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 health care (emergency department physicians), contact centers (agents handling multiple on-line 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 formulate a birth-death process that approximates the baseline system’s performance. Many systems place an upper limit on the number of customers simultaneously handled by each case manager. We examine the impact of these case-load limits on waiting time and describe effective, heuristic methods for setting these limits