Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Gaidamaka, Yuliya; Pechinkin, A. V.; Razumchik, Rostislav; Samouylov, Konstantin; Sopin, Eduard

doi:10.2478/amcs-2014-0038

Cited by 20 publications

(11 citation statements)

References 17 publications

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“…Important conclusions, based on the results of computations, were formulated. The results are going to be extended to the case of batch arrivals similar to the one of Gaidamaka et al (2014), customers impatient during the stay in the pool similar to the case investigated by Dudin et al (2016), a system operating in a random environment similar to the case studied by Kim et al (2014) and a discrete time system similar to the one presented by Atencia (2014).…”

Section: Resultsmentioning

confidence: 99%

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Brugno

D’Apice

Dudin

et al. 2017

International Journal of Applied Mathematics and Computer Science

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A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian arrival process. An individual customer's service time has a phase-type distribution. The service time of a batch is defined as the maximum of the individual service times of the customers which form the batch. The dynamics of such a system are described by a multi-dimensional Markov chain. An ergodicity condition for this Markov chain is derived, a stationary probability distribution of the states is computed, and formulas for the main performance measures of the system are provided. The Laplace-Stieltjes transform of the waiting time is obtained. Results are numerically illustrated.

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Section: Resultsmentioning

confidence: 99%

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Brugno

D’Apice

Dudin

et al. 2017

International Journal of Applied Mathematics and Computer Science

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“…In the course of experiments, a tcpdump probe was forced to filter streams of UDP packets. Examples of models based on queuing theory, including buffer control policies, can be found, for example, in [42,43]. Power consumption monitoring was supported by a standard one-phase electricity meter for active energy measurement equipped with RS485 interface.…”

Section: System Model Identificationmentioning

confidence: 99%

“…For an overview of approaches to server model identification in the context of control system design, see, for example, [38][39][40][41]. Examples of models based on queuing theory, including buffer control policies, can be found, for example, in [42,43]. Finally, let it be noticed that benchmarking capabilities are being constantly improved, especially in the Linux system environment, which sets up promising directions for further research.…”

Section: System Model Identificationmentioning

confidence: 99%

Energy‐efficient CPU frequency control for the Linux system

Karpowicz

2015

Concurrency and Computation

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Efficiency of energy usage in computing systems improves, however, still not at the rate matching the climbing demand for computing capacity. To address this urging problem, computing elements of the latest generation, that is, CPUs/graphics processing units, memory units, and network interface cards, have been designed to operate in multiple modes with differentiated energy consumption levels. Mode switching and high-frequency performance monitoring functions have also been exposed by co-designed abstract programming interfaces. The challenge of energy-efficient computing is to develop hardware control mechanisms taking advantage of the new capabilities. This paper aims at giving an insight into the structure of optimal energy-aware CPU frequency scaling rules. It gives a characterization of solutions to the optimal control problem of energy-efficient real-time packet inspection performed by a Linux server. A class of CPU frequency switching rules, exploiting dynamic voltage and frequency scaling mechanisms, is constructed based on experimentally identified model of server operations. The control rules are demonstrated to outperform the default CPU frequency scaling governor for the Linux kernel, both in terms of achievable power savings and service quality. 421Agency's 50 GFLOPS/W goal ¶ by year 2020 [4,5]. Indeed, limiting power consumption in data centers has become an important engineering problem [6][7][8].Average CPU utilization of a server in data center rarely approaches 100%, most of the time oscillating somewhere between 10% and 50% [9]. Over-provisioning of computing capacity, strongly correlated with the running CPU frequency, has been applied as a sound strategy to eliminate potential breakdowns caused by sudden workload fluctuations or internal disruptions, for example, hardware or software faults. Unfortunately, although efficient from the point of view of service quality, the strategy may be a significant source of energy waste. The challenge of energy-efficient CPU frequency scaling, addressed in the present paper, is therefore to design control rules reducing power consumption subject to quality of service constraints in highly stochastic environment of a server operating system.Dynamic voltage and frequency scaling (DVFS) mechanisms have been commonly used to reduce power usage in routers and application servers. Translation of the commands responsible for the CPU frequency control in the Linux system has been provided by the cpufreq kernel module [10]. The module allows to adjust performance of CPU by activating a desired control policy implemented as a CPU governor. Typically, the calculated control inputs are mapped to admissible performance P-states, as described by the Advanced Configuration and Power Interface standard || , and passed to a processor driver (e.g., acpi_cpufreq). The sleeping state, or Advanced Configuration and Power Interface C-state, which CPU enters during idle periods, is independently and simultaneously determined by the cpuidle kernel module [11].Recent versions of ...

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“…But transitions from each state i > 0 happen with intensities µ i (t), λ i (t) and β i (t) and can be either to state (i − 1) or (i + 1) or 0, respectively. Such subclass of processes finds its application in the study of queueing systems with catastrophes and bulk arrivals (see, for example, [7,1,3,2,8,5,9,11,4,10]). For more details, concerning possible applications, one can refer to [11] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Ergodicity and truncation bounds for inhomogeneous birth and death processes with additional transitions from and to origin

et al. 2017

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In this paper one presents the extension of the transient analysis of the class of continuous-time birth and death processes defined on non-negative integers with special transitions from and to the origin. From the origin transitions can occur to any state. But being in any other state, besides ordinary transitions to neighbouring states, a transition to the origin can occur. All possible transition intensities are assumed to be non-random functions of time and may depend on the state of the process. We improve previously known ergodicity and truncation bounds for this class of processes which were known only for the case when transitions from the origin decay exponentially (other intensities must have unique uniform upper bound). We show how the bounds can be obtained the decay rate is slower than exponential. Numerical results are also provided.

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Analysis of an M|G|1|R queue with batch arrivals and two hysteretic overload control policies

Cited by 20 publications

References 17 publications

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Analysis of an MAP/PH/1 Queue with Flexible Group Service

Energy‐efficient CPU frequency control for the Linux system

Ergodicity and truncation bounds for inhomogeneous birth and death processes with additional transitions from and to origin

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