ÄéáôñéâÞ åðß Äéäáêôïñßá
Ìïíôåëïðïßçóç - Ðñïóïìïßùóç Äñïìïëüãçóçò
êáé Åêôßìçóç Áðüäïóçò ÐïëõâÜèìéá
ÄéáóõíäåìÝíùí Äéêôýùí ìå óêïðü ôç
Âåëôéóôïðïßçóç ôçò Ëåéôïõñãßáò ÊáôáíåìçìÝíùí
Åöáñìïãþí
ÄçìÞôñéïò ÂáóéëåéÜäçò
Ïêôþâñéïò 2009
ÔñéìåëÞò ÓõìâïõëåõôéêÞ ÅðéôñïðÞ
• Êþóôáò ÂáóéëÜêçò, Åðßêïõñïò ÊáèçãçôÞò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Õðïëïãéóôþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõ (ÅðéâëÝðùí) • Ðáíáãéþôçò ÃåùñãéÜäçò, ÊáèçãçôÞò ôïõ ôìÞìáôïò ÐëçñïöïñéêÞò êáé Ôçëåðéêïéíùíéþí ôïõ Ðáíåðéóôçìßïõ Áèçíþí • Óðõñßäùí Óêéáäüðïõëïò, Åðßêïõñïò ÊáèçãçôÞò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Õðïëïãéóôþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõÅðôáìåëÞò ÅîåôáóôéêÞ ÅðéôñïðÞ
• Êþóôáò ÂáóéëÜêçò, Åðßêïõñïò ÊáèçãçôÞò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Õðïëïãéóôþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõ (ÅðéâëÝðùí) • Ðáíáãéþôçò ÃåùñãéÜäçò, ÊáèçãçôÞò ôïõ ôìÞìáôïò ÐëçñïöïñéêÞò êáé Ôçëåðéêïéíùíéþí ôïõ Ðáíåðéóôçìßïõ Áèçíþí • Óðõñßäùí Óêéáäüðïõëïò, Åðßêïõñïò ÊáèçãçôÞò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Õðïëïãéóôþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõ • Êùíóôáíôßíïò ÌáóóÝëïò, ÁíáðëçñùôÞò ÊáèçãçôÞò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Õðïëïãéóôþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõ • ÄçìÞôñéïò ÂëÜ÷ïò, Åðßêïõñïò ÊáèçãçôÞò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Õðïëïãéóôþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõ • Ãåþñãéïò ËÝðïõñáò, Åðßêïõñïò ÊáèçãçôÞò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Õðïëïãéóôþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõ • ÁëÝîáíäñïò Êáëüîõëïò, ËÝêôïñáò ôïõ ôìÞìáôïò ÅðéóôÞìçò êáé Ôå÷íïëïãßáò Ôçëåðéêïéíùíéþí ôïõ Ðáíåðéóôçìßïõ ÐåëïðïííÞóïõAcknowledgements
I would like to express my sincere thanks and gratitude to my advisor Assistant Professor Costa Vassilaki for his helpful suggestions and advice. Collaborating with him has been a pleasant and memorable experience. I would also like to thank the members of my committee Professor Panayioti Georgiadi and Assistant Professor Spiro Skiadopoulo.
Last but by no means least it gives me immense pleasure to express my gratitude to my family which has always been an important source of encouragement and support. I owe so much thanks to my three sons Chris, Tasos, and John who joined me when I was writing my doctorate thesis, for giving me unlimited happiness and pleasure.
Table of Contents
1 Introduction 24
1.1 Classication of Multistage Interconnection Networks and Related Work . 24
1.2 Thesis Contribution . . . 26
2 Internal Priority MINs 29 2.1 Introduction . . . 29
2.2 Related Work . . . 30
2.3 Internal Priority MIN Description and Analytical Model . . . 31
2.3.1 Analysis of MINs . . . 34
2.3.2 Denitions of MINs . . . 34
2.4 Performance Evaluation Methodology of Internal Priority MINs . . . 37
2.5 Simulation and Performance Results of Internal Priority MINs . . . 39
2.6 Conclusions for Internal Priority MINs . . . 45
3 Dual Priority MINs and Asymmetric-sized Buer Queues 47 3.1 Introduction . . . 48
3.2 Related Work . . . 49
3.3 Dual Priority MIN and Analytical Model . . . 49
3.3.1 State Notations for High Priority Queues . . . 51
3.3.2 Denitions for High Priority Queues . . . 52
3.3.3 Mathematical Analysis for High Priority Queues . . . 52
3.3.4 State Notations for Low Priority Queues . . . 55
3.3.5 Denitions for Low Priority Queues . . . 55
3.3.6 Mathematical Analysis for Low Priority Queues . . . 56
3.4 Performance Evaluation Methodology of Dual Priority MINs . . . 58
3.5 Simulation and Performance Results of Dual Priority MINs . . . 59
3.5.1 Dual Priority MINs vs.Single Priority Ones . . . 65
3.5.2 Dual Priority MINs with Asymmetric-sized Buer Queues . . . 70
3.6 Conclusions for Dual Priority MINs . . . 73
4 2-Class Priority Multi-Layer MINs under Hotspot Trac 75 4.1 Introduction . . . 75 4.2 Analysis of 2-Class Priority Multi-Layer MINs under Hotspot Environment 77
4.3 Performance Evaluation Parameters and Methodology of 2-Class Priority
MINs under Hotspot Environment . . . 79
4.4 Simulation and Performance Results of 2-Class Priority Multi-Layer MINs under Hotspot Environment . . . 83
4.4.1 Simulator Validation for 2-Class Priority MINs under Hotspot En-vironment . . . 85
4.4.2 2-Class Priority Single-Layer MINs Performance under Hotspot En-vironment . . . 86
4.4.3 2-Class Priority Multi-Layer MINs Performance under Hotspot En-vironment . . . 88
4.5 Conclusions for 2-Class Priority Multi-Layer MINs under Hotspot Environ-ment . . . 90
5 Multi Priority MINs 92 5.1 Introduction . . . 92
5.2 Analysis of Multi-Priority MINs . . . 94
5.3 Performance Evaluation Parameters and Methodology of Multi-Priority MINs 96 5.4 Simulation and Performance Results of Multi-Priority MINs . . . 97
5.4.1 Simulator Validation for Multi-Priority MINs . . . 100
5.4.2 Multi-Priority MINs Performance . . . 100
5.5 Conclusions for Multi-Priority MINs . . . 104
6 Multi-layer, Multi-priority MINs under Multicast Environment 105 6.1 Introduction . . . 105
6.2 Multi-layer, Multi-priority MIN Description . . . 107
6.3 Conguration and Operational Parameters of Multi-layer MINs . . . 109
6.4 Performance Evaluation Metrics for Multi-layer MINs . . . 111
6.4.1 Metrics for Single-layer Segment of MINs . . . 111
6.4.2 Metrics for multi-layer MINs . . . 113
6.5 Simulation and Performance Results for multi-layer, multi-priority MINs . 115 6.5.1 Simulator Validation for Multicasting . . . 120
6.5.2 Multicasting on Single-priority, Single-layer MINs . . . 121
6.5.3 Multicasting on Dual-priority, Single-layer MINs . . . 122
6.5.4 Multicasting on Dual-priority Multi-layer MINs . . . 124
6.5.5 Multicasting on Multi-layer Segment of Dual-priority MINs . . . 128
List of Figures
1.1 A classication of MINs . . . 25
2.1 A cxc Switching Element . . . 31
2.2 A 3-stage Delta Network consisting of cxc SEs . . . 32
2.3 A state transition diagram of a SE(k) buer . . . 35
2.4 T h of single-buered, 6-stage, single- (or non-) priority MIN . . . 43
2.5 T h of double-buered, n-stage, internal- vs. non-priority scheme . . . 43
2.6 T h of nite-buered (b=4), n-stage, internal- vs. non-priority scheme . . . 44
2.7 T h of nite-buered (b=8), n-stage, internal- vs. non-priority scheme . . . 44
2.8 D of nite-buered, 6-stage, internal- vs. non-priority scheme . . . 45
2.9 Upf of nite-buered, 6-stage, internal- vs. non-priority scheme . . . 45
3.1 2-class priority for 3-stage MIN consisting of 2x2 SEs . . . 50
3.2 A state transition diagram of a high priority buer of SE(k) . . . 53
3.3 A state transition diagram of a low priority buer of SE(k) . . . 57
3.4 T htotal of nite-buered, 10-stage, dual- vs. single-priority MINs . . . 65
3.5 RT h(h) of nite-buered, 10-stage, dual-priority MIN . . . 66
3.6 RT h(l) of nite-buered, 10-stage, dual-priority MIN . . . 66
3.7 D(h) of nite-buered, 10-stage, dual-priority MIN . . . 67
3.8 D(l)of nite-buered, 10-stage, dual-priority MIN . . . 67
3.9 RT h(h) of nite-buered, k-stage, dual-priority MIN . . . 68
3.10 RT h(l) of nite-buered, k-stage, dual-priority MIN . . . 68
3.11 Upf(h) of nite-buered, 10-stage, dual-priority MIN . . . 69
3.12 Upf(l)of nite-buered, 10-stage, dual-priority MIN . . . 69
3.13 T htotal of asymmetric-sized, 10-stage, dual-priority MIN . . . 70
3.14 RT h(h) of asymmetric-sized, 10-stage, dual-priority MIN . . . 71
3.15 RT h(l) of asymmetric-sized, 10-stage, dual-priority MIN . . . 71
3.16 D(h) of asymmetric-sized, 10-stage, dual-priority MIN . . . 72
3.17 D(l)of asymmetric-sized, 10-stage, dual-priority MIN . . . 72
3.18 Upf(h) of asymmetric-sized, 10-stage, dual-priority MIN . . . 73
3.19 Upf(l)of asymmetric-sized, 10-stage, dual-priority MIN . . . 73
4.1 An 8X8 delta-2 network with hotspot trac . . . 77
4.3 Total T h of dual-priority, single-buered, 6-stage MINs . . . 85
4.4 RT h of single-priority, double-buered, 6-stage, single-layer MIN under hotspot trac . . . 86
