Multi-threshold control by a single-server queuing model with a service rate depending on the amount of harvested energy

Kim, Che Soong; Dudin, Sergey; Dudin, Alexander; Samouylov, Konstantin

doi:10.1016/j.peva.2018.09.001

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…Aspects relating to the service rate control, depending on the amount of the harvested e.u., are considered very rare and, as such, they deserve attention. We can mention the paper [33] where the threshold strategy for service rate selection depending on the available amount of e.u. is analyzed.…”

Section: Queuing Systems With Energy Consumption and Harvestingmentioning

confidence: 99%

Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers

D’Apice,

D’Arienzo,

Dudin

et al. 2023

Mathematics

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A queuing system having two different servers is under study. Demands enter the system according to a Markov arrival process. Service times have phase-type distribution. Service of demands is possible only if the fixed number of energy units, probably different for two servers, is available in the system at the potential service beginning moment. Energy units arrive in the system also according to a Markov arrival process and are stored in a stock (battery) of a finite capacity. Leakage of energy units from the stock can occur. Demands waiting in the infinite buffer are impatient and can leave the buffer after an exponentially distributed waiting time. One server is the main one and permanently provides service when the buffer is not empty and the required number of energy units is available. The second server is the assistant server and is switched on or off depending on the availability of energy units and queue length according to the hysteresis strategy defined by two thresholds. The assistant server is switched on when the queue length is not less than the greater threshold and is switched off when the queue length becomes smaller than the smaller threshold. The use of the assistant server has to be paid. Thus, the problem of the optimal selection of the thresholds defining the control strategy naturally arises. To solve this problem, the study of the behavior of the system under any fixed values of the parameters of the control strategy is necessary. Such a study is given in this paper. Numerical results are presented. They illustrate the feasibility of computer realization of the developed algorithms for computation of the stationary distribution of the system states and the main key performance indicators as well as the result of solving one of the possible optimization tasks.

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Section: Queuing Systems With Energy Consumption and Harvestingmentioning

confidence: 99%

Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers

D’Apice,

D’Arienzo,

Dudin

et al. 2023

Mathematics

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“…The considered model is very close to the models in which some additional resource is required to provide service to a customer. These models include, in particular, so-called queueing/inventory models (see, e.g., [4]), queueing systems with energy harvesting (see, e.g., [5]), queueing models with paired customers (see [6]), assembly-like queue (see [7]), passenger-taxi or double-ended queues (see [8]), coupled queues (see [9]), etc. In our model, the role of the additional resource is played by the lag between the critical and current value of the server's temperature.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Queueing Model with Server Heating and Cooling

Dudina

Dudin

2019

Mathematics

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The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.

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