Processor-shared service systems with queue-dependent processors

Jain, Mayank; Sharma, G C; Shekhar, Chandra

doi:10.1016/j.cor.2003.08.009

Cited by 8 publications

(4 citation statements)

References 20 publications

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“…Control for an M/M/s system was discussed by Serfozo (1981) assuming arrival and service rates can be chosen upon arrival based on the current system occupancy. Jain, Sharma, and Shekhar (2005) investigated a queue-dependent multi-processor service system which also adopts dynamic service rates. The trade-off between delay and energy was also studied in Goseling, Boucherie, and van Ommeren (2009) in the context of a system with multiple queues.…”

Section: Related Workmentioning

confidence: 99%

Architecture and robustness tradeoffs in speed-scaled queues with application to energy management

Dinh

Andrew

Nazarathy

2013

International Journal of Systems Science

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We consider single-pass, lossless, queueing systems at steady-state subject to Poisson job arrivals at an unknown rate. Service rates are allowed to depend on the number of jobs in the system, up to a fixed maximum, and power consumption is an increasing function of speed. The goal is to control the state dependent service rates such that both energy consumption and delay are kept low. We consider a linear combination of the mean job delay and energy consumption as the performance measure. We examine both the 'architecture' of the system, which we define as a specification of the number of speeds that the system can choose from, and the 'design' of the system, which we define as the actual speeds available. Previous work has illustrated that when the arrival rate is precisely known, there is little benefit in introducing complex (multi-speed) architectures, yet in view of parameter uncertainty, allowing a variable number of speeds improves robustness. We quantify the tradeoffs of architecture specification with respect to robustness, analysing both global robustness and a newly defined measure which we call local robustness.Keywords: parameter uncertainty; robust design; controlled single server queue; speed scaling IntroductionPerformance analysis, design and control by means of stochastic queueing models (cf. Wolff 1989) has affected a variety of fields, including not only telecommunications and computing systems but also service engineering, manufacturing, logistics, health-care, road traffic and biological modelling. A typical queueing model abstracts unknown job arrival and service requirements by means of stochastic processes and distributions. The resulting dynamics of queue-length, workload or other performance processes are analysed yielding performance measures that ultimately allow for better design and control of the system at hand. Design of the system often refers to an off-line specification of parameters whereas control of the system typically refers to an on-line decision making based on state measurements (e.g. setting service speeds). In this paper we shall use a third term, architecture selection, referring to the action of deciding what are the design and control parameters that are available to process.Almost all of the queueing theoretic, performance analysis, design, control and architecture selection literature is based on the underlying assumption that the probability laws of arrival and service processes are precisely known. A few exceptions to this rule are mentioned later in this section. In practice, this assumption is often too strong, especially due to the fact that obtaining precise a priori parameter estimates is not possible in many settings. Our

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Section: Related Workmentioning

confidence: 99%

Architecture and robustness tradeoffs in speed-scaled queues with application to energy management

Dinh

Andrew

Nazarathy

2013

International Journal of Systems Science

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“…Jain et al [19] investigated the machine repair problem with two types of spares along with reneging and controlled rates by applying the concept of time sharing. Jain et al [22] investigated a time-shared machine repair problem with mixed spares. In this investigation, they have considered that the caretaker of failed machines operates under N -policy.…”

Section: Madhu Jain and Sudeep Singh Sangamentioning

confidence: 99%

Admission control for finite capacity queueing model with general retrial times and state-dependent rates

Jain¹,

Sanga²

2020

Journal of Industrial &Amp; Management Optimization

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The finite state dependent queueing model with F-policy is investigated by considering the general retrial attempts. On arrival in the system, if the job finds the server engaged, it is forced to enter into the retrial orbit. After a random period of time, the job from the retrial orbit re-attempts for the service. According to F-policy, as the system attains its full capacity, the arrivals are restricted to join the system until the number of jobs comes down to the prefixed threshold value 'F '. The supplementary variable corresponding to the remaining retrial time is used to frame the governing equations which are solved by using Laplace-Stieltjes transform and then applying the recursive method. Special models for machine repair and time-sharing queue are deduced by setting the state dependent rates. Several system indices are obtained explicitly which are further used to facilitate the sensitivity analysis by considering a numerical illustration. A cost function is constructed and minimized for evaluating the optimal threshold parameter and optimal service rate.

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“…Adiri and Avi-Itzhak, 1969; Kleinrock et al , 1971; Ohnishi et al , 1995). A cost relationship was constructed by the Jain et al (2005) to determine the optimal threshold level of processors being active in order to gain maximum net profit for the time-shared service systems with queue-dependent processors. Jain et al (2016a, b) obtained the state probabilities for Markovian machine repair problem with spares operating under N -policy and time-sharing basis.…”

Section: Research Backgroundmentioning

confidence: 99%

Optimal (N, F) policy for queue-dependent and time-sharing machining redundant system

Shekhar

Jain

Raina

et al. 2017

IJQRM

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Purpose The purpose of this paper is to study the performance metrics of redundant repairable machining system which is applicable in various systems like computer and communication system, manufacturing and production system, etc. Design/methodology/approach In the present investigation, the authors develop Markov model for the system consisting of identical active operating machines which are prone to breakdown. The operating machines are under the care of one permanent repair facility that provides time-sharing basis repair services. The maintenance is facilitated with the provision of standby machines of mixed type and permanent as well as additional repair facility. From the economic point of view, F-policy and N-policy to control the service and arrival of failed machines effectively are included. Findings For the performance analysis of the system in long run, the authors compute steady-state probabilities using product-type solution method recursively. Sensitivity analysis is performed numerically for various parameters by developing code in MATLAB. Social implications The performance prediction done may be helpful for the system designers and decision makers for the improvement of the existing machining systems in various industries. Originality/value Markovian model for the performance prediction of fault tolerant multi-identical operating and standby machines redundant system is developed in generic frameworks by incorporating many noble features which were not all taken together by other researchers working on the same lines. The key concepts incorporated for the modeling of the concerned system is: F-policy, N-policy, time-sharing, and sensitivity analysis of availability and cost function.

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Processor-shared service systems with queue-dependent processors

Cited by 8 publications

References 20 publications

Architecture and robustness tradeoffs in speed-scaled queues with application to energy management

Architecture and robustness tradeoffs in speed-scaled queues with application to energy management

Admission control for finite capacity queueing model with general retrial times and state-dependent rates

Optimal (N, F) policy for queue-dependent and time-sharing machining redundant system

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