4.5 RT h of dual-priority, double-buered, 6-stage, single-layer MIN under hotspot trac . . . 86
4.6 D of single-priority, double-buered, 6-stage, single-layer MIN under hotspot trac . . . 87
4.7 D of dual-priority, double-buered, 6-stage, single-layer MIN under hotspot trac . . . 87
4.8 Upf of single-priority, double-buered, 6-stage, single-layer MIN under hotspot trac . . . 88
4.9 Upf of dual-priority, double-buered, 6-stage, single-layer MIN under hotspot trac . . . 88
4.10 RT h of dual-priority, double-buered, 6-stage, multi-layer MIN under hotspot trac . . . 89
4.11 D of dual-priority, double-buered, 6-stage, multi-layer MIN under hotspot trac . . . 89
4.12 Upf of dual-priority, double-buered, 6-stage, multi-layer MIN under hotspot trac . . . 90
5.1 An (NXN) Omega Network . . . 94
5.2 A Multi-Priority (2X2) Switching Element . . . 94
5.3 Total T h of multi-priority, single/double-buered, 10-stage MINs . . . 100
5.4 RT h of multi-priority, single-buered, 10-stage MIN . . . 101
5.5 RT h of multi-priority, double-buered, 10-stage MIN . . . 101
5.6 D of multi-priority, single-buered, 10-stage MIN . . . 102
5.7 D of multi-priority, double-buered, 10-stage MIN . . . 102
5.8 Upf of multi-priority, single-buered, 10-stage MIN . . . 103
5.9 Upf of multi-priority, double-buered, 10-stage MIN . . . 103
6.1 4X4 Single-priority multi-layer MIN . . . 107
6.2 8X8 Single-priority multi-layer MIN . . . 107
6.3 T h of single-priority MINs . . . 120
6.4 D of single-priority MINs . . . 120
6.5 Upf of single-priority MINs . . . 121
6.6 P l of single-priority MINs . . . 121
6.7 T h of single-layer MINs (m=0,0.10) . . . 122
6.8 T h of single-layer MINs (m=0.50) . . . 122
6.9 D of single-layer MINs (m=0.50) . . . 123
6.10 D of single-layer MINs (m=0,0.10) . . . 123
6.11 Upf of single-layer MINs . . . 124
6.13 T h of multi-layer MINs (m=0.50) . . . 125
6.14 T h of multi-layer MINs (m=0.10) . . . 125
6.15 D of multi-layer MINs (m=0.50) . . . 126
6.16 D of multi-layer MINs (m=0.10) . . . 126
6.17 Upf of multi-layer MINs (m=0.50) . . . 127
6.18 Upf of multi-layer MINs (m=0.10) . . . 127
6.19 Pl of multi-layer MINs (m=0.50) . . . 127
6.20 T h of multi-layer MINs (m=0.50) . . . 128
6.21 T h of multi-layer MINs (m=0.10) . . . 128
6.22 D of multi-layer MINs . . . 129
6.23 Pl of multi-layer MINs . . . 129
6.24 Upf of multi-layer MINs (m=0.50) . . . 129
List of Algorithms
2.1 Send-queue process for single- and internal-priority MINs . . . 41
2.2 Switching Element process for single-priority MINs . . . 41
2.3 Switching Element process for internal-priority MINs . . . 42
3.1 Send-queue process of high priority packets for dual-priority MINs . . . 61
3.2 Send-queue process of low priority packets for dual-priority MINs . . . 62
3.3 Switching Element process for dual-priority MINs . . . 64
4.1 Input-queue process for 2-class priority MINs under hotspot environment . 85 5.1 Unicast forwarding for multi-priority MINs . . . 98
5.2 Send-queue process for multi-priority MINs . . . 99
6.1 Unicast/Partial forwarding for multi-layer, multi-priority MINs . . . 116
6.2 Broadcast forwarding for multi-layer, multi-priority MINs . . . 118
Abstract
Multistage Interconnection Networks (MINs) have been widely used as ecient intercon-nection structures for parallel computer systems, as well as switching nodes for high-speed communication networks. Their performance is mainly determined by their communi-cation throughput and their mean packet delay. Although MINs are fairly exible in handling varieties of trac loads, they tend to quickly saturate under either hotspot or multicast/broadcast trac, especially as the size of the network increases. As a response to this issue, multi-priority or/and multi-layer MINs have been proposed, however their performance prediction and evaluation has not been studied suciently insofar. In this thesis we studied the performance of nite-buered MINs by introducing schemes that natively support dierent priority classes -e.g. internal, dual or multi priority-. The ra-tionale behind introducing multiple-priority schemes is to provide dierent QoS (Quality of Service) guarantees to trac from dierent applications, which is a highly desired fea-ture for many IP network operators, and particularly for enterprise networks. Thus, we applied unicast and multicast routing under uniform or hotspot trac conditions both at single- and multi-layer Switching Elements (SEs) under various oered loads using simulations. Moreover, dierent test-bed setups were used in order to investigate and analyze the performance of all priority-class trac, under dierent Quality of Service (QoS) congurations. Finally, we introduced and calculated a universal performance fac-tor, which includes the importance aspect of each of the above main performance factors namely packet throughput and delay, and we found, i.e., that the use of asymmetric-sized buered systems leads to better exploitation of network capacity, while the increments in delays can be tolerated. Consequently, the ndings of this performance evaluation can be used by network designers for designing optimal congurations while setting up MINs, so as to best meet the performance and cost requirements under the anticipated trac load and quality of service specications. The presented results also facilitate performance prediction for multi-layer MINs before actual network implementation, through which deployment cost and rollout time can be minimized.
ÅêôåôáìÝíç Ðåñßëçøç óôá ÅëëçíéêÜ
Ôá ÐïëõâÜèìéá ÄéáóõíäåäåìÝíá Äßêôõá (Multistage Interconnection Networks) ðïõ âáóß-æïíôáé óôïõò Óôáõñùôïýò (Crossbar) Óôïé÷åéþäåéò Äéáêüðôåò (2X2 Switching Elements) óõíÞèùò áðïôåëïýí ôç âáóéêÞ áñ÷éôåêôïíéêÞ äéáóýíäåóçò ôüóï ôùí åðåîåñãáóôþí üóï êáé óôïé÷åßùí ìíÞìçò êõñßùò óå ÐïëõåðåîåñãáóôéêÜ ÓõóôÞìáôá [8, 45, 1]. Ôçí ôåëåõôáßá äåêáåôßá, ôá ÐïëõâÜèìéá ÄéáóõíäåäåìÝíá Äßêôõá (ÐÓÄ) üëï êáé ðåñéóóüôåñï ÷ñçóéìïðïé-ïýíôáé óôçí êáôáóêåõÞ ôüóï ÓõóôçìÜôùí ÌåôáãùãÞò üóï êáé Åðéêïéíùíéáêþí Äéêôýùí õøçëÞò ÷ùñçôéêüôçôáò, üðùò ïé ÁÔÌ (Asynchronous Transfer Mode) Ìåôáãùãåßò, ïé Gi-gabit Ethernet Ìåôáãùãåßò êáé ïé Terabit ÄñïìïëïãçôÝò [46, 42, 4]. ¹äç ç áñ÷éôåêôïíéêÞ ôùí ÐÓÄ ÷ñçóéìïðïéåßôáé óå ðïëëÝò äéáöïñåôéêïý ôýðïõ åöáñìïãÝò êáëýðôïíôáò Ýíá åõñý öÜóìá åöáñìïãÞò áðü ôïõò åóùôåñéêïýò äéáýëïõò åðéêïéíùíßáò êõêëùìÜôùí ðïëý õøçëÞò êëßìáêáò ïëïêëÞñùóçò (VLSI - Very Large Scale Integration) Ýùò ôá åõñåßáò ðåñéï÷Þò Äßêôõá Õðïëïãéóôþí (ð.÷. ùò óôïé÷åßá äéáóýíäåóçò êáôáíåìçìÝíá äéáìïéñáæüìåíùí óôïé-÷åßùí ìíÞìçò Ðïëõåðåîåñãáóôéêþí ÓõóôçìÜôùí Þ ùò óôïé÷åéþäç áñ÷éôåêôïíéêÞ ôçò äéêôý-ùóçò âéïìç÷áíéêþí åöáñìïãþí). Ç áðüäïóç ôùí óôïé÷åßùí äéáóýíäåóçò (êüìâùí, åðåîåñãáóôþí, ìíÞìçò êëð.) áðïôåëåß Ýíáí áðü ôïõò êõñéüôåñïõò ðáñÜãïíôåò ðïõ åðçñåÜæïõí ôç óõíïëéêÞ áðüäïóç ôùí ðáñÜë-ëçëùí êáé êáôáíåìçìÝíùí óõóôçìÜôùí. Áõôü åß÷å ùò áðïôÝëåóìá ðïëëÝò Ýñåõíåò íá åóôéÜóïõí ôç ìåëÝôç ôïõò óôïí êáèïñéóìü ôùí ðáñáãüíôùí ðïõ åðçñåÜæïõí ôçí áðüäïóç åíüò äéêôýïõ äéáóýíäåóçò êáé ãåíéêüôåñá åíüò ðáñÜëëçëïõ óõóôÞìáôïò êáèþò åðßóçò êáé óôçí ðñüâëåøç êáé åêôßìçóç ôçò áðüäïóÞò ôïõ. Ç åðéëïãÞ ôçò êáôÜëëçëçò áñ÷éôåêôïíéêÞò äéáóýíäåóçò ð.÷., óôçí êáôáóêåõÞ åíüò óýã÷ñïíïõ ðáñÜëëçëïõ óõóôÞìáôïò äéáóýíäåóçò ðáßæåé óçìáíôéêü ñüëï óôçí óõíïëéêÞ ôïõ áðüäïóç êáé åîáñôÜôáé áðü ðïëëïýò ðáñÜãïíôåò ìåôáîý ôùí ïðïßùí ïé áðáéôÞóåéò óå åýñïò æþíçò (bandwidth), ç äõíáôüôçôá äéáâÜèìéóçò (scalability), ç åðåêôáóéìüôçôá (expandability), ç äõíáôüôçôá ôìçìáôïðïßçóçò (partition-ability), ïé öõóéêïß ðåñéïñéóìïß, ç áîéïðéóôßá êáèþò êáé ç åðéóêåõáóéìüôçôÜ (repairability) ôïõ.
Óôçí âéâëéïãñáößá ôá ÐïëõâÜèìéá ÄéáóõíäåäåìÝíá Äßêôõá (ÐÓÄ) ôáîéíïìïýíôáé óå äýï êýñéåò êáôçãïñßåò: óôïõò ìåôáãùãåßò äéáßñåóçò ÷ñüíïõ (time division switches) êáé ôïõò ìåôáãùãåßò äéáßñåóçò ÷þñïõ (space division switches). Ìéá ôõðéêÞ ôáîéíüìçóç ôùí ÐÓÄ ç ïðïßá ðåñéëáìâÜíåé ôéò ðéï äéáäåäïìÝíåò êáôçãïñßåò äéêôýùí ðáñïõóéÜæåôáé óôï äéÜãñáììá 1.
Ãéá ôïõò ó÷åäéáóôÝò äéêôýùí ôá crossbar äßêôõá ðÜíôïôå áðïôåëïýóáí óçìåßï Ýëîçò åîáéôßáò ôïõ ãåãïíüôïò üôé äåí ðáñïõóéÜæïõí åóùôåñéêÞ áíÜó÷åóç (non-blocking switches).
