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Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Heavy Traffic Regime
2004
Operations Research
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We consider a Markovian model of a multiclass queueing system in which a single large pool of servers attends to the various customer classes. ...
The problem studied is that of dynamically scheduling the various classes. ...
They also thank Rami Atar for his careful reading and helpful comments, and Avi Mandelbaum for providing them with preprints of his work with R. Atar and M. Reiman. ...
doi:10.1287/opre.1030.0084
fatcat:m5wb6sadsvag7hvh7fdj6dzpie
Dynamic Scheduling of a Multiclass Queue in the Halfin-Whitt Regime: A Computational Approach for High-Dimensional Problems
[article]
2023
arXiv
pre-print
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We consider a multi-class queueing model of a telephone call center, in which a system manager dynamically allocates available servers to customer calls. ...
Using this computational method, we propose a policy for the original (pre-limit) call center scheduling problem. ...
Introduction Motivated by call center operations, this paper considers a dynamic scheduling problem for a multiclass queueing system with a single pool of servers. ...
arXiv:2311.18128v1
fatcat:ekl432gynjhkflfs5a2lomvecy
Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems
2018
Manufacturing & Service Operations Management
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One of our main results is that for a class of parameters, we establish sufficient conditions for both the optimality and non-optimality of threshold policies. ...
Problem definition: We study optimal scheduling of customers in service systems, such as call centers. ...
Instead, we need to keep track of the queue-length process for each class to describe the system dynamics, and hence we require a K-dimensional diffusion process to approximate these dynamics. ...
doi:10.1287/msom.2017.0642
fatcat:xdkdejubpbczzalmxn3dhmdqjy
Marginal productivity index policies for scheduling a multiclass delay-/loss-sensitive queue
2006
Queueing systems
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We address the problem of scheduling a multiclass M/M/1 queue with a finite dedicated buffer for each class. ...
We develop new dynamic index policies, prescribing to give higher service priority to classes with larger index values, where the priority index of a class measures the marginal productivity of work at ...
A short version of the paper appeared in the proceedings of the latter conference. See [9] . ...
doi:10.1007/s11134-006-0302-x
fatcat:plkazfvox5cvxla2us6uctwzcm
The achievable region method in the optimal control of queueing systems; formulations, bounds and policies
1995
Queueing systems
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, polling systems, multiclass queueing and loss networks. ...
These relaxations lead to bounds on the performance of an optimal policy. ...
Tsoucas [57] derived the region of achievable performance in the problem of scheduling a multiclass nonpreemptive M/G/1 queue with Bernoulli feedback, introduced by Klimov [35] . ...
doi:10.1007/bf01149167
fatcat:6mljtnhjnvgulfpoozhawm5254
Scheduling control for Markov-modulated single-server multiclass queueing systems in heavy traffic
2014
Queueing systems
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This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. ...
the classical cμ-policy (the priority policy that favors classes with higher values of the product of holding cost c and service rate μ) is asymptotically optimal for an infinite horizon discounted cost ...
We consider a scheduling control problem, where the controller decides (dynamically, at each time point t ≥ 0) which class of jobs should the server process so as to minimize an infinite horizon discounted ...
doi:10.1007/s11134-014-9396-8
fatcat:6zmhysaykjbpvomciuci5rnc2e
Optimal control of queueing networks: an approach via fluid models
2002
Advances in Applied Probability
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We consider a general control problem for networks with linear dynamics which includes the special cases of scheduling in multiclass queueing networks and routeing problems. ...
For scheduling problems in multiclass queueing networks we show the existence of an average-cost optimal decision rule, if the usual traffic conditions are satisfied. ...
the scheduling problem for multiclass queueing networks. ...
doi:10.1239/aap/1025131220
fatcat:lcapxsvk3nfuxapyxgvo53ymbi
On scheduling a multiclass queue with abandonments under general delay costs
2012
Queueing systems
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We consider a multiclass queueing system with abandonments and general delay costs. A system manager makes dynamic scheduling decisions to minimize long-run average delay and abandonment costs. ...
Interpreting that control in the context of the original queueing system, we propose practical policies for each of the three cases considered and demonstrate their effectiveness through a simulation study ...
