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. Limited analytical work, however, has been done to investigate how these behavioral factors affect the overall performance of different queueing system designs. In this paper, 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 on the queue size can be decomposed into a direct impact that reduces the queue size due to an increase in the expected service rate, and an indirect impact that further reduces the queue size due to smoothing. We quantify the performance impacts associated with both behavioral factors and clearly illustrate the conditions where each effect dominates and derive threshold values for these behavioral effects beyond which PQ systems outperform SQ systems. Finally, we consider strategic routing and its impact on the performance of the PQ system. Our analytical contributions and numerical analyses offer generalized managerial guidance regarding the choice of the queueing system design and provide a theoretical foundation for future research in behavioral queueing.

Keywords: Service System Design, Workload-dependent Service Rate, Behavioral Queueing