Efficient Monte-Carlo simulation of a product-form model for a cellular system with dynamic resource sharing

• Authors: Philip J. Fleming;Dennis Schaeffer;Burton Simon
• Venue: ACM Transactions on Modeling and Computer Simulation (TOMACS)
• Year: 1995

There are many ways for users to share the radio spectrum allocated to a cell in a cellular phone system. We analyze a commonly proposed scheme wh ere the cell is divided into s sectors. Each sector has exclusive access to a certain number of channels. The remaining channels reside in a “common pool” and are shared among the sectors. The smallest unit of bandwidth that can be borrowed from the common pool is a “carrier,” which consists of c channels. When viewed as a multidimensional birth-death process, the steady-state distribution of the number of active channels in each sector has a “product form,” but because the state space is large and has a nonlinear boundary, direct calculation of quantities of interest is usually impractical. Ross and Wang have developed a Monte-Carlo technique that applies to our problem. We significantly improve the efficiency of their technique when applied to our problem by including certain (nonlinear) control variates. The kinds of control variates we use can be applied to other loss systems as well. We also explore the effect of importance sampling for our system. In many cases the variance reduction achieved from the combination of importance sampling and control variates is far greater than from either method alone. For systems with blocking probabilities in the range 0.001 to 0.1, the variance of the system-blocking probability estimator can be reduced by several orders of magnitude.