Abstract:We model the work of a front-line service worker as a queueing system. The server interacts with customers in a multi-stage process with random durations. Some stages require an interaction between server and customer, while other stages are performed by the customer as a self-service task or with the help of another resource. Random arrivals by customers at the beginning and during an encounter create random lengths of idle time in the work of the server (breaks and interludes respectively). The server consid… Show more
“…A related set of papers on multitasking are queuing models with one server or group of servers balancing two work queues (Gans andZhou 2003, Legros et al 2020). Legros et al (2020) discuss service operators' switching between customer interaction and back-office tasks. They derive optimal threshold policies for using the interlude time between customer interactions.…”
Section: Literature Reviewmentioning
confidence: 99%
“…Although much emphasis is placed on the primary tasks to be completed, such as patient treatment or surgery (Bartel et al 2020, Youn et al 2022, assembling a car in a factory (Bernstein & Kok 2009), or answering a call in a call center (Aksin et al 2007), operations also include secondary tasks that support the primary work (Dai et al 2015, Legros et al 2020. These might consist of EHR use, hand hygiene (Dai et al 2015) or lab tests in healthcare (Batt and Terwiesch 2017), supply positioning or tool preparation in manufacturing, or data entry in call centers.…”
“…A related set of papers on multitasking are queuing models with one server or group of servers balancing two work queues (Gans andZhou 2003, Legros et al 2020). Legros et al (2020) discuss service operators' switching between customer interaction and back-office tasks. They derive optimal threshold policies for using the interlude time between customer interactions.…”
Section: Literature Reviewmentioning
confidence: 99%
“…Although much emphasis is placed on the primary tasks to be completed, such as patient treatment or surgery (Bartel et al 2020, Youn et al 2022, assembling a car in a factory (Bernstein & Kok 2009), or answering a call in a call center (Aksin et al 2007), operations also include secondary tasks that support the primary work (Dai et al 2015, Legros et al 2020. These might consist of EHR use, hand hygiene (Dai et al 2015) or lab tests in healthcare (Batt and Terwiesch 2017), supply positioning or tool preparation in manufacturing, or data entry in call centers.…”
“…This also makes a difference with our context, where urgent customers can interrupt the treatment of some back-office tasks. In a context with switching time allocation between urgent and nonurgent tasks, Legros et al (2020) showed that idling in the presence of waiting customers may be optimal to avoid too many switches. Further references on queue-blending operations include Keblis and Chen (2006); Pichitlamken et al (2003); Pang and Perry (2014).…”
Section: Literature Reviewmentioning
confidence: 99%
“…Although nonoptimal, this policy has the advantage of not letting the agent leave any customers waiting in the queue since this would not be appreciated in visible systems. It also reduces the frequency of switches between idle and busy states for the agent (Legros et al, 2020). The stationary probabilities are computed via a two‐dimensional Markov chain analysis.…”
This study aims to determine and evaluate dynamic idling policies where an agent can idle while some customers remain waiting. This type of policies can be employed in situations where the flow of urgent customers does not allow the agent to spend sufficient time on back‐office tasks. We model the system as a single‐agent exponential queue with abandonment. The objective is to minimize the system's congestion while ensuring a certain proportion of idling time for the agent. Using a Markov decision process approach, we prove that the optimal policy is a threshold policy according to which the agent should idle above (below) a certain threshold on the queue length if the congestion‐related performance measure is concave (convex) with respect to the number of customers present. We subsequently obtain the stationary probabilities, performance measures, and idling time duration, expressed using complex integrals. We show how these integrals can be numerically computed and provide simpler expressions for fast‐agent and heavy‐traffic asymptotic cases. In practice, the most common way to regulate congestion is to control access to the service by rejecting some customers upon arrival. Our analysis reveals that idling policies allow high levels of idling probability that such rejection policies cannot reach. Furthermore, the greatest benefit of implementing an optimal idling policy occurs when the objective occupation rate is close to 50% in highly congested situations.
“…Then, the agent reservation policy can be implemented, that is, when the number of agents reserved for the inbound calls reaches a threshold, an agent can make an outbound call or respond to an email request. We refer the interested reader for further reading on call blending to Deslauriers et al (2007), Pang and Perry (2014), Legros et al (2015Legros et al ( , 2020.…”
In this paper, we study the M n ∕M n ∕c∕(K 1 + K 2 ) + M n system with two finite-size queues where underlying exponential random variables have state-dependent rates. When all servers are busy, upon arrival customers may join the online or the offline/ callback queue or simply balk. Customers waiting in the online queue are impatient and if their patience expires, they may choose to join the callback queue instead of abandoning the system for good. Customers in the callback queue are assumed to be patient. Customers are served following a threshold policy: when the number of customers in the callback queue surpasses a threshold level, the next customer to serve is picked from here. Otherwise, only after a predetermined number of agents are reserved for future arrivals, customers remaining in the callback queue can be served. We conduct an exact analysis of this system and obtain its steady-state performance measures. The times spent in both queues are expressed as Phase-type distributions. With numerical examples, we present how the policy responds when shorter callback times are promised or customer characteristics vary.
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