Hop Limits in Network Design: What is the Impact on Optimal Network Cost?

We investigate the impact of hop-limited routing paths on the total cost of a telecommunication network. For different survivability settings (no survivability, link and path restoration), the optimal network cost without restrictions on the admissible path set is compared to the results obtained with two strategies to impose hop limits on routing paths. Based on optimal solutions for 10 real-world based problem instances, we show that hop limits may lead to an unpredictable raise in total network cost - even with large hop limits. The total network cost with a hop limit of 7 hops for all demands can be up to 25% higher than without restrictions on the admissible path set. With our second strategy, which imposes demand-dependent hop limits based on the shortest hop count, we obtain similar results. This indicates that column generation techniques should be applied to deal with all admissible paths.