Queueing Models of Case Managers

Many service systems use case managers, servers who are assigned multiple customers and have frequent, repeated interactions with each customer until the customer’s service is completed. Examples may be found in healthcare (emergency department physicians), contact centers (agents handling multiple online chats simultaneously) and social welfare agencies (social workers with multiple clients). We propose a stochastic model of a baseline case‐manager system, formulate models that provide performance bounds and stability conditions for the baseline system, and develop two approximations, one of which is based on a two‐time‐scale approach. Numerical experiments and analysis of the approximations show that increasing case throughput by increasing the probability of case completion can lead to much greater waiting‐time reductions than increasing service speed. Many systems place an upper limit on the number of customers simultaneously handled by each case manager. We examine the impact of these caseload limits on waiting time and describe effective, heuristic methods for setting these limits. This paper was accepted by Yossi Aviv, operations management.