New perspectives on the Erlang-A queue

Daw, Andrew; Pender, Jamol

doi:10.1017/apr.2019.11

Cited by 11 publications

(4 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Foundational results on fluid approximations can be traced back to Mandelbaum et al (1998), Whitt (2006), and Kang et al (2010) for cases with reneging. The precision of fluid approximations are evaluated in Bassamboo and Randhawa (2010); Daw and Pender (2019) while Pender et al (2017) use the approach to analyze the impact of delay announcements. Unlike previous work which grounds the evaluation of system performance on a set of distributional assumptions applied to the fluid model (e.g., Randhawa 2015, Jouini et al 2013), we focus solely on analyzing the performance of the fluid model.…”

Section: Literature Review and Contributionmentioning

confidence: 99%

See 1 more Smart Citation

Customer Acquisition and Retention: A Fluid Approach for Staffing

Furman

Diamant

Kristal

2021

Production and Operations Management

View full text Add to dashboard Cite

W e investigate the trade-off between acquisition and retention efforts when customers are sensitive to the quality of service they receive, that is, whether they get timely access to a company's resources when requested. We model the problem as a multi-class queueing network with new and returning customers, time-dependent arrivals, and abandonment. We derive its fluid approximation; a system of ordinary linear differential equations with continuous, piecewise smooth, right-hand sides. Based on the fluid model, we propose a novel approach to determine optimal stationary staffing levels for new and returning customer queues in anticipation of future time-varying dynamics. Using system accessibility as a proxy for service quality and staffing levels as a proxy for investment, we demonstrate how to apply our approach to two families of time-varying arrival functions motivated by real-world applications: an advertising campaign and a clinical setting. In a numerical study, we demonstrate that our approach creates staffing policies that maximize throughput while balancing acquisition and retention efforts more effectively (i.e., equitable abandonment from each customer class) than commonly used near-stationary methods such as variants of square-root staffing policies. Our model confirms that acquisition and retention efforts are intimately linked; this has been found in empirical studies but not captured in the operations literature. We suggest that in time-varying environments, focusing on either alone is not sufficient to maintain high levels of throughput and service quality.

show abstract

Section: Literature Review and Contributionmentioning

confidence: 99%

“…(2010) for cases with reneging. The precision of fluid approximations are evaluated in Bassamboo and Randhawa (2010); Daw and Pender (2019) while Pender et al. (2017) use the approach to analyze the impact of delay announcements.…”

Section: Literature Review and Contributionmentioning

confidence: 99%

Customer Acquisition and Retention: A Fluid Approach for Staffing

Furman

Diamant

Kristal

2021

Production and Operations Management

View full text Add to dashboard Cite

show abstract

“…We again consider a three phase distributed service and display a pair of scenarios. In both parameter groups θ = [.15, .4, .45] T and µ = [1,4,6] T . In the first setting we consider α = 1 2 , β = 1, and λ * = 2, whereas in the second setting α = 1, β = 2, and λ * = 2.…”

Section: Simulation Studymentioning

confidence: 99%

“…This presents new challenges for deriving analytical formulas and approximations for the moment behavior of this type of queueing model. Work by Massey and Pender [14], Pender [25,24,26,30], Daw and Pender [6] shows that simple closure approximations or spectral expansions can be effective at approximating the dynamics of the Erlang-A model and variants. Thus, a natural extension is to apply these techniques to the Erlang-A setting when it is driven by a Hawkes process.…”

Section: Conclusion and Final Remarksmentioning

confidence: 99%

Queues Driven by Hawkes Processes

Daw

Pender

2018

Stochastic Systems

Self Cite

View full text Add to dashboard Cite

Many stochastic systems have arrival processes that exhibit clustering behavior. In these systems, arriving entities influence additional arrivals to occur through selfexcitation of the arrival process. In this paper, we analyze an infinite server queueing system in which the arrivals are driven by the self-exciting Hawkes process and where service follows a phase-type distribution or is deterministic. In the phase-type setting, we derive differential equations for the moments and a partial differential equation for the moment generating function; we also derive exact expressions for the transient and steady-state mean, variance, and covariances. Furthermore, we also derive exact expressions for the auto-covariance of the queue and provide an expression for the cumulant moment generating function in terms of a single ordinary differential equation. In the deterministic service setting, we provide exact expressions for the first and second moments and the queue auto-covariance. As motivation for our Hawkes queueing model, we demonstrate its usefulness through two novel applications. These applications are trending internet traffic and arrivals to nightclubs. In the web traffic setting, we investigate the impact of a click. In the nightclub or Club Queue setting, we design an optimal control problem for the optimal rate to admit club-goers.

show abstract

On the distributions of infinite server queues with batch arrivals

Daw

Pender

2019

Queueing Syst

View full text Add to dashboard Cite

New perspectives on the Erlang-A queue

Cited by 11 publications

References 48 publications

Customer Acquisition and Retention: A Fluid Approach for Staffing

Customer Acquisition and Retention: A Fluid Approach for Staffing

Queues Driven by Hawkes Processes

On the distributions of infinite server queues with batch arrivals

Contact Info

Product

Resources

About