Virtual allocation policies for many-server queues with abandonment

Long, Zhenghua; Zhang, Jiheng

doi:10.1007/s00186-019-00683-9

Cited by 5 publications

(4 citation statements)

References 35 publications

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“…Our work differs because we optimize scheduling decisions across different classes (distinguished by patience-time distributions and associated abandonment costs) but assume customers are served in the FCFS manner within the same class. Long and Zhang (2015) propose a scheduling policy for a multiclass GI/GI/N+GI system and prove its asymptotic optimality in the fluid scale when the patience-time distribution for each class has a decreasing hazard rate. In our work, the hazard rate function can take any form, and we propose a scheduling policy based on the optimization problem in the diffusion scale.…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems

Kim

Randhawa

Ward

2018

M&SOM

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Problem definition: We study optimal scheduling of customers in service systems, such as call centers. In such systems, customers typically hang up and abandon the system if their wait for service is too long. Such abandonments are detrimental for the system, and so managers typically use scheduling as a tool to mitigate it. In this paper, we study the interplay between customer impatience and scheduling decisions when managing heterogeneous customer classes. Academic/practical relevance: Call centers constitute a large industry that has a global spending of around $300 billion and employs more than 15 million people worldwide. Our work focuses on improving call center operations, which can reduce costs and improve customer satisfaction. Mathematically, customer patience is typically modeled as exponentially distributed for tractability. Our work makes inroads into relaxing this restrictive assumption to allow modeling more realistic call center situations. Methodology: We use heavy traffic-motivated asymptotic queueing machinery that provides us the traction to successfully capture and incorporate the customer impatience distribution into the scheduling problem. In our approach, the scheduling problem reduces to a diffusion control problem, which we solve to propose near-optimal scheduling policies. Results: We propose near-optimal scheduling policies that can be implemented by call centers to improve their quality-of-service metrics. One of our main results is that, for a class of parameters, we establish sufficient conditions for both the optimality and nonoptimality of threshold policies. Managerial implications: Threshold policies are widely used for scheduling. Our work provides additional insight into whether these may be suboptimal. Our work provides an easy-to-implement alternative that can reduce customer abandonments considerably; for instance, our numerical results indicate that for a system with two customer types, the abandonment rate of one class can be lowered by 30% by using our policy relative to the best threshold policy.

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Section: Literature Reviewmentioning

confidence: 99%

Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems

Kim

Randhawa

Ward

2018

M&SOM

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“…When the hazard rate function of the service distribution is decreasing, we use a reformulation in terms of renewal equations, in conjunction with certain recursive estimates, and the convergence of the measure-valued state processes is with respect to the weak topology (see Section 4.3). These arguments are inspired by those used in the work [26], which studies the long-time behavior of fluid equations for the GI/G/N+G model under the assumption that the service time distribution has a concave or convex renewal function (which is implied by decreasing hazard rate functions). However, the fluid equations of [26] are based on a different measure-valued state representation, involving residual service times of customers rather than ages, and moreover, convergence is established in [26] for the queue process, not the measure-valued process.…”

mentioning

confidence: 99%

“…These arguments are inspired by those used in the work [26], which studies the long-time behavior of fluid equations for the GI/G/N+G model under the assumption that the service time distribution has a concave or convex renewal function (which is implied by decreasing hazard rate functions). However, the fluid equations of [26] are based on a different measure-valued state representation, involving residual service times of customers rather than ages, and moreover, convergence is established in [26] for the queue process, not the measure-valued process. Thus the results of [26] do not directly apply.…”

mentioning

confidence: 99%

“…However, the fluid equations of [26] are based on a different measure-valued state representation, involving residual service times of customers rather than ages, and moreover, convergence is established in [26] for the queue process, not the measure-valued process. Thus the results of [26] do not directly apply. Moreover, we also need to establish additional estimates to prove convergence of the measure-valued process ν in the supercritical case.…”

mentioning

confidence: 99%

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Large-time limit of nonlinearly coupled measure-valued equations that model many-server queues with reneging

Atar,

Kang,

Kaspi

et al. 2021

Preprint

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The large-time behavior of a nonlinearly coupled pair of measure-valued transport equations with discontinuous boundary conditions, parameterized by a positive real-valued parameter λ, is considered. These equations describe the hydrodynamic or fluid limit of many-server queues with reneging (with traffic intensity λ), which model phenomena in diverse disciplines, including biology and operations research. For a broad class of reneging distributions with finite mean and service distributions with finite mean and hazard rate function that is either decreasing or bounded away from zero and infinity, it is shown that if the fluid equations have a unique invariant state, then the Dirac measure at this state is the unique random fixed point of the fluid equations, which implies that the stationary distributions of scaled N -server systems converge to the unique invariant state of the corresponding fluid equations. Moreover, when λ = 1, it is shown that the solution to the fluid equation starting from any initial condition converges to this unique invariant state in the large time limit. The proof techniques are different under the two sets of assumptions on the service distribution. When the hazard rate function is decreasing, a reformulation of the dynamics in terms of a certain renewal equation is used, in conjunction with recursive asymptotic estimates. When the hazard rate function is bounded away from zero and infinity, the proof uses an extended relative entropy functional as a Lyapunov function. Analogous large-time convergence results are also established for a system of coupled measure-valued equations modeling a multiclass queue.

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Long-Time Limit of Nonlinearly Coupled Measure-Valued Equations that Model Many-Server Queues with Reneging

Atar,

Kang,

Kaspi

et al. 2023

SIAM J. Math. Anal.

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Virtual allocation policies for many-server queues with abandonment

Cited by 5 publications

References 35 publications

Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems

Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems

Large-time limit of nonlinearly coupled measure-valued equations that model many-server queues with reneging

Long-Time Limit of Nonlinearly Coupled Measure-Valued Equations that Model Many-Server Queues with Reneging

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