On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism Based on Working Vacations

A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the...

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Vydáno v:	Sensors (Basel, Switzerland) Ročník 21; číslo 16; s. 5507
Hlavní autoři:	Kobielnik, Martyna, Kempa, Wojciech
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Basel MDPI AG 16.08.2021 MDPI
Témata:	Communication Customer services Energy consumption energy saving Markov analysis Probability queueing model Random variables Sensors Servers Service stations time to buffer overflow Traffic transient analysis Vacations Wireless networks working vacation policy
ISSN:	1424-8220, 1424-8220
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Abstract	A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the service speed for a random amount of time following an exponential distribution. Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses. A system of equations for the transient time to the first buffer overflow cumulative distribution functions conditioned by the initial state and working mode of the service unit is stated using the idea of an embedded Markov chain and the continuous version of the law of total probability. The explicit representation for the Laplace transform of considered characteristics is found using a linear algebra-based approach. The results are illustrated using numerical examples, and the impact of the key parameters of the model is investigated.
AbstractList	A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the service speed for a random amount of time following an exponential distribution. Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses. A system of equations for the transient time to the first buffer overflow cumulative distribution functions conditioned by the initial state and working mode of the service unit is stated using the idea of an embedded Markov chain and the continuous version of the law of total probability. The explicit representation for the Laplace transform of considered characteristics is found using a linear algebra-based approach. The results are illustrated using numerical examples, and the impact of the key parameters of the model is investigated. A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the service speed for a random amount of time following an exponential distribution. Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses. A system of equations for the transient time to the first buffer overflow cumulative distribution functions conditioned by the initial state and working mode of the service unit is stated using the idea of an embedded Markov chain and the continuous version of the law of total probability. The explicit representation for the Laplace transform of considered characteristics is found using a linear algebra-based approach. The results are illustrated using numerical examples, and the impact of the key parameters of the model is investigated.A single server GI/M/1 queue with a limited buffer and an energy-saving mechanism based on a single working vacation policy is analyzed. The general independent input stream and exponential service times are considered. When the queue is empty after a service completion epoch, the server lowers the service speed for a random amount of time following an exponential distribution. Packets that arrive while the buffer is saturated are rejected. The analysis is focused on the duration of the time period with no packet losses. A system of equations for the transient time to the first buffer overflow cumulative distribution functions conditioned by the initial state and working mode of the service unit is stated using the idea of an embedded Markov chain and the continuous version of the law of total probability. The explicit representation for the Laplace transform of considered characteristics is found using a linear algebra-based approach. The results are illustrated using numerical examples, and the impact of the key parameters of the model is investigated.
Author	Kobielnik, Martyna Kempa, Wojciech
AuthorAffiliation	Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland; wojciech.kempa@polsl.pl
AuthorAffiliation_xml	– name: Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, ul. Kaszubska 23, 44-100 Gliwice, Poland; wojciech.kempa@polsl.pl
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Cites_doi	10.1016/j.cie.2021.107239 10.1016/0377-2217(86)90234-1 10.3390/s19143114 10.1016/j.peva.2016.11.002 10.1287/mnsc.22.2.202 10.1007/s11009-016-9496-5 10.1504/IJMOR.2021.113586 10.1016/j.apm.2012.04.045 10.1007/s11009-019-09724-6 10.1016/S0166-5316(02)00057-3 10.1109/ICFC.2019.00012 10.1007/978-981-15-9700-8_9 10.1504/IJOR.2021.114839 10.1080/16843703.2008.11673177 10.1016/j.peva.2009.01.005 10.3390/s20205772 10.1016/j.camwa.2002.10.017 10.1007/s12190-011-0532-x 10.1137/1119001 10.1007/978-0-387-33723-4 10.1007/978-3-319-93736-6_13 10.1016/j.apm.2018.02.009 10.1016/S0378-3758(01)00148-3 10.1023/A:1019194027833 10.1007/BF01149327
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SubjectTerms	Communication Customer services Energy consumption energy saving Markov analysis Probability queueing model Random variables Sensors Servers Service stations time to buffer overflow Traffic transient analysis Vacations Wireless networks working vacation policy
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Title	On the Time to Buffer Overflow in a Queueing Model with a General Independent Input Stream and Power-Saving Mechanism Based on Working Vacations
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