1 research outputs found
Queueing systems with different types of renovation mechanism and thresholds as the mathematical models of active queue management mechanism
This article is devoted to some aspects of using the renovation mechanism (different types of renovation are considered, definitions and brief overview are also given) with one or several thresholds as the mathematical models of active queue management mechanisms. The attention is paid to the queuing systems in which a threshold mechanism with renovation is implemented. This mechanism allows to adjust the number of packets in the system by dropping (resetting) them from the queue depending on the ratio of a certain control parameter with specified thresholds at the moment of the end of service on the device (server) (in contrast to standard RED-like algorithms, when a possible drop of a packet occurs at the time of arrivals of next packets in the system). The models with one, two and three thresholds with different types of renovation are under consideration. It is worth noting that the thresholds determine not only from which place in the buffer the packets are dropped, but also to which the reset of packets occurs. For some of the models certain analytical and numerical results are obtained (the references are given), some of them are only under investigation, so only the mathematical model and current results may be considered. Some results of comparing classic RED algorithm with renovation mechanism are presented.Π Π°Π±ΠΎΡΠ° ΠΏΠΎΡΠ²ΡΡΠ΅Π½Π° Π½Π΅ΠΊΠΎΡΠΎΡΡΠΌ Π°ΡΠΏΠ΅ΠΊΡΠ°ΠΌ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠ° ΠΎΠ±Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ (ΡΠ°Π·Π»ΠΈΡΠ½ΡΠ΅ Π²Π°ΡΠΈΠ°Π½ΡΡ ΠΎΠ±Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ, ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΠΈ ΠΊΡΠ°ΡΠΊΠΈΠΉ ΠΎΠ±Π·ΠΎΡ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ) Ρ ΠΎΠ΄Π½ΠΈΠΌ ΠΈΠ»ΠΈ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΠΌΠΈ ΠΏΠΎΡΠΎΠ³Π°ΠΌΠΈ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠΎΠ² Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΎΡΠ΅ΡΠ΅Π΄ΡΠΌΠΈ. ΠΠΏΠΈΡΠ°Π½Ρ ΡΠΈΡΡΠ΅ΠΌΡ ΠΌΠ°ΡΡΠΎΠ²ΠΎΠ³ΠΎ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ, Π² ΠΊΠΎΡΠΎΡΡΡ
