The staffing of parallel servers in a queue has interested operations researchers for decades, resulting in countless mathematical models studying queuing behavior. But to achieve tractability, these models typically assume the service rate and productivity of individual servers is independent of other servers and the status of the system. We question this assumption and consider whether inter-server dependence impacts queue performance, specifically through server task selection. Allowing discretion in task pick-up violates the independent-server assumption, but modelling this discretion becomes feasible with an improved understanding of the system. To this end, we evaluate the impact of worker familiarity on system-level outcomes. Using a year of data from multiple hospital emergency departments, we find greater average familiarity between physicians leads to greater patient pick-up likelihood, lower waiting room census and shorter patient wait times, particularly for severe patients. We also find dispersion in familiarity leads to a reduced patient pick-up likelihood and greater waiting room census with no impact on patient wait times. Furthermore, both effects vary with workload, a common catalyst for further violations of the independent server assumption. We discuss the implications of our work for queuing system managers and healthcare operations, in general.
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