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**Some Unsolved Problems in High Speed Packet Swtiching**

Shivendra S. Panwar Joint work with: Yihan Li, Yanming Shen and H. Jonathan Chao Polytechnic University, Brooklyn, NY NY State Center for Advanced Technology in Telecommunications

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**Advice to Woodward and Bernstein:**

“Follow the money” -- Deep Throat (aka Mark Felt)

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**Advice to performance analysts:**

“Find the bottleneck”

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Packet Switching

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**Buffering in a Packet Switch**

Fixed-size packet switches Operates in a time-slotted manner The slot duration is equal to the cell transmission time Contention occurs when multiple inputs have arrivals destined to the same output Buffering is needed to avoid packet loss Buffering schemes in a packet switch Output queueing (IQ) Input queueing (OQ) Virtual output queueing (VOQ) / combined input-output-queueing (CIOQ)

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**Output Queuing (OQ) 100% throughput Internal speedup of N**

Impractical for large N Input 1 Output 1 3 Input 2 3 Output 2 Input 3 Output 3 3 Output 4 Input 4 3

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**Input Queuing (IQ) Easy to implement HOL Blocking, throughput 58.6%**

Output 1 2 1 Head of Line Blocking Input 2 2 3 Output 2 Input 3 4 3 Output 3 Input 4 4 2 Output 4

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**Virtual Output Queuing (VOQ)**

Overcome HOL blocking No speedup requirement Need scheduling algorithms to resolve contention Complexity Performance guarantee 1 2 3 4

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**Challenges in Switch Design**

Stability 100% throughput Delay performance Scalability Scale to high number of linecards and to high linecard speeds Distributed scheduler is more desirable than a centralized scheduler Scheduler complexity Pin count

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**High Speed Packet Switches**

VOQ switches and scheduling algorithms Buffered crossbar switch Load Balanced switch Multi-stage switch

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**VOQ Switch Architecture**

Input 1 Input 2 Input 3 Input 4 Output 1 Output 2 Output 3 Output 4 Switch Fabric VOQ ISM ORM 1 N Input Segmentation Module (ISM): Segment packets to fixed-length cells. Output Reassembly Module (ORM): Reassemble cells into packets.

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**Scheduling for VOQ Switch**

Scheduling is needed to avoid output contention A scheduling problem can be modeled as a matching problem in a bipartite graph An input and an output are connected by an edge if the corresponding VOQ is not empty Each edge may have a weight, which can be The length of the VOQ The age of the HOL cell

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**Maximum Weight Matching (MWM)**

7 MWM always finds a match with the maximum weight Stable under any admissible traffic Very high complexity O(N3), impractical 4 3 7 8 5 6 References L. Tassiulas, A. Ephremides, ``Stability properties of constrained queueing systems and scheduling for maximum throughput in multihop radio networks,'' IEEE Transactions on Automatic Control, Vol. 37, No. 12, pp , December 1992. E. Leonardi, M. Mellia, F. Neri, Marco A. Marsan, “On the stability of Input-Queued Switches with speed-up”, IEEE/ACM Transactions on Networking, Vol.9, No.1, pp , ISSN: S (01)01313, February 2001 10 5 2 Weight of the match: 25 N. McKeown, V. Anantharam, and J. Walrand, “Achieving 100% Throughput in an Input-Queued Switch,” IEEE Transaction on Comm., vol. 47, no. 8, Aug. 1999, pp J.G. Dai and B. Prabhakar, “The throughput of data switches with and without speedup,” INFOCOM 2000.

