On the Pooling of Queues: How Server Behavior Affects Performance

It is widely accepted that multi-server single-queue (SQ) systems outperform multi-server parallel-queue (PQ) systems due to the pooling effect. However, humans are not machines, and the assumption that servers perform identically regardless of the queueing system, is not necessarily true in practice. In this paper, we investigate the impact of two human server behaviors - social loafing and workload-dependent speedup - and one physical factor - walking time - on the performance of the SQ and PQ systems. We develop theoretical models and comparatively analyze them with respect to three queueing performance measures: expected wait time, pre-service time, and total system time. We propose functional forms for social loafing and speedup effects and evaluate the performance of the models numerically. We find that social loafing worsens the performance of the SQ system. Server speedup improves performance of the PQ system. Moreover, this improvement is greater than the direct impact of a comparable average increase in the server's speed. We derive thresholds beyond which PQ outperform SQ systems for all three performance measures. Our findings provide managers with guidance in the design of their queueing operations and serve as a foundation for future research on service systems with behavioral elements.