Impact of Behavioral Factors on Performance of Multi‐Server Queueing Systems

Abstract

Recent studies have shown that the processing speed of employees in service‐based queueing systems is impacted by various behavioral factors. However, there is limited analytical work to investigate how these behavioral factors affect the overall performance of different queueing system designs. In this study, we focus on the response of human servers to the design and congestion level of the queueing system in which they operate. Specifically, we incorporate two behavioral factors into multi‐server analytical queueing models: (1) server speedup due to increase of workload, and (2) server slowdown due to social loafing when multiple workers share the workload. We evaluate how these factors affect the performance of both the multi‐server single‐queue ( SQ) and multi‐server parallel‐queue ( PQ) system and the relative superiority of each system with respect to the number of customers in queue and the expected wait time in queue. We show that the impact of workload‐dependent speedup can be decomposed into a direct effect and indirect effect on system performance. The direct effect leads to a reduced queue size due to increased expected service rate, while the indirect effect decreases queue size due to the “smoothing” effect. We quantify the performance impacts associated with both behavioral factors, illustrate the conditions where each effect dominates, and derive threshold values for these behavioral effects beyond which PQ systems outperform SQ systems. We also consider strategic routing and its impact on the performance of PQ systems. Our analytical contributions and numerical analyses offer important managerial guidance regarding the choice of the queueing system design and provide a theoretical foundation for future research in behavioral queueing.

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