ÄéÜãñáììá 1 Ôáîéíüìçóç ÐïëõâÜèìéá ÄéáóõíäåäåìÝíùí Äéêôýùí Ðáñüëá áõôÜ, ç áñ÷éôåêôïíéêÞ ôùí ÐÓÄ ðïõ âáóßæåôáé óôá crossbar äßêôõá ðáñïõóéÜæåé åîáéñåôéêÜ õøçëÞ ðïëõðëïêüôçôá ôüóï óôéò äéáóõíäÝóåéò (paths) üóï êáé óôéò äéáêëáäþóåéò (crosspoints) ç ïðïßá åßíáé ôÜîçò Ï(N2) , üðïõ N åßíáé ï áñéèìüò ôùí èõñþí åéóüäïõ Þ åîüäïõ ôïõ åí ëüãù äéêôýïõ, áðïôñÝðïíôáò Ýôóé ôçí åöáñìïãÞ ôçò óå äßêôõá ìåãÜëïõ ìåãÝèïõò. Óõíåðþò ç ôå÷íïëïãßá crossbar äéêôýùí åíäåßêíõôáé ãéá ôçí êáôáóêåõÞ ìåóáßïõ ìåãÝèïõò Äéêôõáêþí ÓõóôçìÜôùí ôá ïðïßïé äåí ðáñïõóéÜæïõí åóùôåñéêÞ áíÜó÷åóç, åíþ Ý÷ïõí ðáñÜëëçëá ôç äõíáôüôçôá ôçò áõôü-äñïìïëüãçóçò (self-routing). Áðü ôçí Üëëç ðëåõñÜ ôá äßêôõá ôýðïõ Banyan [16] ÷áñáêôçñßæïíôáé áðü ôï ãåãïíüò üôé õðÜñ÷åé Ýíá êáé ìïíáäéêü ìïíïðÜôé ìåôáîý êÜèå èýñáò åéóüäïõ êáé åîüäïõ, äéáèÝôïõí ôç äõíáôüôçôá ôçò áõôü-äñïìïëüãçóçò (self-routing), áëëÜ ðáñïõóéÜæïõí åóùôåñéêÞ áíÜó÷åóç óôçí ðñïþèçóç ôùí ðáêÝôùí ôïõò üôáí ç áíôßóôïé÷ç ïõñÜ ðñïïñéóìïý åßíáé ãåìÜôç. Ç ðïëõðëïêüôçôá üìùò ôùí äéêôýùí ôýðïõ Banyan õðïëïãßæåôáé ùò óõíÜñôçóç Nlog2N êáé åßíáé áéóèçôÜ ìéêñüôåñç åêåßíçò ôùí crossbar äéêôýùí, ìåôáôñÝðïíôáò Ýôóé ôçí åí ëüãù áñ÷éôåêôïíéêÞ ùò âÜóç ãéá ôçí êáôáóêåõÞ ìåãáëýôåñùí óå ìÝãåèïò Äéêôõáêþí ÓõóôçìÜôùí. Äõóôõ÷þò üëåò ïé õðïêáôçãïñßåò ôùí äéêôýùí ôýðïõ Banyan [16] ðáñïõóéÜæïõí åóùôåñéêÞ áíÜó÷åóç êáé åîáéôßáò áõôïý ôïõ ãåãïíüôïò ç áðüäïóÞ ôïõò ðÝöôåé ñáãäáßá êáèþò ôï ìÝãåèüò ôïõò áõîÜíåé åéäéêüôåñá êÜôù áðü óõíèÞêåò öïñôßïõ ôýðïõ multicast Þ hotspot. Ðáñüëá áõôÜ õðÜñ÷ïõí ìåñéêïß ôñüðïé ðïõ ìðïñïýí íá ìåéþóïõí ôçí ðéèáíüôçôá åóùôåñéêÞò áíÜó÷åóçò ôùí ðáêÝôùí, üðùò ç åöáñìïãÞ ðñïôåñáéïôÞôùí Þ ç áñ÷éôåêôïíéêÞ ðïëëáðëþí åðéðÝäùí, óå åðßðåäá ðïõ íá èåùñïýíôáé áðïäåêôÜ áðü ôéò äéáöüñùí ôýðùí åöáñìïãÝò, üðïõ ï áêñéâÞò êáèïñéóìüò ôùí áíåêôéêþí ïñßùí ôçò åêÜóôïôå åöáñìïãÞò ó÷åôßæåôáé Üìåóá ìå ôçí ðïéüôçôá ôçò ðñïóöåñüìåíçò õðçñåóßáò. ¸ôóé üëåò ïé õðïêáôçãïñßåò ôùí äéêôýùí ôýðïõ Banyan, üðùò ôá Omega [26], Delta [35] êáé Generalized Cube [2] äßêôõá ðñïôéìïýíôáé Ýíáíôé ôùí Üëëùí ôýðùí äéêôýùí, äéüôé åßíáé öèçíüôåñá óôçí êáôáóêåõÞ ôïõò êáé åõêïëüôå-ñá óôéò äéáäéêáóßåò Ýëåã÷ïõ.
ÄéÜãñáììá 2 3-óôáäßùí Delta äßêôõï êáôáóêåõáóìÝíï ìå cxc Óôïé÷åéþäåéò Äéáêüðôåò Óôï äéÜãñáììá 2 áðåéêïíßæåôáé Ýíá NXN Delta äßêôõï ôï ïðïßï áðáñôßæåôáé áðü n= logcN óôÜäéá êáé åßíáé êáôáóêåõáóìÝíï áðü cxc Óôïé÷åéþäåéò Äéáêüðôåò (ÓÄ), üðïõ c åßíáé ï âáèìüò ôïõ êÜèå ÓÄ. Óýìöùíá ìå ôï äéÜãñáììá 2 êÜèå óôÜäéï áðáñôßæåôáé áðü N c ÓÄ êáé åðïìÝíùò ï óõíïëéêüò áñéèìüò ÓÄ óå Ýíá ÐÓÄ åßíáé N c ∗logcN. Óôï äéÜãñáììá 3 áðåéêïíßæåôáé Ýíá 8×8 ðïëõåðßðåäï Delta äßêôõï, ôï ïðïßï áðïôåëåßôáé áðü äýï ìÝñç: ôï áñ÷éêü ôï ïðïßï åßíáé ìïíïåðßðåäï êáé óõíßóôáôáé áðü ôïõò ÓÄ ôùí äýï ðñþôùí óôáäßùí êáé ôï åðüìåíï ôï ïðïßï åßíáé äýï åðéðÝäùí êáé óõíßóôáôáé áðü ôïõò ÓÄ ôïõ ôåëåõôáßïõ óôáäßïõ. Óýìöùíá ìå ôï äéÜãñáììá 3 ç ðñïþèçóç åíüò ðáêÝôïõ áðü ôï äåýôåñï ðñïò ôï ôñßôï óôÜäéï ðñáãìáôïðïéåßôáé ÷ùñßò áíáó÷Ýóåéò, äéüôé ôá ðáêÝôá ôïõ äåýôåñïõ óôáäßïõ äåí áíôáãùíßæïíôáé ìåôáîý ôïõò ãéá ôçí ßäéá èÝóç åíäéÜìåóçò ìíÞìçò ôïõ åðüìåíïõ óôáäßïõ êáé óõíåðþò êÜèå unicast Þ multicast åêðïìðÞ åßíáé åëåýèåñç óõãêñïý-óåùí óôï ôåëåõôáßï ðïëõåðßðåäï ôìÞìá ôïõ äéêôýïõ. Ãåíéêüôåñá, áí ï âáèìüò áíáäßðëùóçò (replication) ôïõ åðüìåíïõ óôáäßïõ i+ 1ôïí ïðïßï óõìâïëßæïõìå ìå li+1 éóïýôáé ìå 2∗li ç åêðïìðÞ áðü ôï ôñÝ÷oí ðñïò ôï åðüìåíï óôÜäéï ðñáãìáôïðïéåßôáé Üíåõ óõãêñïýóåùí.
ÄéÜãñáììá 3 8x8 Delta äßêôõï ðïëëáðëþí åðéðÝäùí Óõíåðþò áí ãéá Ýíá ÐÓÄ ìå n óôÜäéá õðÜñ÷åé Ýíáò áñéèìüò nb(1≤nb < n)ôÝôïéïò þóôå ∀k :lk+1 = 2∗lk (nb≤k < n), ôüôå ôï ÐÓÄ èåùñåßôáé üôé ëåéôïõñãåß ÷ùñßò óõãêñïýóåéò ôá ôåëåõôáßá (n−nb) óôÜäéá. ÅðéðëÝïí, óýìöùíá ìå ôïí [50] áíáó÷Ýóåéò èá ìðïñïýóå íá óõìâïýí êáé óôçí Ýîïäï ôïõ ÐÓÄ, åÜí åßôå ï ðïëõðëÝêôçò åßôå ç ãñáììÞ åîüäïõ äåí åß÷áí åðáñêÞ ÷ùñçôéêüôçôá. Ðáñüëá áõôÜ óôç äéáôñéâÞ áõôÞ èåùñïýìå üôé ç Ýîïäïò ôùí ðáêÝôùí áðü ôï ÐÓÄ ðñáãìáôïðïéåßôáé ÷ùñßò óõãêñïýóåéò, äéüôé ï âáèìüò áíáäßðëùóçò ôïõ ÐÓÄ åðéëÝãåôáé ìå ôÝôïéï ôñüðï þóôå íá åðéôõã÷Üíåôáé ç ìÝãéóôç äõíáôÞ áðüäïóç ôïõ äéêôýïõ ìå ôï ÷áìçëüôåñï äõíáôü êüóôïò êáôáóêåõÞò. ÄéÜãñáììá 4 8x8 Delta äßêôõï ìå öïñôßï hotspot ÔÝëïò, óôï äéÜãñáììá 4 áðåéêïíßæåôáé Ýíá (8×8) ÐÓÄ ðïõ äéáèÝôåé ìéá hotspot Ýîïäï ç ïðïßá óôï ðáñáäåéãìÜ ìáò èåùñåßôáé üôé åßíáé ç Ýîïäïò 0 êáé óôçí ïðïßá üëåò ïé åßóïäïé (0-7) óôÝëíïõí Ýíá óçìáíôéêü ìÝñïò ôçò êßíçóÞò ôïõò. ¸ôóé, óýìöùíá ìå ôï äéÜãñáììá
4 üëïé ïé ÓÄ ôïõ ÐÓÄ ìðïñïýí íá ôáîéíïìçèïýí óå äýï êáôçãïñßåò: óôçí ïìÜäá Group-hst êáé Group-nt, üðïõ Group-hst óõìâïëßæåé åêåßíïõò ôïõò ÓÄ ðïõ ëáìâÜíïõí êáé ðñïùèïýí hotspot öïñôßï, åíþ ôï nt óõìâïëßæåé åêåßíïõò ôïõò ÓÄ ðïõ ëáìâÜíïõí êáé ðñïùèïýí ìüíï êáíïíéêü (normal trac or non-hotspot) öïñôßï. Ìå âÜóç ôï áíùôÝñù äéÜãñáììá äéáêñßíïõìå ôéò åîÞò êáôçãïñßåò åîüäùí: • Ýîïäïò 0, ç ìïíáäéêÞ hotspot Ýîïäïò. • Ýîïäïò 1, ç ðëáúíÞ (adjacent) Ýîïäïò. Ôá ðáêÝôá ðïõ äñïìïëïãïýíôáé ðñïò áõôÞ ôçí Ýîïäï óõãêñïýïíôáé ìå ôá ðáêÝôá ðïõ êáôåõèýíïíôáé ðñïò ôç hotspot Ýîïäï êáôÜ ôç äéÜñêåéá üëùí ôùí åíäéÜìåóùí óôáäßùí êáé åßíáé åëåýèåñá ôÝôïéùí óõãêñïýóåùí ìüíï üôáí äéáó÷ßæïõí ôçí Ýîïäï (output link). • Ýîïäïé 2 êáé 3, ïé ïðïßåò åßíáé åëåýèåñåò óõãêñïýóåùí ìå ðáêÝôá ðïõ äñïìïëïãïýíôáé ðñïò ôç hotspot Ýîïäï êáôÜ ôç äéÜñêåéá ôïõ ôåëåõôáßïõ óôáäßïõ ôïõ ÐÓÄ. ÁõôÝò ïé Ýîïäïé ïíïìÜæïíôáé Cold-1, äéüôé áêñéâþò åßíáé åëåýèåñåò óõãêñïýóåùí ìå hotspot öïñôßï ìüíï êáôÜ Ýíá óôÜäéï. • Ýîïäïé 4-7, ïé ïðïßåò åßíáé åëåýèåñåò óõãêñïýóåùí ìå ðáêÝôá ðïõ äñïìïëïãïýíôáé ðñïò ôç hotspot Ýîïäï êáôÜ ôç äéÜñêåéá ôùí äýï ôåëåõôáßùí óôáäßùí ôïõ ÐÓÄ êáé ïíïìÜæïíôáé Cold-2. Ãåíéêåýïíôáò óå Ýíá i-óôáäßùí ÐÓÄ, ïé èýñåò åîüäïõ ôïõ ìðïñïýí íá ôáîéíïìçèïýí óôéò áêüëïõèåò (i+ 1) æþíåò: hotspot, adjacent, and cold-j (1≤j ≤i−1).