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**Maximum Weight Matching**

The maximum weight matching algorithm is strongly stable under any admissible traffic pattern Lyapunov function Strongly stable Admissible References Emilio Leonardi, Marco Mellia, Fabio Neri, Marco Ajmone Marsan, “On the stability of Input-Queued Switches with speed-up”, IEEE/ACM Transactions on Networking, Vol.9, No.1, pp , ISSN: S (01)01313, February 2001 N. McKeown, V. Anantharam, and J. Walrand, “Achieving 100% Throughput in an Input-Queued Switch,” IEEE Transaction on Comm., vol. 47, no. 8, Aug. 1999, pp

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**Maximum Weight Matching**

Fluid model The maximum weight matching is rate stable if: The arrival processes satisfy a strong law of large numbers (SLLN) with probability one , and References J.G. Dai and B. Prabhakar, “The throughput of data switches with and without speedup,” INFOCOM 2000, pp

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Approximate MWM 1-APRX A function f(.) is a sub-linear function if limx∞ f(x)/x = 0 Let the weight of a schedule obtained by a scheduling algorithm B be WB Let the weight of the maximum weight match for the same switch state be W* If WB ≥ W* - f(W*) B is a 1-APRX to MWM B is stable if Makes it possible to find stable matching algorithms with lower complexity than MWM. References D. Shah, M. Kopikare, “Delay bounds for approximate Maximum weight matching algorithms for input-queued switches”, IEEE INFOCOM, New York, USA, June 2002.

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**Average Delay Bound Delay bound for MWM Lyapunov function References**

E. Leonardi, M. Melia, F. Neri, and M. Ajmone Marson. Bounds on average delays and queue size averages and variances in input-queued cell-based switches. Proceedings of IEEE INFOCOM, 2001.

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**Average Delay Bound (contd.)**

Delay bound for approximate-MWM Lyapunov function Cb: weight difference to the MWM matching Uniform traffic, they have the same result References D. Shah, M. Kopikare, “Delay bounds for approximate Maximum weight matching algorithms for input-queued switches”, IEEE INFOCOM, New York, USA, June 2002.

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Open Issues With simulations, MWM has the best delay performance (Cell delay) Average delay: Choose the weight of a queue as Qa , then delay is increasing with a for a>0 Is MWM the optimal scheduling scheme for achieving the minimum average cell delay? What is the optimal scheduling scheme to achieve the minimum average packet delay (Including reassembly delay)?

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**Maximal Matching Maximal Matching**

7 4 3 8 5 6 10 2 Weight of the match: 23 Maximal Matching Add connections incrementally, without removing connections made earlier No more matches can be made trivially by the end of the operation Solution may not be unique Complexity O(NlogN)

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Maximal Matching A maximal matching achieves 100% throughput with speed-up S≥2 under any admissible traffic pattern [Leonardi, ToN 2001] 100% throughput if with probability 1 A maximal matching algorithm is rate stable with speed-up S≥2 [Dai, Infocom 2000] References Emilio Leonardi, Marco Mellia, Fabio Neri, Marco Ajmone Marsan, “On the stability of Input-Queued Switches with speed-up”, IEEE/ACM Transactions on Networking, Vol.9, No.1, pp , ISSN: S (01)01313, February 2001 J.G. Dai and B. Prabhakar, “The throughput of data switches with and without speedup,” INFOCOM 2000, pp

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**Multiple Iterative Matching**

Use multiple iterations to converge on a maximal matching Parallel Iterative Matching (PIM) iSLIP and DRRM complexity of each iteration is O(logN) O(logN) iterations are needed to converge on a maximal matching (iSLIP) 100% throughput only under uniform traffic

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**iSLIP Step 1: Request Step 2: Grant Step 3: Accept**

Each input sends a request to every output for which it has a queued cell. Step 2: Grant If an output receives multiple requests it chooses the one that appears next in a fixed round-robin schedule. The output arbiter pointer is incremented by one location beyond the granted input if, and only if, the grant is accepted in step 3. Step 3: Accept If an input receives multiple grants, it accepts the one that appears next in a fixed round-robin schedule. The input arbiter pointer is incremented by one location beyond the accepted output. Output Input Request Grant Accept

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**Achieving 100% Throughput without Speedup**

Matching algorithms using memory Polling system based matching

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**Low Complexity Algorithms with 100% Throughput**

