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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Veröffentlicht in:Sensors (Basel, Switzerland) Jg. 21; H. 16; S. 5507
Hauptverfasser: Kobielnik, Martyna, Kempa, Wojciech
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 16.08.2021
MDPI
Schlagworte:
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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Zusammenfassung: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.
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ISSN:1424-8220
1424-8220
DOI:10.3390/s21165507