¼ëá ôá ÐïëõâÜèìéá ÄéáóõíäåäåìÝíá Äéêôýá ðïõ åîåôÜæïõìå óå áõôÞ ôç äéáôñéâÞ áíÞêïõí óôçí êáôçãïñßá ôùí Banyan Switches êáé ëåéôïõñãïýí êÜôù áðü ôéò áêüëïõèåò èåùñÞóåéò:
• Ç äñïìïëüãçóç åêôåëåßôáé ùò ìéá pipeline äéåñãáóßá ìå ôçí Ýííïéá üôé åêôåëåßôáé ðáñÜëëçëá óå êÜèå óôÜäéï. Ï óõã÷ñïíéóìüò ôùí åóùôåñéêþí ñïëïãéþí ëåéôïõñãåß óå äéáêåêñéìÝíá ÷ñïíéêÜ äéáóôÞìáôá (slotted time model) [44] êáé ïé Óôïé÷åéþäåéò 2X2 Äéáêüðôåò (ÓÄ) Ý÷ïõí åðáêñéâþò ðñïêáèïñéóìÝíï ÷ñüíï åîõðçñÝôçóçò ôùí ðáêÝôùí (deterministic service time).
• Ç Üöéîç ôùí ðáêÝôùí óå êÜèå åßóïäï ôïõ äéêôýïõ åßíáé ìéá áðëÞ äéåñãáóßá Bernoulli, ð.÷., ç ðéèáíüôçôá Üöéîçò åíüò ðáêÝôïõ óå Ýíá ùñïëïãéáêü êýêëï åßíáé óôáèåñÞ êáé ïé áößîåéò åßíáé ìåôáîý ôïõò áíåîÜñôçôåò. • ÅðéðëÝïí, êáôÜ ôçí Üöéîç åíüò ðáêÝôïõ óôçí åßóïäï (äçë. óå ìéá ïõñÜ åíüò ÓÄ ôïõ ðñþôïõ óôáäßïõ) åÜí ç åíäéÜìåóç ìíÞìç (buer) ôçò åí ëüãù ïõñÜò åßíáé ãåìÜôç ôï ðáêÝôï áõôü áðïññßðôåôáé. • ¸íá ðáêÝôï èåùñåßôáé üôé âñßóêåôáé óå êáôÜóôáóç áíÜó÷åóçò óå ìéá ïõñÜ ôïõ ôñÝ÷ïíôïò óôáäßïõ åÜí ç åíäéÜìåóç ìíÞìç ðñïïñéóìïý ôïõ åðüìåíïõ óôáäßïõ åßíáé ãåìÜôç.
• ¼ôáí äõï ðáêÝôá óå Ýíá óôÜäéï áíôáãùíßæïíôáé ãéá ôçí ÷ñÞóç ôçò ßäéáò åíäéÜìåóçò ìíÞìçò ôçò ïõñÜò ðñïïñéóìïý ôïõ åðïìÝíïõ óôáäßïõ åîáéôßáò ôïõ ãåãïíüôïò üôé äåí õðÜñ÷åé åðáñêÞò ÷þñïò ãéá íá áðïèçêåõôïýí êáé ôá äõï ðáêÝôá, ôüôå óõìâáßíåé óýãêñïõóç êáé óôçí ðåñßðôùóç ðïõ äåí õðïóôçñßæïíôáé ðñïôåñáéüôçôåò Ýíá áðü ôá äýï ðáêÝôá ìå ôõ÷áßï ôñüðï ãßíåôáé áðïäåêôü óôçí åí ëüãù ïõñÜ, åíþ ôï Üëëï ðáñáìÝíåé óå êáôÜóôáóç áíÜó÷åóçò óôï ôñÝ÷ïí óôÜäéï. Óôçí ðåñßðôùóç üìùò ôçò ðñïôåéíüìåíçò (internal-priority) äñïìïëüãçóçò üðïõ õðïóôçñßæåôáé ç ðñïôåñáéüôçôá åêåßíùí ôùí ðáêÝôùí ðïõ ïé ïõñÝò ôïõò Ý÷ïõí ìåãáëýôåñï ðëçèõóìü, óå êáôÜóôáóåéò óýãêñïõóçò ðñïçãïýíôáé åêåßíá ôá ðáêÝôá ðïõ ðñïÝñ÷ïíôáé áðü ÓÄ üðïõ ôï ìÝãåèïò ôçò åíäéÜìåóçò ìíÞìçò ôùí åí ëüãù ïõñþí åßíáé ìåãáëýôåñï ôùí áíôßóôïé÷ùí ïõñþí ôùí áíôáãùíéæüìåíùí ðáêÝôùí. • Óå ðåñéðôþóåéò õëïðïßçóçò äéêôýùí ðïõ õðïóôçñßæïõí ðñùôïãåíþò ðïëëáðëÝò ðñïôå-ñáéüôçôåò êáôÜ ôçí ðñïþèçóç ôùí ðáêÝôùí, ïé åí ëüãù ðñïôåðñïôå-ñáéüôçôåò áíôáíáêëïýí ôçí ðïéüôçôá ôçò ðáñå÷üìåíçò õðçñåóßáò. Ãéá ôçí êáôáóêåõÞ ôùí ÓÄ ôùí ÐÓÄ ÷ñçóéìïðïéþíôáé äéáöïñåôéêÝò ïõñÝò áðïèÞêåõóçò áíÜ êáôçãïñßá ðñïôåñáéüôçôáò, åíþ êÜèå ðáêÝôï óôçí åßóïäï ôïõ äéêôýïõ óçìáäåýåôáé ìå ôçí êáôÜëëçëç ðñïôåñáéüôç-ôá ðñéí ïäçãåéèåß óôçí áíôßóôïé÷çò ôÜîçò ïõñÜ. ¸ôóé êáôÜ ôç äéáäéêáóßá åðßëõóçò óõãêñïýóåùí ëáìâÜíåôáé õðüøç ç ðñïôåñáéüôçôá êÜèå ðáêÝôïõ, üðïõ ðñïöáíþò ôá ðáêÝôá ìå ôçí õøçëüôåñç ðñïôåñáéüôçôá ðñïçãïýíôáé óôç äñïìïëüãçóç åêåßíùí ðïõ äéáèÝôïõí ÷áìçëüôåñç ðñïôåñáéüôçôá. • Óå ðåñéðôþóåéò õðïóôÞñéîçò hotspot öïñôßïõ õðÜñ÷åé Ýíá áñ÷éêü êëÜóìá fhs ôïõ óõíïëéêïý öïñôßïõ óå êÜèå åßóïäï ôïõ ÐÓÄ ôï ïðïßï äñïìïëïãåßôáé ðñïò ìéá óõãêåêñéìÝíç hotspot Ýîïäï, ç ïðïßá ãéá üëåò ôéò ðåñéðôþóåéò ìåëÝôçò èåùñåßôáé üôé åßíáé ç Ýîïäïò 0. Óå Ýíá äßêôõï üðïõ õðïóôçñßæåé ðïëëáðëÝò ðñïôåñáéüôçôåò ôï hotspot öïñôßï ÷áñáêôçñßæåôáé åî áñ÷Þò ùò öïñôßï ÷áìçëÞò ðñïôåñáéüôçôáò (low priority trac). ¸ôóé óå Ýíá ÐÓÄ ðïõ õðïóôçñßæåé äýï êáôçãïñßåò ðñïôåñáéïôÞôùí (dual-priority scheme) ôá åíáðïìåßíáíôá ðáêÝôá[∗(1−fhs)]äýíáôáé íá ÷áñáêôçñé-óôïýí åßôå ùò õøçëÞò åßôå ùò ÷áìçëÞò ðñïôåñáéüôçôáò êáé êáôáíÝìïíôáé ïìïéüìïñöá óå üëåò ôéò åîüäïõò. Áõôü óçìáßíåé üôé ïðïéáäÞðïôå Ýîïäïò ôïõ ÐÓÄ, åêôüò âÝâáéá ôçò hotspot åîüäïõ Ý÷åé áêñéâþò ôçí ßäéá ðéèáíüôçôá íá áðïôåëÝóåé ôç äéåýèõíóç ðñïïñéóìïý åíüò ðáêÝôïõ. ÐÝñáí ôïõ öïñôßïõ ðïõ åîáñ÷Þò ÷áñáêôçñßæåôáé ùò hotspot ï õðüëïéðïò ñõèìüò åéóüäïõ ðáêÝôùí[∗(1−fhs)]óôï ÐÓÄ äñïìïëïãåßôáé ïìïéüìïñ-öá ðñïò üëåò ôéò èýñåò åîüäïõ, óõìðåñéëáìâáíïìÝíçò êáé ôçò hotspot, Ýôóé Ýíá åðéðëÝïí öïñôßï [( ∗ (1− fhs))=N] ðñïùèåßôáé ðñïò ôç hotspot Ýîïäï, ôï ïðïßï óõìðåñéëáìâÜíåé ôüóï ÷áìçëÞò üóï êáé õøçëÞò ðñïôåñáéüôçôáò ðáêÝôá. • Óå ðåñéðôþóåéò õðïóôÞñéîçò multicast öïñôßïõ, ç åðéêåöáëßäá êÜèå ðáêÝôïõ ðåñéëáìâÜ-íåé ôá áêüëïõèá äýï éóïìåãÝèç ðåäßá Routing Address (RA) êáé Multicast Mask (MM), üðïõ ôï êáèÝíá áðü áõôÜ êáôáëáìâÜíåé n bits, üðïõ n åßíáé ï óõíïëéêüò áñéèìüò ôùí óôáäßùí ôïõ ÐÓÄ. ¸ôóé, êáôÜ ôçí Üöéîç åíüò ðáêÝôïõ óå Ýíá ÓÄ ôïõ k óôáäßïõ, áñ÷éêÜ åîåôÜæåôáé ôï áíôßóôïé÷ï bit ôçò MM êáé áí áõôü âñåèåß ßóï ìå
1 ôüôå ôï ðáêÝôï åêôåëåß ìéá multicast áíôß unicast åêðïìðÞò, áíôéãñÜöïíôáò ôï êáé óôéò äõï åîüäïõò ôïõ ÓÄ. Áíôßèåôá üôáí ôï åí ëüãù bit ôçò MM âñåèåß üôé åßíáé 0, ôüôå êáé ìüíï ôüôå åîåôÜæåôáé ôï áíôßóôïé÷ï bit ôçò RA, þóôå ôï ðáêÝôï íá áêïëïõèÞóåé ôçí êáôÜëëçëç unicast åêðïìðÞ. Åßíáé ðñïöáíÝò üôé üôáí üëá ôá bits ôçò MM åíüò ðáêÝôïõ åßíáé ìçäÝí, ôüôå ôï ðáêÝôï áêïëïõèåß ìéá áðëÞ äéáäñïìÞ (unicast), öôÜíïíôáò óå ìéá óõãêåêñéìÝíç Ýîïäï. Áðü ôçí Üëëç ðëåõñÜ, óôçí áêñáßá ðåñßðôùóç, ðïõ üëá ôá bits ôçò MM Ý÷ïõí ôåèåß ßóá ìå ôç ìïíÜäá, ôüôå ôï åí ëüãù ðáêÝôï åêðÝìðåôáé óå üëåò ôéò åîüäïõò (broadcast) ôïõ ÐÓÄ. Óå üëåò ôéò Üëëåò ðåñéðôþóåéò ôï ðáêÝôï ðñïùèåßôáé óå ìéá ïìÜäá èõñþí åîüäïõ ç ïðïßá áðïôåëåß ôçí ïìÜäá Multicast Group (MG). • ÔÝëïò üëá ôá ðáêÝôá óôéò èýñåò åéóüäïõ ðåñéëáìâÜíïõí ôüóï ôá äåäïìÝíá ðïõ ðñÝðåé íá ìåôáöåñèïýí üóï êáé ôéò åôéêÝôåò äñïìïëüãçóçò (routing tags). ¸ôóé, êáèüóïí ôá ðáêÝôá öôÜíïõí óôç äéåýèõíóç ðñïïñéóìïý ôïõò áðïìáêñýíïíôáé Üìåóá áðü ôï ÐÓÄ ìå áðïôÝëåóìá íá ìçí ëáìâÜíåé ÷þñá áíÜó÷åóç ðáêÝôùí êáôÜ ôç äéÝëåõóÞ ôùí áðü ôï ôåëåõôáßï óôÜäéï ôïõ ÐÓÄ . Ãéá ôïí õðïëïãéóìü åíüò (N X N) ÐÓÄ áðïôåëïýìåíï áðü n=logcN åíäéÜìåóá óôÜäéá ìå (cxc) ÓÄ, ÷ñçóéìïðïéïýìå ôéò áêüëïõèåò ìïíÜäåò ìÝôñçóçò. ¸óôù T Ýíá ó÷åôéêÜ ìåãÜëï ÷ñïíéêü äéÜóôçìá äéáéñåìÝíï óå u äéáêñéôÜ ÷ñïíéêÜ äéáóôÞìáôá (1; 2;· · · ; u)
