coupling constraints amongst components of the occupancy vector. Approximate tractable models have been proposed, which have product form stationary state distributions. However, for real channel assignment schemes, the product form is a poor approximation and it is necessary to simulate the actual occupancy process in order to estimate the blocking probabilities. Meaningful estimates of the blocking probability typically require an enormous amount of CPU time for simulation, since blocking events are usually rare. Advanced simulation approaches use importance sampling (IS) to overcome this problem. In this article, we study two regimes under which blocking is a rare event: low-load and high cell capacity. Our simulations use the standard clock (SC) method. For low load, we propose a change of measure that we call static ISSC, which has bounded relative error. For high capacity, we use a change of measure that depends on the current state of the network occupancy. This is the dynamic ISSC method. We prove that this method yields zero variance estimators for single clique models, and we empirically show the advantages of this method over naive simulation for networks of moderate size and traffic loads.