Managing Queues with Heterogeneous Servers

Kim, Jung Hyun; Ahn, Hyun‐Soo; Righter, Rhonda

doi:10.1017/s002190020000797x

Cited by 7 publications

(11 citation statements)

References 19 publications

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“…Kim, et al [7] considered the multiple server case of the slow server problem assuming two customer classes: primary and secondary. Primary customers have non-preemptive priority over secondary customers and arrive according to a Poisson process.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control of a Two-Server Queueing System With Failures

Özkan¹,

Kharoufeh²

2014

Prob. Eng. Inf. Sci.

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We consider the problem of controlling a two-server Markovian queueing system with heterogeneous servers. The servers are differentiated by their service rates and reliability attributes (i.e., the slower server is perfectly reliable, whereas the faster server is subject to random failures). The aim is to dynamically route customers at arrival, service completion, server failure, and server repair epochs to minimize the long-run average number of customers in the system. Using a Markov decision process model, we prove that it is always optimal to route customers to the faster server when it is available, irrespective of its failure and repair rates, if the system is stable. For the slower server, there exists an optimal threshold policy that depends on the queue length and the state of the faster server. Additionally, we analyze a variant of the main model in which there are multiple unreliable servers with identical service rates, but distinct reliability characteristics. For that case it is always optimal to route customers to idle servers, and the optimal policy is insensitive to the servers’ reliability characteristics.

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Section: Introductionmentioning

confidence: 99%

“…This was done by first showing that the individual optimal policy for a primary customer is of threshold type and, subsequently, that the individual optimal policy is also socially optimal. An interesting point in [7] is that the inclusion of a secondary customer class actually simplifies the proofs significantly.…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Two-Server Queueing System With Failures

Özkan¹,

Kharoufeh²

2014

Prob. Eng. Inf. Sci.

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“…• < 1 is not fulfilled (in which case the geometric series in (14) does not converge). Various approaches are possible, of which we present two possibilities.…”

Section: Bounds and Relative Errormentioning

confidence: 99%

“…In many practical situations, however, this assumption is overly restrictive as has been recognized in the work of, e.g., Refs. [1,14] (as well as in other references that deal with the problem of routing in systems with heterogeneous servers). Not much is known, however, about the tail distribution of such heterogeneous multi-server systems.…”

Section: Introductionmentioning

confidence: 99%

Efficient simulation of tail probabilities in a queueing model with heterogeneous servers

Kühn

Mandjes

2018

Stochastic Models

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This paper considers a multi-server queue with Markovmodulated Poisson input and server-dependent phase-type service times. We develop an efficient rare-event simulation technique to estimate the probability that the number of customers in this system reaches a high value. Relying on explicit bounds on the probability under consideration as well as the associated likelihood ratio, we succeed in proving that the proposed estimator is of bounded relative error. Simulation experiments illustrate the significant speed-up that can be achieved by the proposed algorithm.

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“…They proposed an efficient service requirement (job size) based policy referred to as size interval task assignment or SITA for short, which Feng et al [12] later proved to be the optimal policy in the given setting (see also [15]). [21] and [36]. Additionally, dispatching problems have been studied in, e.g.…”

Section: Prior Workmentioning

confidence: 99%

On the Value Function of the M/G/1 FCFS and LCFS Queues

Hyytiä¹,

Aalto²,

Penttinen³

et al. 2012

J. Appl. Probab.

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We consider a single-server queue with Poisson input operating under first-come-firstserved (FCFS) or last-come-first-served (LCFS) disciplines. The service times of the customers are independent and obey a general distribution. The system is subject to costs for holding a customer per unit of time, which can be customer specific or customer class specific. We give general expressions for the corresponding value functions, which have elementary compact forms, similar to the Pollaczek-Khinchine mean value formulae. The results generalize earlier work where similar expressions have been obtained for specific service time distributions. The obtained value functions can be readily applied to develop nearly optimal dispatching policies for a broad range of systems with parallel queues, including multiclass scenarios and the cases where service time estimates are available.

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Managing Queues with Heterogeneous Servers

Cited by 7 publications

References 19 publications

Optimal Control of a Two-Server Queueing System With Failures

Optimal Control of a Two-Server Queueing System With Failures

Efficient simulation of tail probabilities in a queueing model with heterogeneous servers

On the Value Function of the M/G/1 FCFS and LCFS Queues

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