A throughput-centric view of the performance of datacenter topologies

Cerberus

“…Very recently, and in parallel to our work, the throughput of expander-net was also shown in[45] 2. In Greek mythology, Cerberus is a dog with three heads (corresponding to our three topology parts).Proc.…”

“…We acknowledge that these algorithms do not obtain optimal solutions, e.g., in contrast to solving a multi-commodity flow problem [45] or our derived upper bounds. Rather they trade-off tractability of simulations at the desired scale and performance.…”

“…Let 𝑇 = [𝑡 𝑢𝑣 ] be an 𝑛 × 𝑛 demand matrix (entries in 𝑇 are traditionally given as rates [40], so we consider them as bits per second, denoted as bps) for a datacenter network consisting of 𝑛 switches which are used to interconnect a set of racks. Each switch has 𝑘 links of rate 𝑟 connected to other switches, plus 𝑘 links connected to servers in its rack (also called uni-regular topologies [45]). In the following, it suffices to focus on the rack-level network, i.e., we consider the demand matrix between racks (resp.…”

“…We first extend the throughput definition by Jyothi et al [40] from a demand matrix 𝑇 to our general traffic generation model T (in Section 5.1). We further extend the definition to apply also to dynamic network topologies rather than only static topologies [40,45]. In turn, we present a mathematical framework that allows us to evaluate analytically the performance and trade-offs of arbitrary demands using different optical switches, considering real traffic distributions like in Figure 1 (a) [22,42,46].…”

Self-Adjusting Ego-Trees Topology for Reconfigurable Datacenter Networks

“…Specifically, static networks often use expander graphs [5] or hierarchical (e.g., FatTree [6]) topologies to optimize the network diameter which give an upper bound for the (average) path length. While there are several metrics of interest when studying a network's topology, this work focuses on the average path length since a shorter route length leads to better utilization of links and higher network throughput [18]. As we will see formally later, our network model provides the designer (i.e., our algorithm) a set of k matchings of size < l a t e x i t s h a 1 _ b a s e 6 4 = " b B n / 9 j V k A + l E E p a 5 r m 7 J y N i x B m c = " > A A A B 6 n i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e x G U U 8 S 8 O I x o n l A s o T Z S W 8 y Z H Z 2 m Z k N h J B P 8 O J B E a 9 + k T f / x k m y B 0 0 s a C i q u u n u C h L B t X H d b y e 3 t r 6 x u Z X f L u z s 7 u 0 f F A + P G j p O F c M 6 i 0 W s W g H V K L j E u u F G Y C t R S K N A Y D M Y 3 s 3 8 5 g i V 5 r F 8 M u M E / Y j 2 J Q 8 5 o 8 Z K j 6 N u p V s s u W V 3 D r J K v I y U I E O t W / z q 9 G K W R i g N E 1 T r t u c m x p 9 Q Z T g T O C 1 0 U o 0 J Z U P a x 7 a l k k a o / c n 8 1 C k 5 s 0 q P h L G y J Q 2 Z q 7 8 n J j T S e h w F t j O i Z q C X v Z n 4 n 9 d O T X j j T 7 h M U o O S L R a F q S A m J r O / S Y 8 r Z E a M L a F M c X s r Y Q O q K D M 2 n Y I N w V t + e Z U 0 K m X v q n z x c F m q 3 m Z x 5 O E E T u E c P L i G K t x D D e r A o A / P 8 A p v j n B e n H f n Y 9 G a c 7 K Z Y / g D 5 / M H C 5 C N o w = = < / l a t e x i t > v 2 < l a t e x i t s h a 1 _ b a s e 6 4 = " m d + 9 M J + t g i f o Y B S e Y d r w C P T M Q G s = " > A A A B 6 n i c b V B N S 8 N A E J 3 U r 1 q / q h 6 9 L B b B U 0 l U 1 J M U v H i s a D + g D W W z n b R L N 5 u w u y m U 0 J / g x Y M i X v 1 F 3 v w 3 b t s c t P p g 4 P H e D D P z g k R w b V z 3 y y m s r K 6 t b x Q 3 S 1 v b O 7 t 7 5 f 2 D p o 5 T x b D B Y h G r d k A 1 C i 6 x Y b g R 2 E 4 U 0 i g Q 2 A p G t z O / N U a l e S w f z S R B P 6 I D y U P O q L H S w 7 j n 9 c o V t + r O Q f 4 S L y c V y F H v l T + 7 / Z i l E U r D B N W 6 4 7 m J 8 T O q D G c C p 6 V u q j G h b E Q H 2 L F U 0 g i 1 n 8 1 P n Z I T q / R J G C t b 0 p C 5 + n M i o 5 H W k y i w n R E 1 Q 7 3 s z c T / v E 5 q w m s / 4 z J J D U q 2 W B S m g p i Y z P 4 m f a 6 Q G T G x h D L F 7 a 2 E D a m i z N h 0 S j Y E b / n l v 6 R 5 V v U u q + f 3 F 5 X a T R 5 H E Y 7 g G E 7 B g y u o w R 3 U o Q E M B v A E L / D q C O f Z e X P e F 6 0 F J 5 8 5 h F 9 w P r 4 B C g y N o g = = < / l a t e x i t > v 1 < l a t e x i t s h a 1 _ b a s e 6 4 = " t D z I R 1 + P i U W h 4 N n n x q 8 1 o z 0 g 4 M 8 = " > A A A B 6 n i c b V D L S g N B E O y N r x h f U Y 9 e B o P g K e w a U U 8 S 8 O I x o n l A s o T Z S W 8 y Z H Z 2 m Z k N h J B P 8 O J B E a 9 + k T f / x k m y B 0 0 s a C i q u u n u C h L B t X H d b y e 3 t r 6 x u Z X f L u z s 7 u 0 f F A + P G j p O F c M 6 i 0 W s W g H V K L j E u u F G Y C t R S K N A Y D M Y 3 s 3 8 5 g i V 5 r F 8 M u M E / Y j 2 J Q 8 5 o 8 Z K j 6 N u p V s s u W V 3 D r J K v I y U I E O t W / z q 9 G K W R i g N E 1 T r t u c m x p 9 Q Z T g T O C 1 0 U o 0 J Z U P a x 7 a l k k a o / c n 8 1 C k 5 s 0 q P h L G y J Q 2 Z q 7 8 n J j T S e h w F t j O i Z q C X v Z n 4 n 9 d O T X j j T 7 h M U o O S L R a F q S A m J r O / S Y 8 r Z E a M L a F M c X s r Y Q O q K D M 2 n Y I N w V t + e Z U 0 L s r e V b n y c F m q 3 m Z x 5 O E E T u E c P L i G K t x D D e r A o A / P 8 A p v j n B e n H f n Y 9 G a c 7 K Z Y / g D 5 / M H D R S N p A = = < / l a t e x i t >…”