Design and evaluation of overloaded service systems with skill based routing, under FCFS policies

We study an overloaded service system with servers of types S = {s_1, …, s_J}, serving customers of types C = {c_1, …, c_I} under FCFS. Customers arrive in Poisson streams, join the queue and then abandon or get served. Service is skill based, which is described by a compatibility graph G, where (I, j) in G if server type s_j is trained to serve customer type c_i . The service duration depends on both server and customer type. This system is motivated by applications in areas as diverse as manufacturing, call centers, housing assignment, health care and data servers. At this level of generality, the design in terms of sta¿ng and cross-training decisions is a challenging problem. Based on recent results in [1, 2] and on some asymptotic assumptions, we propose an algorithm to determine, for given data, the required levels of sta¿ng to meet target levels of service quality and labor division. The algorithm is validated through a systematic simulation study, showing that it is remarkably robust and accurate. As such, we believe that the algorithm will prove to be useful in aiding the design and e¿ective operation of complex systems with skill based routing.