Diagnostic Accuracy Under Congestion

Abstract

I n diagnostic services, agents typically need to weigh the benefit of running an additional test and improving the accuracy of diagnosis against the cost of delaying the provision of services to others. Our paper analyzes how to dynamically manage this accuracy/congestion trade-off. To that end, we study an elementary congested system facing an arriving stream of customers. The diagnostic process consists of a search problem in which the service provider conducts a sequence of imperfect tests to determine the customer's type. We find that the agent should continue to perform the diagnosis as long as her current belief that the customer is of a given type falls into an interval that depends on the congestion level as well as the number of performed tests thus far. This search interval should shrink as congestion intensifies and as the number of performed tests increases if additional conditions hold. Our study reveals that, contrary to diagnostic services without congestion, the base rate (i.e., the prior probability of the customer type) has an effect on the agent's search strategy. In particular, the optimal search interval shrinks when customer types are more ambiguous a priori, i.e., as the base rate approaches the value at which the agent is indifferent between types. Finally, because of congestion effects, the agent should sometimes diagnose the customer as being of a given type, even if test results indicate otherwise. All these insights disappear in the absence of congestion.T 0ĉ e − t dt ≥ 0, and hence this term can be dropped from the right-hand side. Next, because J u x k p provides a lower bound for J * x k p , we have

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