Analysis of a Multiserver Queue with Setup Times

Artalejo, Jesús R.; Economou, Antonis; Lopez-Herrero, M. J.

doi:10.1007/s11134-005-1740-6

Cited by 63 publications

(28 citation statements)

References 16 publications

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“…In such models once a server is reactivated, a generally random time is required for setup before it can begin serving customers. Bischof, Choudhury, He and Jewkes [4,8,9,16] and the references therein consider various single server systems with setup times, while Borthakur, Choudhury, Artalejo et al [3,5] deal with some multiserver models. In particular, the performance evaluation for an M/M/1 queue with server setups has been carried in [1, p. 51-54], and its multiserver counterpart in [3].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium customer strategies in a single server Markovian queue with setup times

2007

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We consider a single server Markovian queue with setup times. Whenever this system becomes empty, the server is turned off. Whenever a customer arrives to an empty system, the server begins an exponential setup time to start service again. We assume that arriving customers decide whether to enter the system or balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait.We examine customer behavior under various levels of information regarding the system state. Specifically, before making the decision, a customer may or may not know the state of the server and/or the number of present customers. We derive equilibrium strategies for the customers under the various levels of information and analyze the stationary behavior of the system under these strategies. We also illustrate further effects of the information level on the equilibrium behavior via numerical experiments.

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Section: Introductionmentioning

confidence: 99%

Equilibrium customer strategies in a single server Markovian queue with setup times

2007

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“…Artalejo et. al [34] give steady-state results for an M/M/k with setup delays, where idle servers are switched off and at most one server can be in an exponentially distributed setup phase. Gandhi and Harchol-Balter [35] consider an M/G/k with an exponential setup delay and give an exact formula for the mean sojourn time in an M/M/k also assuming that at most one server can be undergoing the switching on process.…”

Section: Related Workmentioning

confidence: 99%

“…Gandhi and Harchol-Balter [35] consider an M/G/k with an exponential setup delay and give an exact formula for the mean sojourn time in an M/M/k also assuming that at most one server can be undergoing the switching on process. In [36,37] switch idle servers off with at most one server undergoing the switching on (as in [34,35]). Similarly, Mitrani [38] also considered a scheduling problem with a central queue.…”

Section: Related Workmentioning

confidence: 99%

Task assignment in a heterogeneous server farm with switching delays and general energy-aware cost structure

Hyytiä

Righter

Aalto

2014

Performance Evaluation

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We consider the task assignment problem to heterogeneous parallel servers with switching delay, where servers can be switched off to save energy. However, switching a server back on involves a constant server-specific delay. We will use one step of policy iteration from a starting policy such as Bernoulli splitting, in order to derive efficient task assignment (dispatching) policies that minimize the long-run average cost. To evaluate our starting policy, we first analyze a single work-conserving M/G/1 queue with a switching delay and derive a value function with respect to a general cost structure. Our costs include energy related switching and processing costs, as well as general performance-related costs, such as costs associated with both means and variability of waiting time and sojourn time. The efficiency of our dispatching policies is illustrated with numerical examples.

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“…Artalejo et. al [18] give steady-state results for an M/M/k, where at most one server can be in an exponentially distributed setup phase. Gandhi and Harchol-Balter [19] consider a similar M/G/k with an exponential setup delay.…”

Section: A Related Workmentioning

confidence: 99%

Energy-aware job assignment in server farms with setup delays under LCFS and PS

Hyytiä

Righter

Aalto

2014

2014 26th International Teletraffic Congress (ITC)

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Abstract-We consider the job (or task) assignment problem to heterogeneous parallel servers, where servers can be switched off to save energy. However, switching a server back on involves a constant server-specific delay. We will use one step of policy iteration from a starting policy such as Bernoulli splitting, in order to derive efficient job assignment (dispatching) policies that minimize the long-run average cost. In our earlier work, we assumed FCFS scheduling at the servers. In this paper, we focus on LCFS and PS, where the latter in particular serves as an important model, e.g., for server farms where jobs are processed concurrently. LCFS, on the other hand, is a robust policy that works especially well when service times are highly variable, and is easier to implement than the standard alternative policy for high variability, LAS (least attained service time). Our costs include energy related running costs, as well as performance related mean response times. The efficiency of the resulting operating policies is illustrated with numerical examples, where we also compare FCFS to LCFS and PS.

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Analysis of a Multiserver Queue with Setup Times

Cited by 63 publications

References 16 publications

Equilibrium customer strategies in a single server Markovian queue with setup times

Equilibrium customer strategies in a single server Markovian queue with setup times

Task assignment in a heterogeneous server farm with switching delays and general energy-aware cost structure

Energy-aware job assignment in server farms with setup delays under LCFS and PS

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