Dynamic Allocation of Reconfigurable Resources in a Two-Stage Tandem Queueing System With Reliability Considerations

Wu, Cheng-Hung; Lewis, Michael M.; Veatch, Michael H.

doi:10.1109/tac.2005.863518

Cited by 42 publications

(47 citation statements)

References 15 publications

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“…Finally, Andradóttir, Ayhan, and Down [3] consider the dynamic assignment of servers to maximize the long-run average throughput of queueing networks with infinite buffers and failure-prone servers and stations. Note that both Wu, Lewis, and Veatch [13] and Wu, Down, and Lewis [12] assume that only a subset of the servers are flexible and subject to failures, and both Wu, Down, and Lewis [12] and Andradóttir, Ayhan, and Down [3] focus on systems with infinite buffers.…”

Section: Introductionmentioning

confidence: 99%

Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Andradóttir¹,

Ayhan²,

Down³

2008

Prob. Eng. Inf. Sci.

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Consider a tandem queueing network with an infinite supply of jobs in front of the first station, infinite room for completed jobs after the last station, finite buffers between stations, and a number of flexible servers who are subject to failures. We study the dynamic assignment of servers to stations with the goal of maximizing the long-run average throughput. Our main conclusion is that the presence of server failures does not have a major impact on the optimal assignment of servers to stations for the systems we consider. More specifically, we show that when the servers are generalists, any non-idling policy is optimal, irrespective of the reliability of the servers. We also provide theoretical and numerical results for Markovian systems with two stations and two or three servers that suggest that the structure of the optimal server assignment policy does not depend on the reliability of the servers, and that ignoring server failures when assigning servers to stations yields near-optimal throughput. Finally, we present numerical results that illustrate that simple server assignment heuristics designed for larger systems with reliable servers also yield good throughput performance in Markovian systems with three stations and three failure-prone servers.

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Section: Introductionmentioning

confidence: 99%

Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Andradóttir¹,

Ayhan²,

Down³

2008

Prob. Eng. Inf. Sci.

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“…Also, because the work in Dai and Meyn (1995) is for a single server, the focus is on incorporating failure models into the fluid limit methodology rather than on how server flexibility can compensate for failures, which is the focus of our work. While this work was being completed, we became aware of an unpublished paper by Wu et al (2006). They look at a model with two classes, a general number of dedicated servers at each class, and a general number of flexible servers.…”

mentioning

confidence: 99%

“…The objective is to minimize holding cost. However, in Wu et al (2006), the focus does not appear to be on how server flexibility can compensate for failures.…”

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confidence: 99%

Compensating for Failures with Flexible Servers

Andradóttir

Ayhan

Down

2007

Operations Research

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We consider the problem of maximizing capacity in a queueing network with flexible servers, where the classes and servers are subject to failure. We assume that the interarrival and service times are independent and identically distributed, that routing is probabilistic, and that the failure state of the system can be described by a Markov process that is independent of the other system dynamics. We find that the maximal capacity is tightly bounded by the solution of a linear programming problem and that the solution of this problem can be used to construct timed, generalized round-robin policies that approach the maximal capacity arbitrarily closely. We then give a series of structural results for our policies, including identifying when server flexibility can completely compensate for failures and when the implementation of our policies can be simplified. We conclude with a numerical example that illustrates some of the developed insights.

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“…The following lemma implies that when 0 ≤ α ≤ min{ The next lemma provides properties of f 2 that will allow us to study the optimal switch point when µ 11 > µ 21 …”

Section: Properties Of the Optimal Policymentioning

confidence: 99%

“…In the interest of space, we do not provide a complete literature review here, but refer the interested reader to Hopp and Van Oyen [13] for a comprehensive review of the literature in this area, and to Akşin, Armony, and Mehrotra [4], Akşin, Karaesmen, andÖrmeci [5], and Gans, Koole, and Mandelbaum [12] for thorough reviews of the literature on flexible servers in call centers. This paper is most closely related to other works that employ Markov decision process techniques and sample path analysis in determining effective server allocation schemes, see for example Ahn, Duenyas, and Zhang [1], Ahn and Lewis [2], Ahn and Righter [3], Andradóttir and Ayhan [6], Andradóttir, Ayhan, and Down [7,8], Kaufman, Ahn, and Lewis [15],Örmeci [17], Sennott, Van Oyen, and Iravani [19], Van Oyen, Gel, and Hopp [20], and Wu, Lewis, and Veatch [21]. However, these papers only consider cases where the combined rate of a set of collaborating servers is additive (i.e., α = 1).…”

Section: Introductionmentioning

confidence: 99%

Optimal assignment of servers to tasks when collaboration is inefficient

2013

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Consider a Markovian system of two stations in tandem with finite intermediate buffer and two servers. The servers are heterogeneous, flexible, and more efficient when they work on their own than when they collaborate. We determine how the servers should be assigned dynamically to the stations with the goal of maximizing the system throughput. We show that the optimal policy depends on whether or not one server is dominant (i.e., faster at both stations) and on the magnitude of the efficiency loss of collaborating servers. In particular, if one server is dominant then he must divide his time between the two stations and we identify the threshold policy the dominant server should use; otherwise each server should focus on the station where he is the faster server. In all cases, servers only collaborate to avoid idleness when the first station is blocked or the second station is starved, and we determine when collaboration is preferable to idleness as a function of the efficiency loss of collaborating servers.

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Dynamic Allocation of Reconfigurable Resources in a Two-Stage Tandem Queueing System With Reliability Considerations

Cited by 42 publications

References 15 publications

Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Compensating for Failures with Flexible Servers

Optimal assignment of servers to tasks when collaboration is inefficient

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