Algorithms with memory Use the previous schedule as a candidate References L. Tassiulas, “Linear complexity algorithms for maximum throughput in radio networks and input queued switches,” IEEE INFOCOM 1998, vol.2, New York, 1998, pp P. Giaccone, B. Prabhakar, D. Shah “Toward simple, high-performance schedulers for high-aggregate bandwidth switches”, IEEE INFOCOM 2002, New York, 2002. Polling system based matching algorithms Improve the efficiency by using exhaustive service Y. Li, S. Panwar, H. J. Chao, “Exhaustive service matching algorithms for input queued switches,” 2004 Workshop on High Performance Switching and Routing (HPSR 2004), April 2004. Y. Li, S. Panwar, H. J. Chao, “ Performance Analysis of a Dual Round Robin Matching Switch with Exhaustive Service,” IEEE GLOBECOM 2002.

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**Matching Algorithms with Memory**

The queue length of each VOQ does not change much during successive time slots In each time slot, there can be At most one cell arrives to each input At most one cell departs from each input It is likely that a busy connection will continue to be busy over a few time slots, if the queue length is used as the weight of a connection Use the match in the previous time slot as an candidate for the new match Important results: Randomized algorithm with memory [Tassiulas 98] Derandomized algorithm with memory [Giaccone 02] With higher complexity: APSARA, LAURA, SERENA [Giaccone 02]

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**Notations For a NxN switch, there are N! possible matches**

Q(t)=[qij]NxN, qij is the queue length of VOQij M(t), a match at time t The weight of M(t) W(t)=<M(t),Q(t)> the sum of the lengths of all matched VOQs

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**Randomized algorithm with memory**

Let S(t) be the schedule used at time t At time t+1, uniformly select a match R(t+1) at random from the set of all N! possible matches Let Stable under any Bernoulli i.i.d. admissible arrival traffic Very simple to implement, complexity O(logN) Delay performance is very poor

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**Derandomized Algorithm with Memory**

Hamiltonian walk A walk which visits every vertex of a graph exactly once. In a NxN switch, N! vertices (possible schedules), a Hamiltonian walk visits each vertex once every N! time slots H(t): the value of the vertex which is visited at time t The complexity of generating H(t+1) when H(t) is known is O(1) Derandomized algorithm with memory Use the match generated by Hamiltonian walk instead of the random match Similar performance as randomized algorithm

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Compared to MWM … Simple matching algorithms can achieve stability as MWM does Not necessary to find “the best match” in each time slot to achieve 100% throughput MWM has much better delay performance than randomized and derandomized matching “better” matches lead to better delay performance

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**With Higher Complexity and Lower Delay**

Introduce higher complexity for much lower delay than the randomized and derandomized algorithms APSARA include the neighbors of the latest match as candidates LAURA: merge the latest match with a random match to remember the heavy edges SERENA Merge the latest match with the arrival figure Figure: generated from the current arrival pattern Complexity O(N)

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**Polling System Based Matching**

Exhaustive Service Matching Inspired by exhaustive service polling systems All the cells in the corresponding VOQ are served after an input and an output are matched Slot times wasted to achieve an input-output match are amortized over all the cells waiting in the VOQ instead of only one Cells within the same packet are transferred continuously Hamiltonian walk is used to guarantee stability

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**Exhaustive Service Matching with Hamiltonian Walk (EMHW)**

Let S(t) be the match at time t. At time t+1, generate match Z(t+1) by the Exhaustive Service Matching algorithm based on S(t), and H(t+1) by Hamiltonian walk Let where <S,Q(t+1)> is the weight of S at time t+1. Stable under any admissible traffic Analyzed by an exhaustive service polling system Implementation complexity HE-iSLIP: O(logN)

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**E-iSLIP Average Delay Analysis**

Exhaustive random polling system model Symmetric system -- only consider one input N VOQs per input, exhaustive service policy -- an exhaustive service polling system with N stations The service order of the VOQs are not fixed -- random polling system, assume all station VOQs have the same probability of selection for service after a VOQ is served Switch over time S Average delay T [Levy and Kleinrock]