Average throughput T havg åßíáé ï ìÝóïò áñéèìüò ðáêÝôùí ðïõ ãßíïíôáé áðïäåêôÜ óå
üëïõò ôïõò ðñïñéóìïýò åîüäïõ áíÜ äéêôõáêü êýêëï. ÁõôÞ ç ìïíÜäá ìÝôñçóçò áíáöÝñåôáé êáé ùò åýñïò æþíçò. ¸ôóé ôï T havg ìðïñåß íá ïñéóôåß ùò åîÞò T havg = limu→∞ Pu k=1na(k) u (1) üðïõ ôï na(k)äçëþíåé ôïí áñéèìü ôùí ðáêÝôùí ôá ïðïßá öôÜíïõí óôïõò ðñïïñéóìïýò ôïõò êáôÜ ôç äéÜñêåéá ôïõ kth ÷ñïíéêïý äéáóôÞìáôïò.
Normalized throughput T h åßíáé ôï ðçëßêï ôïõ average throughput T havg ðñïò ôïí
óõíïëéêü áñéèìü ôùí èõñþí åîüäïõ ôïõ äéêôýïõ N. ¸ôóé ôï T h ìðïñåß íá åêöñáóôåß ìå ôïí áêüëïõèï ôýðï
T h= T havg
N (2)
Average packet delay Davg åßíáé ï ìÝóïò ÷ñüíïò ðïõ áðáéôåßôáé ãéá íá äéáó÷ßóåé Ýíá
ðáêÝôï ôï äßêôõï êáé ìðïñåß íá åêöñáóôåß ìå ôïí áêüëïõèï ôýðï Davg = limu→∞ Pna(u) k=1 td(k) na(u) (3) üðïõ ôï na(u)äçëþíåé ôï óõíïëéêü áñéèìü ðáêÝôùí ðïõ ãßíïíôáé áðïäåêôÜ êáôÜ ôç äéÜñêåéá ôùí u ÷ñïíéêþí äéáóôçìÜôùí åíþ ôï td(k)áíáðáñéóôÜíåé ôç óõíïëéêÞ êáèõóôÝñçóç ãéá ôï kth ðáêÝôï. Áíáëõôéêüôåñá, èåùñïýìå üôé t d(k) = tw(k) + ttr(k) üðïõ tw(k) äçëþíåé ôç óõíïëéêÞ êáèõóôÝñçóç ðïõ ëáìâÜíåé ÷þñá óå üëåò ôéò ïõñÝò áðü üðïõ äéÝñ÷åôáé ôï kth ðáêÝôï, åíþ áõôü âñßóêåôáé óå êáôÜóôáóç áíáìïíÞò ìÝ÷ñé ôçí ýðáñîç äéáèåóéìüôçôáò ìéáò
åíäéÜìåóçò ìíÞìçò ôïõ åðüìåíïõ óôáäßïõ ãéá ôçí ðñïþèçóç ôïõ åí ëüãù ðáêÝôïõ. Ï äåýôåñïò üñïò ttr(k) äçëþíåé ôç óõíïëéêÞ êáèõóôÝñçóç ðïõ áðáéôåßôáé ãéá ôçí äéÜäïóç ôïõ
kth ðáêÝôïõ óå êÜèå åíäéÜìåóï óôÜäéï ôïõ äéêôýïõ êáé ôï ïðïßï éóïýôáé ìå n∗nc, üðïõ
n =log2N åßíáé ï áñéèìüò üëùí ôùí åíäéÜìåóùí óôáäßùí, åíþ ôï nc óõìâïëßæåé ôï ÷ñüíï
åíüò äéêôõáêïý êýêëïõ.
Normalized packet delay D åßíáé ôï ðçëßêï ôïõ Davgðñïò ôçí åëÜ÷éóôç êáèõóôÝñçóç
åíüò ðáêÝôïõ ç ïðïßá èåùñåßôáé üôé åßíáé ç êáèõóôÝñçóç äéÜäïóçò n ∗nc (ð.÷., üôáí ç
êáèõóôÝñçóç óå üëåò ôéò ïõñÝò åßíáé ìçäåíéêÞ). ¸ôóé, ôï D ìðïñåß íá ïñéóôåß ùò D= Davg
n∗nc (4)
Universal performance factor Upf êáèïñßæåôáé áðü ìéá ó÷Ýóç ðïõ ðåñéëáìâÜíåé ôïõò äõï ðáñáðÜíù êýñéïõò ðáñÜãïíôåò áðüäïóçò D êáé T h. Ç áðüäïóç åíüò ÐÓÄ èåùñåßôáé âÝëôéóôç üôáí ï ðáñÜãïíôáò D åëá÷éóôïðïéåßôáé êáé ï ðáñÜãïíôáò T h ìåãéóôïðïé-åßôáé, Ýôóé ç öüñìïõëá ãéá ôïí õðïëïãéóìü ôïõ Upf ìðïñåß íá åêöñáóôåß ìå ôçí áêüëïõèç ó÷Ýóç Upf = r wd∗D2+wth∗ T h12 (5) üðïõ ïé äåßêôåò wdêáé wthäçëþíïõí ôéò áíôßóôïé÷åò âáñýôçôåò ôùí óõíéóôùóþí ðáñáãü-íôùí ôïõ Upf, êáèïñßæïíôáò Ýôóé åðáêñéâþò ôç óðïõäáéüôçôá ôçò êÜèå óõíéóôþóáò ìå ôï ðåñéâÜëëïí ëåéôïõñãßáò. Óõíåðþò ç áðüäïóç åíüò ÐÓÄ ìðïñåß íá åêöñáóôåß áðü ìéá óõíäõáóôéêÞ ìïíÜäá ìÝôñçóçò üðïõ ðñïöáíþò üôáí ï ðáñÜãïíôáò packet delay ãßíåôáé ìéêñüôåñïò Þ/êáé ï ðáñÜãïíôáò throughput ãßíåôáé ìåãáëýôåñïò ïé ôéìÝò ôïõ Upf ìéêñáß-íïõí, Ýôóé þóôå ìéêñüôåñåò ôéìÝò ãéá ôï Upf íá õðïäçëþíïõí êáëýôåñç óõíïëéêÞ áðüäïóç ãéá ôï ÐÓÄ. ÅðåéäÞ ïé áíùôÝñù óõíéóôþóåò D êáé T h Ý÷ïõí äéáöïñåôéêÝò êëßìáêåò ôéìþí, ìå ôçí êáíïíéêïðïßçóÞ ôïõò ðñïêýðôåé Ýíá êïéíü ðåäßï áíáöïñÜò. Ç êáíïíéêïðïßçóç ðñáãìáôïðïéåßôáé ìå ôç äéáßñåóç ôçò ôéìÞò ôïõ êÜèå ðáñÜãïíôá ìå ôçí áëãåâñéêÞ ôïõ åëÜ÷éóôç Þ ìÝãéóôç ôéìÞ ðïõ ï êÜèå ðáñÜãïíôáò ëáìâÜíåé. ¸ôóé, ç åîßóùóç 2 ìðïñåß íá áíôéêáôáóôáèåß ìå ôçí áêüëïõèç ðáñÜóôáóç: Upf = s wd∗ µ D−Dmin Dmin ¶2 +wth∗ µ T hmax−T h T h ¶2 (6) üðïõ Dmin åßíáé ç åëÜ÷éóôç ôéìÞ ôïõ normalized packet delay (D) êáé T hmax ç ìÝãéóôç
ôéìÞ ôïõ normalized throughput. ÅðïìÝíùò, üôáí ï óõíäõáóôéêüò ðáñÜãïíôáò univer-sal performance factor Upf, ôåßíåé óôï 0, ç áðüäïóç ôïõ ÐÓÄ èåùñåßôáé âÝëôéóôç, åíþ üôáí ï ðáñÜãïíôáò Upf áõîÜíåé ç óõíïëéêÞ áðüäïóç ôïõ ÐÓÄ èåùñåßôáé üôé ÷åéñïôåñýåé. ÔÝëïò, ëáìâÜíïíôáò õðüøç üôé ïé äýï ôéìÝò ôùí óõíéóôùóþí delay êáé throughput ðïõ óõììåôÝ÷ïõí óôïõò áíùôÝñù ôýðïõò åßíáé êáíïíéêïðïéçìÝíåò éó÷ýåé Dmin = T hmax = 1, êáé åðïìÝíùò ç ðáñáðÜíù ðáñÜóôáóç ìðïñåß íá áðëïðïéçèåß ìå ôçí ðáñáêÜôù åîßóùóç Upf = s wd∗(D−1)2+wth∗ µ 1−T h T h ¶2 (7)
