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

Abstract

R ecent 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.

Can we work more safely and healthily with robot partners? A human‐friendly robot–human‐coordinated order fulfillment scheme

“…However, such an ideal state of Subsystem 3 is obtained at the cost of the picker's accumulated fatigue ($${\rho }_k$$). Worker fatigue is multidimensional and often increases with time (Glock, Grosse, Kim, et al., 2019; Jaber et al., 2013), stress, and workload (Do et al., 2018; Kc & Terwiesch, 2009; MacDonald, 2003), particularly when a picker must perform repetitive picking and packaging tasks. Based on the learning–forgetting–fatigue–recovery models established in the ergonomics‐related literature (Glock, Grosse, Kim, et al., 2019; Jaber et al., 2013), the commonly used deterministic exponential form of accumulated fatigue is extended herein into a dynamic stochastic form.…”

“…Do et al. (2018) assumed that the service rate has a multiplicative form under the effect of overwork. With reference to the fatigue‐recovery model of Jaber et al.…”

“…However, such an ideal state of Subsystem 3 is obtained at the cost of the picker's accumulated fatigue (𝜌 k ). Worker fatigue is multidimensional and often increases with time (Glock, Grosse, Kim, et al, 2019;Jaber et al, 2013), stress, and workload (Do et al, 2018;Kc & Terwiesch, 2009;MacDonald, 2003), particularly when a picker must perform repetitive picking and packaging tasks.…”

To Pool or Not to Pool? The Effect of Loss Aversion on Queue Configurations

“…Armony et al (2021) further categorize numerous drivers that reduce the benefits of pooled queues across two dimensions (customer/server-related and exogenous/endogenous). In addition to the two human-related factors mentioned above, Do et al (2018) emphasize that the effect of the physical factor "walking time" (from the head of the queue to a server) may also make dedicated queues more preferable. Cao et al (2020) demonstrate that a dedicated structure along with the join-the-shortest-queue routing policy may achieve a lower probability of delay or a higher service level than a pooled structure.…”

Analytical thinking, Little's Law understanding, and stock‐flow performance: two empirical studies

“…Gerst, 2004) and queuing systems (e.g. Andalib et al ., 2018; Do et al ., 2018; Ghaffarzadegan and Larson, 2018; Sankaranarayanan et al ., 2012). Thus, it can be inferred that Little's Law can be applied to stock‐flow systems, and its understanding can mediate the effect of analytical thinking on performance in stock‐flow problems.…”