Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines

Kırkızlar, Eser; Andradóttir, Sigrún; Ayhan, Hayriye

doi:10.1002/nav.20424

Cited by 18 publications

(16 citation statements)

References 41 publications

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“…The set A s of allowable actions in state s is given as Andradóttir, and Ayhan [16] to eliminate actions that allow servers to idle (exploiting the fact that when servers collaborate, their combined service rate at each station is faster than the rate of the faster server at that station). Since the number of possible states and actions are both finite, the existence of an optimal Markovian stationary deterministic policy follows from Theorem 9.1.8 of Puterman [18], which provides sufficient conditions under which such a policy exists.…”

Section: Discussionmentioning

confidence: 99%

“…The set A s of allowable actions in state s is the same as the one described in the proof of Theorem 3.4, where we again use the results of Kırkızlar, Andradóttir, and Ayhan [16] to eliminate idling actions for the specified range of α. Since the number of possible states and actions are both finite, the existence of an optimal Markovian stationary deterministic policy follows from Theorem 9.1.8 of Puterman [18].…”

Section: Proof Of Theorem 44mentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Proof Of Theorem 44mentioning

confidence: 99%

Optimal assignment of servers to tasks when collaboration is inefficient

2013

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“…Indeed, cascade queueing networks are related to systems composed of flexible servers, where a server may transfer some service capacity to accommodate workload accumulated in another server. Such networks with flexible servers have been studied, for instance, in [3,13,17,21,25]. Related to this concept is that of cross-trained servers, whereby some servers can serve a reduced set of customers types, whereas others accept all types [1,2,22,23].…”

Section: Introductionmentioning

confidence: 98%

Stability analysis of cascade networks via fluid models

Delgado

Morozov

2014

Performance Evaluation

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“…We provide a review of results about the dynamic server assignment problem with setups. We refer the reader to Hopp and Van Oyen [15] for a more extensive review of flexible workforce research, and to Andradóttir, Ayhan, and Down [1] or Kırkızlar, Andradóttir, and Ayhan [19] for more concentrated reviews of research on the dynamic server assignment problem.…”

Section: Introductionmentioning

confidence: 99%

Flexible servers in tandem lines with setup costs

2011

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We study the dynamic assignment of flexible servers to stations in the presence of setup costs that are incurred when servers move between stations. The goal is to maximize the long-run average profit. We provide a general problem formulation and some structural results, and then concentrate on tandem lines with two stations, two servers, and a finite buffer between the stations. We investigate how the optimal server assignment policy for such systems depends on the magnitude of the setup costs, as well as on the homogeneity of servers and tasks. More specifically, for systems with either homogeneous servers or homogeneous tasks, small buffer sizes, and constant setup cost, we prove the optimality of "multiple threshold" policies (where servers' movement between stations depends on both the number of jobs in the system and the locations of the servers) and determine the values of the thresholds. For systems with heterogeneous servers and tasks, small buffers, and constant setup cost, we provide results that partially characterize the optimal server assignment policy. Finally, for systems with larger buffer sizes and various service rate and setup cost configurations, we present structural results for the optimal policy and provide numerical results that strongly support the optimality of multiple threshold policies.

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Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines

Cited by 18 publications

References 41 publications

Optimal assignment of servers to tasks when collaboration is inefficient

Optimal assignment of servers to tasks when collaboration is inefficient

Stability analysis of cascade networks via fluid models

Flexible servers in tandem lines with setup costs

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