¼ëåò ïé áíùôÝñù åîéóþóåéò ìðïñïýí íá ðñïóáñìïóôïýí êáôÜëëçëá Ýôóé þóôå íá éó÷ýïõí êáé óå ðåñéðôþóåéò ÐÓÄ ðïõ õðïóôçñßæïõí ðñïôåñáéüôçôåò, hotspot öïñôßï, multicast öïñôßï Þ áêüìç ðïëõåðßðåäïõò ÓÄ. Óôçí äéáôñéâÞ áõôÞ õðïëïãßæïõìå ôüóï ôéò óõíéóôþóåò ðáñáìÝôñïõò üóï êáé ôç óõíïëéêÞ áðüäïóç ôùí ÐÓÄ áíáðôýóóïíôáò åéäéêïý óêïðïý ðñïãñÜììáôá åîïìïßùóçò óå C++, ôá ïðïßá äýíáôáé íá ëåéôïõñãïýí êÜôù áðü äéáöïñåôéêÜ ðåñéâÜëëïíôá ëåéôïõñãßáò. Ç åêôßìçóç áðüäïóçò åíüò ÐÓÄ ðñáãìáôïðïéåßôáé êõñßùò åöáñìüæïíôáò ôå÷íéêÝò åîïìïßùóçò óå ó÷Ýóç ìå ôçí åöáñìïãÞ ðëÞñïõò ìáèçìáôéêÞò ìïíôåëïðïßçóçò [13], åîáéôßáò ôçò õøçëÞò ðïëõðëïêüôçôáò ç ïðïßá ðçãÜæåé áðü ôï óõíäõáóìü äéáöüñùí ðáñáìÝôñùí üðùò ç åíóùìÜ-ôùóç ðïëëáðëþí ðñïôåñáéïôÞôùí, ç õðïóôÞñéîç öïñôßïõ multicast Þ hotspot, êáèþò êáé ç ÷ñÞóç ðïëëáðëþí åíäéÜìåóùí ìíçìþí óôïõò ÓÄ. Ôá ðñïãñÜììáôá åîïìïßùóçò õðïóôçñß-æïõí äéáöüñùí ôýðùí åêðïìðþí üðùò ð.÷., full-multicast åêðïìðÞ, üðïõ Ýíá ðáêÝôï ðñïù-èåßôáé åÜí êáé ìüíï åÜí êáé ïé äõï ïõñÝò ôïõ åðïìÝíïõ óôáäßïõ äéáèÝôïõí åðáñêÞ åíäéÜìåóç ìíÞìç ãéá ôçí áðïèÞêåõóç êáé ôùí äýï áíôéãñÜöùí Þ partial-multicast åêðïìðÞ (äåò ðáñáêÜôù áëãüñéèìï ðñïþèçóçò), üðïõ Ýíá ðáêÝôï äýíáôáé íá åîõðçñåôçèåß åßôå ðëÞñùò, äçëáäÞ êáé ðñïò ôéò äýï êáôåõèýíóåéò, åßôå ìåñéêþò, äçëáäÞ ìüíï ùò ðñïò ôç ìßá êáôåýèõíóç, ðáñáìÝíïíôáò óôçí ïõñÜ åêðïìðÞò åùóüôïõ åîõðçñåôçèåß êáé ùò ðñïò ôç äåýôåñç êáôåýèõí-óç. ÊáôÜ ôçí åöáñìïãÞ ôçò åîïìïßùóçò ôïõ ðåñéâÜëëïíôïò ëåéôïõñãßáò åíüò ÐÓÄ, ëáìâÜ-íïíôáé õðüøç áñêåôÝò ðáñÜìåôñïé üðùò ôï ìÞêïò ôçò åíäéÜìåóçò ìíÞìçò (buer-length), ï áñéèìüò åéóüäùí êáé åîüäùí (number of input and output ports), ï áñéèìüò ôùí óôáäßùí (number of stages), ôï óõíïëéêü öïñôßï óôçí åßóïäï (oered load), ôï ðïóïóôü multicast åêðïìðÞò (multicast ratio), ôï áñ÷éêü ðïóïóôü hotspot öïñôßïõ (initial hotspot fraction), ï áñéèìüò ôùí ðñïôåñáéïôÞôùí êáé ôá áíôßóôïé÷á ðïóïóôÜ ôïõò (number of priority classes and ratios), êáèþò êáé ï áñéèìüò ôùí åðéðÝäùí (number of layers).
Áëãüñéèìoò broadcast åêðïìðÞò ðáêÝôùí ðïëëáðëþí ðñïôåñáéïôÞôùí óå ÐÓÄ ðïëëáðëþí åðéðÝäùí Broadcast Forwarding (csid; clid; nlid; sqid; uqid; lqid; prid; mp; bm) Input: ôñÝ÷ïí óôÜäéï (csid) ; åðßðåäï ôñÝ÷ïíôïò êáé åðüìåíïõ óôáäßïõ (clid; nlid) ôùí ïõñþí áðïóôïëÞò êáé ðñïïñéóìïý áíôßóôïé÷á ; ïõñÜ áðïóôïëÞò (sqid) ôñÝ÷ïíôïò óôáäßïõ ; åðüìåíïõ óôáäßïõ ïõñÜ Üíù êáé êÜôù èýñáò åîüäïõ áíôßóôïé÷á uqid; lqid ; êáôçãïñßá ðñïôåñáéüôçôáò (prid) ; ðïëéôéêÞ äñïìïëüãçóçò multicast ðáêÝôùí (mp) ; ìç÷áíéóìüò áíÜó÷åóçò (bm). Output: Ðëçèõóìüò ïõñþí áðïóôïëÞò êáé ðñïïñéóìïý(P op); óõíïëéêüò áñéèìüò ðáêÝôùí êÜèå ïõñÜò áðïóôïëÞò ðïõ åîõðçñåôÞèçêáí Þ áíáó÷Ýèçêáí áíôßóôïé÷á(Serviced; Blocked) ; óõíïëéêüò áñéèìüò êýêëùí êáèõóôÝñçóçò ãéá êÜèå ïõñÜ áðïóôïëÞò(Delay) ; äéåýèõíóç äñïìïëüãçóçò ðáêÝôïõ RA óå êÜèå èÝóç åíäéÜìåóçò ìíÞìçò; äåßêôçò ìåñéêÞò åîõðçñÝôçóçò multicast ðáêÝôùí óôçí êïñõöÞ êÜèå ïõñÜò áðïóôïëÞò (P S). { if (P op[uqid][csid+ 1][nlid][prid] =B) or (P op[lqid][csid+ 1][nlid][prid] = B)
// êáôÜóôáóç áíÜó÷åóçò
{
Blocked[sqid][csid][clid][prid] =Blocked[sqid][csid][clid][prid] + 1 ;
if (mp= “full”)and (bm= “blm”)// block and lost mechanism;
{ P op[sqid][csid][clid][prid] =P op[sqid][csid][clid][prid]−1 ; for (bfid = 1;bfid >=P op[sqid][csid][clid][prid];bfid+ +) RA[sqid][csid][clid][prid][bfid] =RA[sqid][csid][clid][prid][bfid+ 1] ; // üðïõ RA åßíáé ç äéåýèõíóç äñïìïëüãçóçò // ðáêÝôïõ ôçò (bfid)th èÝóçò åíäéÜìåóçò ìíÞìçò ïõñÜò áðïóôïëÞò } } if (P op[uqid][csid+ 1][nlid][prid]< B) and (P op[lqid][csid+ 1][nlid][prid]< B) { // ðñïþèçóç broadcast Serviced[sqid][csid][clid][prid] = Serviced[sqid][csid][clid][prid] + 1 ; P op[sqid][csid][clid][prid] =P op[sqid][csid][clid][prid]−1 ; P op[uqid][csid+ 1][nlid][prid] = P op[uqid][csid+ 1][nlid][prid] + 1 ; P op[lqid][csid+ 1][nlid][prid] =P op[lqid][csid+ 1][nlid][prid] + 1 ; RA[uqid][csid+1][nlid][prid][P op[uqid][csid+1][nlid][prid]] =RA[sqid][csid][clid][prid][1]; RA[lqid][csid+1][nlid][prid][P op[lqid][csid+1][nlid][prid]] =RA[sqid][csid][clid][prid][1]; for (bfid = 1;bfid >=P op[sqid][csid][clid][prid];bfid+ +) RA[sqid][csid][clid][prid][bfid] =RA[sqid][csid][clid][prid][bfid+ 1] ; P S[sqid][csid][clid][prid] =−1 ; // áñ÷éêïðïßçóç äåßêôç îáíÜ }
if (mp= “partial”)// partial multicast ðïëéôéêÞ äñïìïëüãçóçò
{ if (P op[uqid][csid+ 1][nlid][prid]< B)and (P op[lqid][csid+ 1][nlid][prid] =B) { // Üíù èýñáò partial multicast åîõðçñÝôçóç P op[uqid][csid+ 1][nlid][prid] = P op[uqid][csid+ 1][nlid][prid] + 1 ; RA[uqid][csid+1][nlid][prid][P op[uqid][csid+1][nlid][prid]] =RA[sqid][csid][clid][prid][1]; P S[sqid][csid][clid][prid] = 0 ; } if (P op[uqid][csid+ 1][nlid][prid] =B)and (P op[lqid][csid+ 1][nlid][prid]< B) { // êÜôù èýñáò partial multicast åîõðçñÝôçóç P op[lqid][csid+ 1][nlid][prid] =P op[lqid][csid+ 1][nlid][prid] + 1 ;
RA[lqid][csid+1][nlid][prid][P op[lqid][csid+1][nlid][prid]] =RA[sqid][csid][clid][prid][1];
P S[sqid][csid][clid][prid] = 1 ;
} }
Delay[sqid][csid][clid][prid] =Delay[sqid][csid][clid][prid] +P op[sqid][csid][clid][prid] ;
return P op; Serviced; Blocked; Delay; RA; P S ;
}
