Hazard Rate Scaling for the GI/M/n + GI Queue

We obtain a heavy-traffic limit for the GI/M/n+GI queue which includes the entire abandonment distribution. Our main approach is to scale the hazard rate function in an appropriate way such that our resulting diffusion approximation contains the entire hazard rate function. We then show through numerical studies that for various key performance measures, our approximations outperform those commonly used in practice which only involved the abandonment distribution through the value of its density at the origin. The robustness of our results is also demonstrated by applying them to solving constraint satisfaction problems arising in the context of telephone call centers.