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**Delay Performance of HE-iSLIP**

Packet delay: the sum of cell delay and reassembly delay Cell delay: measured from VOQ to destination output Reassembly delay: time spent in an ORM, often ignored in other work Input 1 Input 2 Input 3 Input 4 Output 1 Output 2 Output 3 Output 4 Switch Fabric VOQ ISM ORM 1 N

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**packet delay performance**

Performance Summary schemes complexity stable packet delay performance iSLIP O(logN) No Always higher than HE-iSLIP. HE-iSLIP Yes Lowest when packet size is larger than 1 cell. Derandomized Highest for all traffic patterns. SERENA O(N) Lower than HE-iSLIP only under nonuniform diagonal traffic. MWM O(N3) Lowest when packet size is 1 cell.

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**Packet Delay under Uniform Traffic**

Pattern 1: packet size is 1 cell. SERENA iSLIP HE-iSLIP MWM

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**Packet Delay under Uniform Traffic**

Pattern 2: packet length is 10 cells Pattern 3: packet length is variable, the average is 10 cells (Internet packet size distribution) SERENA SERENA iSLIP MWM iSLIP MWM HE-iSLIP HE-iSLIP

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**When packet length is larger than 1 cell**

Why does HE-iSLIP have a lower packet delay than MWM? For example, when packet length is 10 cells: Cell delay Reassembly delay HE-iSLIP MWM HE-iSLIP MWM Low cell delay + low reassembly delay needed for low packet delay Open Problem: Which scheduler minimizes packet delay performance?

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**Packet-Based Scheduling**

Packet-based scheduling algorithm once it starts transmitting the first cell of a packet to an output port, it continues the transmission until the whole packet is completely received at the corresponding output port Packet-based MWM is stable for any admissible Bernoulli i.i.d. traffic Lyapunov function, MA. Marsan, A. Bianco, P. Giaccone, E. Leonardi, and F. Neri, “Packet Scheduling in Input-Queued Cell-Based Swithces,” INFOCOM 2001, pp Packet-based MWM is stable under regenerative admissible input traffic Fluid model, Y. Ganjali, A. Keshavarzian, D. Shah, “Input Queued Switches: Cell switching v/s Packet switching", Proceedings of Infocom, 2003. regenerative: Let T be the time between two successive occurrences of the event that all ports are free with E(T) being finite Modified waiting PB-MWM algorithm is stable under any admissible traffic

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**Buffered Crossbar Switch**

One buffer for each crosspoint Distributed arbitration for inputs and outputs From each input, one cell can be sent to a crosspoint buffer if it has space One cell can be sent to an output if at least one crosspoint buffer to that output is nonempty References Y. Doi and N. Yamanaka, “A High-Speed ATM Switch with Input and Cross-Point Buffers,” IEICE TRANS. COMMUN., VOL. E76, NO.3, pp , March 1993. R. Rojas-Cessa, E. Oki, Z. Jing, and H. J. Chao, “CIXB-1: Combined Input-One-Cell-Crosspoint Buffered Switch,” Proceedings of IEEE Workshop of High Performance Switches and Routers 2001.

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**Birkhoff-von Neumann Switch**

When traffic matrix is known Birkhoff-von Neumann decomposition Reference Cheng-Shang Chang, Wen-Jyh Chen and Hsiang-Yi Huang, "On service guarantees for input buffered crossbar switches: a capacity decomposition approach by Birkhoff and von Neumann," IEEE IWQoS'99, pp , London, U.K., 1999.