ÅóùôåñéêÜ, êÜèå ÓÄ ðåñéëáìâÜíåé Ýíáí ðßíáêá áðü p ìç äéáìïéñáæüìåíá æåýãç åíäéÜìå-óùí ìíçìþí (non-shared buer queue pairs), üðïõ p åêöñÜæåé ôï óõíïëéêü áñéèìü êáôçãï-ñéþí ðñïôåñáéïôÞôùí, üðïõ ãéá êÜèå êáôçãïñßáò æåýãïò ïõñþí, ç ìéá åíäéÜìåóç ìíÞìç ÷ñçóéìïðïéåßôáé áðïêëåéóôéêÜ áðü ôçí Üíù óõóôïé÷ßá, åíþ ç äåýôåñç áðïêëåéóôéêÜ áðü ôçí êÜôù óõóôïé÷ßá ïõñþí. Óå üëåò ôéò ðåñéðôþóåéò ÷ñÞóçò åíäéÜìåóçò ìíÞìçò ç ëåéôïõñãßá ôïõò âáóßæåôáé óôçí áñ÷Þ FCFS (First Come First Serviced). ÅðéðëÝïí óå ðåñéðôþóåéò áíôáãùíéóìïý êÜëõøçò ìéáò åíäéÜìåóçò ìíÞìçò üôáí õðïóôçñßæïíôáé ðïëëáðëÝò ðñïôåñáéü-ôçôåò ôá ðáêÝôá ìå ôçí õøçëüôåñçò ôÜîçò ðñïôåñáéüôçôá ðñïçãïýíôáé Ýíáíôé üëùí ôùí Üëëùí. ¼ëåò ïé ðåñéðôþóåéò ìåëÝôçò åêðïìðÞò ðïõ âáóßóôçêáí óôçí ôå÷íéêÞ ðñïóïìïßùóçò åêôåëÝóôçêáí ìå ôçí åöáñìïãÞ ðñïþèçóçò ðáêÝôùí óôáèåñïý ìÞêïõò ìÝóá óå óôáèåñÜ ÷ñïíéêÜ äéáóôÞìáôá, üðïõ êÜèå êýêëïò åêðïìðÞò èåùñåßôáé ï ÷ñüíïò ðïõ áðáéôåßôáé ãéá ôçí ðñïþèçóç åíüò Þ äýï áíôéãñÜöùí ôïõ ðáêÝôïõ óå ðåñéðôþóåéò unicast Þ broadcast åêðïìðÞò áíôßóôïé÷á. ÊáôÜ ôç äéÜñêåéá åêôÝëåóçò ôùí ðåéñáìÜôùí óõãêåíôñþíïíôáé ôéìÝò ãéá üëá ôá ìåãÝèç áðüäïóçò ðïõ åîåôÜæïõìå ãéá ôï ÐÓÄ êáé ðéï óõãêåêñéìÝíá ãéá ôï åýñïò æþíçò (packet throughput), ôçí êáèõóôÝñçóç (packet delay) êáèþò êáé ôçí ðéèáíüôçôá áðþëåéáò ðáêÝôùí (loss probability), üðïõ ç ïñèüôçôÜ ôïõò äéáóöáëßæåôáé ìå ôçí åêôåôáìÝíç åêôÝëåóç ðåéñáìÜ-ôùí êáôÜ ôçí ïðïßá ëáìâÜíïíôáé óôáôéóôéêÝò ôéìÝò üëùí ðåéñáìÜ-ôùí ìåãåèþí êáôÜ ôç äéÜñêåéá105 êýêëùí ñïëïãéïý. Ï óõãêåêñéìÝíïò áñéèìüò åðáíáëÞøåùí åðéëÝ÷èçêå þóôå íá äéáóöáëßæå-ôáé Ýíá óôáèåñü ðåñéâÜëëïí ëåéôïõñãßáò ãéá ôï ÐÓÄ , üðïõ êáôÜ ôçí áñ÷éêÞ öÜóç åêôÝëåóçò ôùí ðåéñáìÜôùí êáé ðéï óõãêåêñéìÝíá ôùí ðñþôùí 103 êýêëùí äåí óõëëÝãïíôáé äåäïìÝíá , äéüôé ôï äßêôõï èåùñåßôáé üôé äåí Ý÷åé Ýñèåé áêüìá óå óôáèåñÞ êáôÜóôáóç (steady state) ëåéôïõñãßáò. Ôï äéáäßêôõï áðïôåëåß ðëÝïí êïéíü ôüðï üðïõ ìåôáêéíåßôáé ôåñÜóôéïò üãêïò äåäïìÝíùí. Ç áñ÷éôåêôïíéêÞ ôùí äéêôýùí åðüìåíçò ãåíéÜò ðñïóðáèåß íá ðåôý÷åé õøçëü åýñïò æþíçò ìå ÷áìçëÝò êáèõóôåñÞóåéò óôç ìåôáöïñÜ ôùí ðáêÝôùí ãéá ôïõò ôåëéêïýò ÷ñÞóôåò. Ôá ÐÓÄ åíþ ìðïñïýí íá ÷ñçóéìïðïéçèïýí óôçí êáôáóêåõÞ äéêôýùí åðüìåíçò ãåíéÜò ìå åõÝëéêôï êáé áîéüðéóôï ôñüðï ìå äéÜöïñá öïñôßá óôçí åßóïäï ôïõ äéêôýïõ, åíôïýôïéò ôåßíïõí ãñÞãïñá íá öôÜóïõí óå êïñåóìü õðü óõíèÞêåò hotspot Þ multicast/broadcast öïñôßùí, åéäéêÜ üôáí ôï ìåãåèüò ôïõò áõîÜíåé. Ùò ëýóç ôïõ åí ëüãù ðñïâëÞìáôïò ðñïôåßíåôáé ç ÷ñÞóç ðïëõåðßðåäùí ÐÓÄ ôùí ïðïßùí ç óõìðåñéöïñÜ êáé ç åêôßìçóç ôçò áðüäïóÞò ôùí äåí Ý÷åé åðáñêþò ìåëåôçèåß.
¸ôóé, ç óõíåéóöïñÜ áõôÞò ôçò äéáôñéâÞò åßíáé äéðëÞò óçìáóßáò. Áðü ôçí ìßá ðëåõñÜ ðáñÝ÷ïõìå Ýíá åõñý öÜóìá óôáôéóôéêþí áíáëýóåùí êáé åêôéìÞóåùí ôçò áðüäïóçò åíüò ÐÓÄ ôá ïðïßá ìðïñïýí íá ÷ñçóéìïðïéçèïýí ùò âÜóç áðü ôïõò ó÷åäéáóôÝò äéêôýùí óôçí êáôáóêåõÞ áðïôåëåóìáôéêþí äéêôõáêþí óõóôçìÜôùí ìåéþíïíôáò ôï êüóôïò áíÜðôõîÞò ôïõò. Áðü ôçí Üëëç ðëåõñÜ, áíáðôýóóïõìå áðïäïôéêïýò áëãüñéèìïõò ãéá ôç ìåëÝôç ÐÓÄ êÜôù áðü äéáöïñåôéêÝò óõíèÞêåò ëåéôïõñãßáò üðùò hotspot öïñôßï, multicast êáé broad-cast äñïìïëüãçóç óå ðïëëáðëþí ðñïôåñáéïôÞôùí ó÷Þìáôá åöáñìüæïíôáò ðïëõåðßðåäåò óõóôïé÷ßåò ÓÄ . Ðéï óõãêåêñéìÝíá óôï äåýôåñï êåöÜëáéï ðñïôåßíåôáé Ýíá êáéíïôüìï ó÷Þìá åóùôåñéêÞò-ðñïôåñáéüôçôáò (internal-priority) ãéá ôçí äñïìïëüãçóç ôùí ðáêÝôùí ìÝóá óôï ÐÓÄ. Ôï ðñïôåéíüìåíï ó÷Þìá ëáìâÜíåé õðüøç ôïí ôñÝ÷ïíôá ðëçèõóìü ôùí ïõñþí áðïóôïëÞò, äßíïíôáò ðñïôåñáéüôçôá óôá ðáêÝôá åêåßíùí ôùí ïõñþí ìå ôï ìåãáëýôåñï ðëçèõóìü. Ôï óêåðôéêü áõôÞò ôçò ðñïóÝããéóçò âáóßæåôáé óôï ãåãïíüò üôé ìå ôçí áðïóõìöüñçóç ôùí ìåãáëýôåñùí ïõñþí óå ðëçèõóìü, ç ðéèáíüôçôá íá âñåèåß ãåìÜôç ìéá ïõñÜ åëáôôþíåôáé, ìå áðïôÝëåóìá íá áðïññßðôïíôáé ëéãüôåñá ðáêÝôá åîáéôßáò ôçò Ýëëåéøçò ÷þñïõ åíäéÜìåóçò ìíÞìçò áðïèÞêåõóçò. ¸ôóé, óå ðåñéðôþóåéò óõãêñïýóåùí ðáêÝôùí ãéá íá ìðïñåß íá ëçöèåß õðüøç ìéá ôÝôïéá áðüöáóç åßíáé áðáñáßôçôï êáôÜ ôç ëÞøç ôùí ðáêÝôùí óôïõò ÓÄ íá ãíùóôïðïéåßôáé ï ðëçèõóìüò ôçò áíôßóôïé÷çò ïõñÜò åêðïìðÞò, äçëáäÞ íá ðáñÝ÷åôáé ìéá åðéðëÝïí ðëçñïöïñßá ç ïðïßá äåí åßíáé äéáèÝóéìç óå ìéá ôõðéêÞ áñ÷éôåêôïíéêÞ ÐÓÄ. ÅðïìÝíùò, ïé ÓÄ ðïõ ëåéôïõñãïýí ìå ôï ðñïôåéíüìåíï åóùôåñéêÞò-ðñïôåñáéüôçôáò (internal-priority) ó÷Þìá åíóùìáôþíïõí êáôÜ ôçí áðïóôïëÞ êÜèå ðáêÝôïõ ôçí áíôßóôïé÷ç ðëçñïöïñßá ãéá ôï ìÝãåèïò ôçò ïõñÜò áðïóôïëÞò (length of their transmission packet queue) óå Ýíá ðñïïßìéï (preamble) ðåäßï óôçí áñ÷Þ ôïõ ðáêÝôïõ. ¸ôóé üôáí ï ÓÄ ôïõ åðüìåíïõ óôáäßïõ áíé÷íåýóåé êáôÜóôáóç óýãêñïõóçò óõãêñßíåé ôá áíôßóôïé÷á ìåãÝèç ôùí ïõñþí (queue sizes) åêðïìðÞò êáé ðáñá÷ùñåß ðñïôåñáéüôçôá óôá ðáêÝôá ìå ôçí õøçëüôåñç ôéìÞ óôï ðñïïßìéï (preamble) ðåäßï. Ôï ãåãïíüò áõôü áíáìÝíåôáé íá áõîÞóåé ôçí óõíïëéêÞ áðüäïóç ôïõ ÐÓÄ. Ãéá ôïõò äýï óçìáíôéêüôåñïõò ðáñÜãïíôåò áðüäïóçò åíüò ÐÓÄ, äçëáäÞ ôï åýñïò æþíçò (packet throughput) êáé ôï ìÝóï ÷ñüíï (mean time) ðïõ áðáéôåßôáé ãéá Ýíá ðáêÝôï íá äéáó÷ßóåé ôï äßêôõï, óõãêåíôñþíïíôáé óõãêñéôéêÜ óôáôéóôéêÜ óôïé÷åßá ìåôáîý ôùí äýï áñ÷éôåêôïíéêþí, äçëáäÞ ôïõ åóùôåñéêÞò-ðñïôåñáéüôçôáò (internal-priority) êáé ôïõ áðëÞò ðñïôåñáéüôçôáò (single-priority) ó÷Þìáôïò. ÔÝëïò, ðñïóäéïñßæïíôáé ðïóïôéêÜ êáé ðáñïõóéÜæïíôáé ôá êÝñäç ðïõ ðñïêýðôïõí áðü ôç ÷ñÞóç åóùôåñéêÞò äñïìïëüãçóçò üóïí áöïñÜ ôüóï ôï åýñïò æþíçò (throughput) üóï êáé ôïí óõíïëéêü ðáñÜãïíôá áðüäïóçò (combined performance indicator).
