Fast Optimization Algorithms for Designing Cellular Networks with Guard Channel

In this paper we consider the optimal design problems for two cellular networks with guard channel, and develop fast algorithms to derive the optimal number of channels in terms of both the dropping and blocking probabilities. First we examine algebraic properties of the new call blocking probability and the handoff call dropping probability for the base station system with both guard channel and mobile-assisted handoff, and give a stable optimization algorithm under three conjectures which can be numerically validated. Next, we consider an extended model for a cellular network, where the base station system with channel failure and repair are assumed. We provide the exact steady-state probabilities for the associated continuous-time Markov chain, and also develop an optimal design algorithm to determine the number of channels and guard channels simultaneously under the same conjectures.