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- research-articleJanuary 2024
Adaptive service rate control of an M/M/1 queue with server breakdowns
Queueing Systems: Theory and Applications (QSYS), Volume 106, Issue 1-2Feb 2024, Pages 159–191https://doi.org/10.1007/s11134-023-09900-zAbstractWe study service rate control problems for an M/M/1 queue with server breakdowns in which the breakdown rate is assumed to be a function of the service rate. Assuming that the queue has infinite capacity, we first establish the optimality ...
- research-articleNovember 2023
- research-articleNovember 2023
Join-Up-To(m): improved hyperscalable load balancing
Queueing Systems: Theory and Applications (QSYS), Volume 105, Issue 3-4Dec 2023, Pages 291–316https://doi.org/10.1007/s11134-023-09897-5AbstractVarious load balancing policies are known to achieve vanishing waiting times in the large-scale limit, that is, when the number of servers tends to infinity. These policies either require a communication overhead of one message per job or require ...
- research-articleDecember 2022
On the Gittins index for multistage jobs
Queueing Systems: Theory and Applications (QSYS), Volume 102, Issue 3-4Dec 2022, Pages 353–371https://doi.org/10.1007/s11134-022-09760-zAbstractOptimal scheduling in single-server queueing systems is a classic problem in queueing theory. The Gittins index policy is known to be the optimal nonanticipating policy minimizing the mean delay in the M/G/1 queue. While the Gittins index is ...
- research-articleDecember 2022
A general “power-of-d” dispatching framework for heterogeneous systems
Queueing Systems: Theory and Applications (QSYS), Volume 102, Issue 3-4Dec 2022, Pages 431–480https://doi.org/10.1007/s11134-022-09736-zAbstractIntelligent dispatching is crucial to obtaining low response times in large-scale systems. One common scalable dispatching paradigm is the “power-of-d,” in which the dispatcher queries d servers at random and assigns the job to a server based only ...
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- research-articleOctober 2022
- research-articleOctober 2022
- research-articleOctober 2022
Queueing and risk models with dependencies
Queueing Systems: Theory and Applications (QSYS), Volume 102, Issue 1-2Oct 2022, Pages 69–86https://doi.org/10.1007/s11134-022-09863-7AbstractThis paper analyzes various stochastic recursions that arise in queueing and insurance risk models with a ‘semi-linear’ dependence structure. For example, an interarrival time depends on the workload, or the capital, immediately after the previous ...
- research-articleOctober 2022
- research-articleOctober 2022
Optimal staffing for ticket queues
Queueing Systems: Theory and Applications (QSYS), Volume 102, Issue 1-2Oct 2022, Pages 309–351https://doi.org/10.1007/s11134-022-09854-8AbstractTicket queues are popular in many service systems. Upon arrival, each customer is issued a numbered ticket and receives service on a first-come-first-served basis according to the ticket number. There is no physical queue; customers may choose to ...
- research-articleSeptember 2022
- research-articleAugust 2022
Age of information using Markov-renewal methods
Queueing Systems: Theory and Applications (QSYS), Volume 103, Issue 1-2Feb 2023, Pages 95–130https://doi.org/10.1007/s11134-022-09852-wAbstractWhen designing a message transmission system, from the point of view of making sure that the information transmitted is as fresh as possible, two rules of thumb seem reasonable: use small buffers and adopt a last-in-first-out policy. In this ...
- research-articleAugust 2022
- research-articleAugust 2022
Asymptotics of waiting time distributions in the accumulating priority queue
Queueing Systems: Theory and Applications (QSYS), Volume 101, Issue 3-4Aug 2022, Pages 221–244https://doi.org/10.1007/s11134-022-09839-7AbstractWe analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by Kleinrock in the 60s—he coined it time-dependent priority—to ...
- research-articleAugust 2022
Applying optimization theory to study extremal GI/GI/1 transient mean waiting times
Queueing Systems: Theory and Applications (QSYS), Volume 101, Issue 3-4Aug 2022, Pages 197–220https://doi.org/10.1007/s11134-021-09725-8AbstractWe study the tight upper bound of the transient mean waiting time in the classical GI/GI/1 queue over candidate interarrival-time distributions with finite support, given the first two moments of the interarrival time and the full service-time ...
- research-articleJune 2022
Tandem fluid queue with long-range dependent inputs: sticky behaviour and heavy traffic approximation
Queueing Systems: Theory and Applications (QSYS), Volume 101, Issue 1-2Jun 2022, Pages 165–196https://doi.org/10.1007/s11134-022-09798-zAbstractEmpirical studies have shown that traffic in communication networks exhibits long-range dependence. Cumulative network traffic is often thought to be well modelled by a fractional Brownian motion (fBm). FBm approximations of queueing systems have ...
- research-articleJune 2022
Heavy traffic limits for queues with non-stationary path-dependent arrival processes
Queueing Systems: Theory and Applications (QSYS), Volume 101, Issue 1-2Jun 2022, Pages 113–135https://doi.org/10.1007/s11134-021-09728-5AbstractIn this paper, we develop a diffusion approximation for the transient distribution of the workload process in a standard single-server queue with a non-stationary Polya arrival process, which is a path-dependent Markov point process. The path-...
- research-articleJune 2022
- letterApril 2022