ΡΠ΅Π°Π»ΠΈΠ·ΠΎΠ²Π°Π½ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌ ΠΎΠ±Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ Ρ ΠΏΠΎΡΠΎΠ³Π°ΠΌΠΈ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠΉ ΡΠΏΡΠ°Π²Π»ΡΡΡ ΡΠΈΡΠ»ΠΎΠΌ Π·Π°ΡΠ²ΠΎΠΊ Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ ΠΏΡΡΠ΅ΠΌ ΠΈΡ
ΡΠ±ΡΠΎΡΠ° ΠΈΠ· Π½Π°ΠΊΠΎΠΏΠΈΡΠ΅Π»Ρ Π² Π·Π°Π²ΠΈΡΠΈΠΌΠΎΡΡΠΈ ΠΎΡ Π·Π½Π°ΡΠ΅Π½ΠΈΡ Π½Π΅ΠΊΠΎΡΠΎΡΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»ΡΡΡΠ΅Π³ΠΎ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ° ΠΈ ΠΏΠΎΡΠΎΠ³ΠΎΠ²ΡΡ
Π·Π½Π°ΡΠ΅Π½ΠΈΠΉ. Π‘Π±ΡΠΎΡ Π·Π°ΡΠ²ΠΎΠΊ ΠΈΠ· Π½Π°ΠΊΠΎΠΏΠΈΡΠ΅Π»Ρ ΠΏΡΠΎΠΈΡΡ
ΠΎΠ΄ΠΈΡ Π² ΠΌΠΎΠΌΠ΅Π½Ρ ΠΎΠΊΠΎΠ½ΡΠ°Π½ΠΈΡ ΠΎΠ±ΡΠ»ΡΠΆΠΈΠ²Π°Π½ΠΈΡ Π·Π°ΡΠ²ΠΊΠΈ Π½Π° ΠΏΡΠΈΠ±ΠΎΡΠ΅, ΡΡΠΎ ΠΎΡΠ»ΠΈΡΠ°Π΅Ρ Π΄Π°Π½Π½ΡΠΉ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌ ΡΠ±ΡΠΎΡΠ° ΠΎΡ RED-ΠΏΠΎΠ΄ΠΎΠ±Π½ΡΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ², Π΄Π»Ρ ΠΊΠΎΡΠΎΡΡΡ
ΡΠ±ΡΠΎΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ΅Π½ Π² ΠΌΠΎΠΌΠ΅Π½Ρ ΠΏΠΎΡΡΡΠΏΠ»Π΅Π½ΠΈΡ Π² ΡΠΈΡΡΠ΅ΠΌΡ. ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΠΌΠΎΠ΄Π΅Π»ΠΈ Ρ ΠΎΠ΄Π½ΠΈΠΌ, Π΄Π²ΡΠΌΡ ΠΈΠ»ΠΈ ΡΡΠ΅ΠΌΡ ΠΏΠΎΡΠΎΠ³Π°ΠΌΠΈ. Π ΡΡΠΈΡ
ΠΌΠΎΠ΄Π΅Π»ΡΡ
ΠΏΠΎΡΠΎΠ³ΠΎΠ²ΡΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΡΡ Π½Π΅ ΡΠΎΠ»ΡΠΊΠΎ ΠΌΠ΅ΡΡΠΎ, Ρ ΠΊΠΎΡΠΎΡΠΎΠ³ΠΎ Π² Π½Π°ΠΊΠΎΠΏΠΈΡΠ΅Π»Π΅ Π½Π°ΡΠΈΠ½Π°Π΅ΡΡΡ ΡΠ±ΡΠΎΡ Π·Π°ΡΠ²ΠΎΠΊ, Π½ΠΎ ΠΈ Π΄ΠΎ ΠΊΠ°ΠΊΠΎΠΉ ΠΏΠΎΠ·ΠΈΡΠΈΠΈ Π·Π°ΡΠ²ΠΊΠΈ ΠΌΠΎΠ³ΡΡ Π±ΡΡΡ ΡΠ±ΡΠΎΡΠ΅Π½Ρ. ΠΠ»Ρ Π½Π΅ΠΊΠΎΡΠΎΡΡΡ
ΠΈΠ· ΠΎΠΏΠΈΡΡΠ²Π°Π΅ΠΌΡΡ
ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ ΡΠΆΠ΅ ΠΏΠΎΠ»ΡΡΠ΅Π½Ρ Π°Π½Π°Π»ΠΈΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈ ΡΠΈΡΠ»Π΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ (ΡΡΡΠ»ΠΊΠΈ Π½Π° ΡΠ°Π±ΠΎΡΡ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ), Π½ΠΎ Π±ΠΎΠ»ΡΡΠ°Ρ ΡΠ°ΡΡΡ ΠΌΠΎΠ΄Π΅Π»Π΅ΠΉ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π² ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ, ΠΏΠΎΡΡΠΎΠΌΡ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ ΡΠΎΠ»ΡΠΊΠΎ ΠΎΠΏΠΈΡΠ°Π½ΠΈΡ ΠΈ Π½Π΅ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ΅ΠΊΡΡΠΈΠ΅ Π΄Π°Π½Π½ΡΠ΅. ΠΡΠΈΠ²Π΅Π΄Π΅Π½Ρ Π½Π΅ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΡ ΠΊΠ»Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° RED Ρ ΠΌΠ΅Ρ
Π°Π½ΠΈΠ·ΠΌΠΎΠΌ ΠΎΠ±Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