Approximations for the M/GI/N+GI type call center

In this study, we propose approximations to compute the steady-state performance measures of the M/GI/N + GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single server M/GI/1 + GI queue for which we suggest a practical way to compute the waiting time distributions and their moments. To do this, we make use of the Laplace transform of the workload density function. Our first contribution is within the context of the M/GI/1 + GI queue in obtaining the workload Laplace transform when abandonment-time distributions are of Phase-type. Next, we scale-up the M/GI/1 + GI queue giving rise to our approximations to capture the behavior of the multi-server system. As a practical application area, we further employ the approximations in determining the minimum staffing levels in a call center to meet the target values of certain performance measures, such as serving a proportion of customers within a specified time, and keeping the portion of abandoning customers below set limits.