Óôï ôñßôï êåöÜëáéï åéóÜãåôáé ìéá ðáñáëëáãÞ ôùí ÐÓÄ äéðëÞò åíäéÜìåóçò ìíÞìçò (double-buered) ìå ôç ÷ñÞóç áóýììåôñçò êáôáíïìÞò ôçò óôïõò ÓÄ ôïõ ÐÓÄ (asym-metric buer sizes) ìå óêïðü ôçí ðáñï÷Þ äéáöïñåôéêþí ðáñå÷üìåíùí õðçñåóéþí (quality-of-service) óôá ðáêÝôá áíÜëïãá ìå ôçí ðñïôåñáéüôçôá ðïõ áõôÜ äéáèÝôïõí, åíþ ðáñÜëëçëá ðáñÝ÷åôáé ç ìÝãéóôç äõíáôÞ áðüäïóç ôïõ óõóôÞìáôïò. Óçìåéþíåôáé üôé ôï óõãêåêñéìÝíï ìÝãåèïò åíäéÜìåóçò ìíÞìçò (buer size) åðéëÝ÷èçêå, äéüôé ìå âÜóç ôá ðåéñÜìáôÜ ìáò áðïäåß÷èçêå üôé ðáñÝ÷åé ôç âÝëôéóôç óõíïëéêÞ áðüäïóç. Ðéï óõãêåêñéìÝíá ðáñáôçñÞèçêå
üôé ãéá ìéêñüôåñá ìåãÝèç åíäéÜìåóçò ìíÞìçò (buer size =1 ) ïé ôéìÝò ôïõ åýñïõò æþíçò (network throughput) ðÝöôïõí åîáéôßáò ôçò áýîçóçò ôçò ðéèáíüôçôáò áíÜó÷åóçò (blocking probabilities), åíþ ãéá ìåãáëýôåñåò ôéìÝò óôï ìåãÝèïò ôçò åíäéÜìåóçò ìíÞìçò (buer size =4, 8 ) ç êáèõóôÝñçóç óôçí ðñïþèçóç åíüò ðáêÝôïõ (packet delay) áõîÜíåé óçìáíôéêÜ óå óõíäõáóìü ìå ôçí áýîçóç ôïõ êüóôïõò õëéêïý (hardware) ôùí ÓÄ. ¼óïí áöïñÜ ôçí ÷ñÞóç áóýììåôñïõ ìåãÝèïõò åíäéÜìåóçò ìíÞìçò âñÝèçêå üôé ïäçãåß óå êáëýôåñç åêìåôÜëëåõóç ôùí ðüñùí ôïõ äéêôýïõ êáé ôçò ÷ùñçôéêüôçôÜò ôïõ ãåíéêüôåñá, äéüôé õðÜñ÷åé ðåñéóóüôåñç äéáèÝóéìç åíäéÜìåóç ìíÞìç óôá ÷áìçëüôåñçò ðñïôåñáéüôçôáò ðáêÝôá, üðïõ ï ðëçèõóìüò ôïõò èåùñåßôáé üôé åßíáé ðïëý õøçëüôåñïò. Ðéï óõãêåêñéìÝíá, óõãêñßíïíôáò ôçí áðüäïóç åíüò áóýììåôñïõ (asymmetric buer size) ÐÓÄ ìå Ýíá áíôßóôïé÷ï ôõðéêü ÐÓÄ êáôáóêåõá-óìÝíï ìå ßóïõ ìåãÝèïõò åíäéÜìåóåò ìíÞìåò óå üëïõò ôïõò ÓÄ (equal-sized buer) âñÝèçêå üôé ç ðñþôç áñ÷éôåêôïíéêÞ ðáñÝ÷åé êáëýôåñç óõíïëéêÞ áðüäïóç (overall throughput), åîåôÜ-æïíôáò áèñïéóôéêÜ üëá ôá ðáêÝôá êáé óçìáíôéêüôåñá êáëýôåñç áðüäïóç ôüóï ôïõ åýñïõò æþíçò (packet throughput) üóï êáé ôçò êáèõóôÝñçóçò (delay) üóïí áöïñÜ ôá ðáêÝôá ÷áìçëüôåñçò ðñïôåñáéüôçôáò. Áíôßèåôá, ãéá ôá õøçëüôåñçò ðñïôåñáéüôçôáò ðáêÝôá âñÝèçêå üôé áðüäïóÞ ôïõò äåí áëëÜæåé óçìáíôéêÜ. ¸ôóé, ìå ôç ÷ñÞóç áóýììåôñïõ ìåãÝèïõò åíäéÜìåóçò ìíÞìçò (asymmetric-sized buer) åðéôõã÷Üíïíôáé óçìáíôéêÜ êÝñäç óôç óõíïëé-êüôåñç áðüäïóç ôïõ ÐÓÄ, äéüôé ç ìïñöÞ ôïõ üëïõ öïñôßïõ ôáéñéÜæåé êáëýôåñá ìå áõôïý ôïõ åßäïõò áóýììåôñçò êáôáíïìÞò ôçò åíäéÜìåóçò ìíÞìçò. Óôï ôÝôáñôï êåöÜëáéï åîåôÜæåôáé ç áðüäïóç åíüò äéðëÞò-ðñïôåñáéüôçôáò (2-class prior-ity) ÐÓÄ õðü óõíèÞêåò hotspot öïñôßïõ êÜôù áðü äéáöïñåôéêïýò ñõèìïýò Üöéîçò ðáêÝôùí óôçí åßóïäï (oered load). ÅðéðëÝïí, ëáìâÜíïõìå õðüøç ôéò äéáöïñÝò óôçí áðüäïóç ôùí èõñþí åîüäïõ ôïõ ÐÓÄ õðü óõíèÞêåò hotspot öïñôßïõ, üðùò áõôÝò êáèïñßæïíôáé áðü ôïí [37] óýìöùíá ìå ôïí ïðïßï ç áðüäïóç ôçò êÜèå èýñáò åîüäïõ åîáñôÜôáé áðü ôïí áñéèìü ôùí åðéêáëýøåùí ôçò óõãêåêñéìÝíçò äéáäñïìÞò ìå ôç äéáäñïìÞ ôçò hotspot åîüäïõ. Áíáëõôéêüôåñá, ðáñïõóéÜæïõìå ôéò óôáôéóôéêÝò ìåôñÞóåéò, üðùò áõôÝò ðñïêýðôïõí áðü åêôåôáìÝíá ðåéñÜìáôá êáé áöïñïýí ôïõò äýï óçìáíôéêüôåñïõò ðáñÜãïíôåò áðüäïóçò ôïõ ÐÓÄ, ôï åýñïò æþíçò (throughput) êáé ôçí êáèõóôÝñçóç (delay), êáèþò åðßóçò õðïëïãßæïõ-ìå êáé áíáëýïõõðïëïãßæïõ-ìå ôï óõíäõáóôéêü ðáñÜãïíôá (Universal performance factor) ÷ñçóéìïðïéþ-íôáò äéáöïñåôéêÝò âáñýôçôåò (weights) óôéò äýï óõíéóôþóåò ðáñÜìåôñåò, åêöñÜæï÷ñçóéìïðïéþ-íôáò Ýôóé ôçí óðïõäáéüôçôá ôçò êÜèå ðáñáìÝôñïõ óôï ðñïóäéïñéóìü ôçò óõíïëéêüôåñçò áðüäïóçò ôïõ ÐÓÄ. ÅðéðëÝïí, äéáðéóôþíïõìå üôé åíþ ôá ÐÓÄ åßíáé áñêåôÜ åõÝëéêôá óôï ÷åéñéóìü äéáöüñùí öïñôßùí åéóüäïõ, ç áðüäïóÞ ôïõò õðïâáèìßæåôáé óçìáíôéêÜ êÜôù áðü óõíèÞêåò hotspot öïñôßïõ, åéäéêüôåñá óôá ìåãáëýôåñá äßêôõá. Ùò áðÜíôçóç óôï ðñüâëçìá ôïõ äåíäñïåéäïýò êïñåóìïý, ç ÷ñÞóç ðñïôåñáéïôÞôùí óôá ðáêÝôá ôùí äéáöüñùí åöáñìïãþí ðáñÝ÷åé êáëýôåñç áðüäïóç óôéò õøçëüôåñçò ðñïôåñáéüôçôáò õðçñåóßåò -QoS-. ÔÝëïò, ï ëüãïò ðïõ ðñïôåßíåôáé ç ÷ñÞóç åíüò êáéíïôüìïõ ðïëõåðßðåäïõ ÐÓÄ åßíáé ç ðåñáéôÝñù âåëôßùóç ôçò áðüäïóçò ôùí ÷áìçëüôåñçò ðñïôåñáéüôçôáò ðáêÝôùí ðïõ åê ôùí ðñáãìÜôùí åßíáé åîáéñåôéêÜ õðïâáèìéóìÝíç. Ìå âÜóç ôá óôáôéóôéêÜ äåäïìÝíá ðïõ ðñïêýðôïõí áðü ôçí åöáñìïãÞ ðïëõåðßðåäùí ÐÓÄ êáé èÝëïíôáò íá éóïññïðÞóïõìå ìåôáîý ôçò ðñïóöåñüìåíçò áðüäïóçò êáé ôïõ êüóôïõò êáôáóêåõÞò åíüò ÐÓÄ ðñïôåßíïõìå Ýíá êáéíïôüìï 4-åðéðÝäùí