Introduction This paper studies dynamic scheduling of a multiclass queue with abandonments in the heavy traffic regime. The objective is to minimize the average delay and abandonment costs. ...
doi:10.1007/s11134-012-9326-6
fatcat:pafhkup7yffvboavv4qbpbo5de
On the optimality of exhaustive service policies in multiclass queueing systems with modulated arrivals and switchovers
1997
Sadhana (Bangalore)
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Consider a single-server multiclass queueing system with K classes where the individual queues are fed by K-correlated interrupted Poisson streams generated in the states of a K-state stationary modulating ...
It is required to minimize the sum of discounted inventory and setup costs over an infinite horizon. We provide sufficient conditions under which exhaustive service policies are optimal. ...
This research was supported in part by the Office of Naval Research and the Department of Science and Technology grant N00014-93-1017. ...
doi:10.1007/bf02744127
fatcat:mtydvzx7qrhsnizgclo562zw2a
Optimal control of Markov-modulated multiclass many-server queues
[article]
2018
arXiv
pre-print
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We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. ...
We address the infinite-horizon discounted and long-run average (ergodic) optimal control problems and establish asymptotic optimality. ...
Acknowledgement This work is supported in part by an Army Research Office grant W911NF-17-1-0019, in part by NSF grants DMS-1715210, CMMI-1635410, and DMS/CMMI-1715875, and in part by Office of Naval Research ...
arXiv:1808.04049v1
fatcat:nznq5cdo2fhkvit4mx3i32wja4
Stochastic scheduling of parallel queues with set-up costs
1995
Queueing systems
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We partially characterize an optimal policy and provide a simple heuristic scheduling policy. ...
The heuristic's performance is evaluated in the cases of two and three queues by comparison with a numerically obtained optimal policy. ...
In this paper, we address the stochastic scheduling of a system with several different types of jobs and switching costs in the context of a multiclass M/G/1 queue. ...
doi:10.1007/bf01151932
fatcat:komdwikruveklemxailn7ncqaq
The Gittins Policy in the M/G/1 Queue
[article]
2021
arXiv
pre-print
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The Gittins policy is a highly general scheduling policy that minimizes a wide variety of mean holding cost metrics in the M/G/1 queue. ...
For example, the well-known "cμ rule", which minimizes class-weighted mean response time in the multiclass M/M/1, is a special case of Gittins. ...
SYSTEM MODEL: THE M B /G MP /1 QUEUE We study scheduling in a generalization of the M/G/1 queue to minimize a variety of mean holding cost metrics. ...
arXiv:2111.10703v1
fatcat:g5jtxypzkffmbg5l7cqicoilkm
Dynamic Scheduling for Markov Modulated Single-server Multiclass Queueing Systems in Heavy Traffic
[article]
2012
arXiv
pre-print
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The file type is application/pdf.
This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. ...
the classical c\mu -policy (the priority policy that favors classes with higher values of the product of holding cost c and service rate \mu) is asymptotically optimal for an infinite horizon discounted ...
We consider a scheduling control problem, where the controller decides (dynamically, at each time point t ≥ 0) which class of jobs should the server process so as to minimize an infinite horizon discounted ...
arXiv:1211.6831v1
fatcat:5wo3gb46ljdmviisjwg5o54oga
An ergodic control problem for many-server multiclass queueing systems with cross-trained servers
[article]
2017
arXiv
pre-print
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We provide a complete analysis for the limiting ergodic control problem and establish asymptotic convergence of the value functions for the queueing model ...
We formulate an ergodic control problem where the running cost is given by a non- negative convex function with polynomial growth. ...
It should be noted that for our queueing model we have fixed a cross-training structure and we are trying to investigate the optimal dynamic scheduling policy that will optimize the pay-off function. ...
arXiv:1502.02779v4
fatcat:xlhwx7thfzaatns6y4bp7yhj2e
An Explicit Solution for the Value Function of a Priority Queue
2004
Queueing systems
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We consider a multiclass preemptive-resume priority queue with Poisson arrivals and general service times. ...
We derive explicit expressions for the discounted expected and long-run average weighted queue lengths and switching costs, the latter one only in the case of exponential service times. ...
Another related study is the work by Harrison [6] who found a closedform expression for the total expected discounted holding cost in a multiclass non-preemptive resume priority queue with Poisson inputs ...
doi:10.1023/b:ques.0000035315.17476.0b
fatcat:dzaw2lt225hvfoh5646u3oel5m
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