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**Birkhoff-von Neumann Switch**

Example High complexity, impractical

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**Load-Balanced Switch Load-balanced switch**

Convert the traffic to uniform, then fixed switching 100% throughput for broad class of traffic No centralized scheduler needed, scalable Switching ... Load-balancing … 1 k N

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**Original Work on LB Switch**

Stability: the load-balanced switch is stable Delay: burst reduction Problem: unbounded out-of-sequence delays Reference C.-S. Chang, D.-S. Lee and Y.-S. Jou, “Load balanced Birkhoff-von Neumann switches, Part I: one-stage buffering,” Computer Comm., Vol. 25, pp , 2002.

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**LB Switch variants Solve the out-of-sequence problem**

FCFS (First come first serve) Jitter control mechanism Increase the average delay EDF (Earliest deadline first) Reduce the average delay High complexity Mailbox switch Prevent packets from being out-of-sequence Not 100% throughput References C.-S. Chang, D.-S. Lee and C.-M. Lien, “Load balanced Birkhoff-von Neumann switches, Part II: multi-stage buffering,” Computer Comm., Vol. 25, pp , 2002. C.S. Chang, D. Lee, and Y. J. Shih, “Mailbox switch: A scalable twostage switch architecture for conflict resolution of ordered packets,” In Proceedings of IEEE INFOCOM, Hong Kong, March 2004.

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**More LB switch variants**

FFF (Full frames first) (Infocom 2002, Mckeown) Frame-based No need for resequencing Require multi-stage buffer communication-high complexity FOFF (Full ordered frames first) (Sigcomm 2003, Mckeown) Maximum resequencing delay N2 Bandwidth wastage References I. Keslassy and N. McKeown, “Maintaining packet order in two-stage switches,” Proc. of the IEEE Infocom, June 2002. I. Keslassy, S.-T. Chuang, K. Yu, D. Miller, M. Horowitz, O. Solgaard and N. McKeown , “Scaling Internet routers using optics,” ACM SIGCOMM ’03, Karlsruhe, Germany, Aug

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**Byte-Focal Switch Architecture**

Re-sequencing buffer 1st stage switch fabric 2nd stage switch fabric Arrival Input VOQ Second-stage VOQ … 1 2 N i (1,1) (1,1) ... ... 1 1 1 (1,k) (1,k) (1,N) (1,N) … 1 2 N … … (i,1) (j,1) ... ... … j k i (i,k) (j,k) (i,N) (j,N) … … (N,1) ... (N,1) ... (N,k) … N N N (N,k) (N,N) (N,N)

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**Byte-Focal Switch Packet-by-packet scheduling**

Improves the average delay performance The maximum resequencing delay is N2 The time complexity of the resequencing buffer is O(1) Does not need communications between linecards References Y. Shen, S. Jiang, S.S.Panwar, H.J. Chao, “Byte-Focal: a practical load-balanced swtich”, HPSR 2005, Hongkong.

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**Multi-Stage Switches Single Stage Switches (e.g., Cross-point switch)**

Single path between each input-output pair Cannot meet the increasing demands of Internet traffic No packets out-of-sequence Easy to design Lack of scalability Multi-stage Switches (e.g., Clos-network switch) Multiple paths between each input-output pair Better tradeoff between the switch performance and complexity Highly scalable and fault tolerant Memory-less multi-stage switches No packets out-of-sequence, may encounter internal blocking Buffered multi-stage switches Packet may be out-of-sequence, easy scheduling

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**Multi-Stage Architecture**

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**Trueway: A Multi-Plane Multi-Stage Switch**

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Trueway Switch The switch fabric consists of multiple switching planes, with each being a three-stage Clos network with m center modules Each input/output pair has multiple routing paths Highly scalable 1 n 2 Cross-point buffered memory

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**Challenges in Multi-Stage Switching**

How to efficiently allocate and share the limited on-chip memory? How to schedule packets on multiple paths to maximize memory utilization and system performance? How to minimize link congestion and prevent buffer overflow (i.e., stage-to-stage flow control)? How to maintain cells/packet order if they are delivered over multiple paths (i.e., port-to-port flow control)? How to achieve 100% throughput?

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**Conclusion Introduced switch architecture trends**

Many open research problems Bottleneck keeps changing!

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