Computer Simulations of a Modified MiMa-algorithm for a Crossbar Packet Switch

Transcription

1 INSTITUTE OF INFORMATION AND COMMUNICATION TECHNOLOGIES BULGARIAN ACADEMY OF SCIENCE Computer Simulations of a Modified MiMa-algorithm for a Crossbar Packet Switch Tasho Tashev, Vladimir Monov {ttashev,vmonov}@iit.bas.bg CompSysTech 14, 27 June 2014, Ruse, Bulgaria 1 /acomi n

2 Abstract The paper presents computer simulations of an algorithm for non-conflict packet commutation in a crossbar switch node. In particular, we study a version of the MiMa-algorithm with a new selection of the initial element of the traffic matrix as compared to the original version of the algorithm. Our simulation studies use the Generalized Nets (GN) model of the MiMa-algorithm. Our simulations utilize independent, identically distributed (i.i.d.) Bernoulli uniform load packet traffic. We have used the family of patterns for this traffic. The obtained results indicate that the original MiMa-algorithm yields better results with respect to the throughput of the crossbar switch in comparison to the modified version. 2

3 Introduction Crossbar switch node is an example of a device which maximizes the speed of data transfer using parallel existing flows between a communication network s nodes. The ideal case is when the switch sends packets with a speed corresponding to the speed with which the nodes produce these packets [1]. This is obtained by means of a contention-free match schedule calculated by the switch node s control block (Central Scheduler). Csaszar, A. et all, IEEE Network, 2007, Vol. 4 3

4 Typical crossbar architecture: Cisco 5596 The unified crossbar fabric (UCF) is a single-stage high-performance 100-by-100 crossbar with an integrated scheduler. The scheduler coordinates the use of the crossbar between inputs and outputs, allowing a contention-free match between I/O pairs [2]. 4

5 A randomly incoming traffic (McKeown, 2006) 1122 R Input Output R 11 R Input Switch Fabric Output R R Input Output R Scheduler 5

6 Non-conflict schedule The randomly incoming traffic must be controlled and scheduled to eliminate conflicts at the crossbar switch. The goal of the traffic-scheduling for the crossbar switches is to maximize the throughput of packet through a switch minimize packet blocking probability, minimize packet waiting time. The attempts to reach simultaneously three goals leads to problems with non-polinomial completeness of the solutions. (NP-hard). Some solutions, which satisfy the goals partially are suggested: PIM, islip, DRR, BvN, CIXB-1, StablePlus, CTC(N) In Cisco Nexus 5500 platform the scheduling algorithm is based on an enhanced islip algorithm [2]. We synthesized the our MiMa-algorithm using the apparatus of Generalized nets (GN). 6

7 GN-model of MiMa-algorithm Initial characteristic for token in l_1: ch 0 = (pr 1 ch 0, pr 2 ch 0, pr 3 ch 0 ) = (i, n, T). It is shown that throughput of switch node with MiMa-algorithm asymptotically tends to 100%. For values of the commutation field n equals to power of 2, the throughput is exactly 100%. Question arises, can we modify the algorithm so as to further improve the throughput ability. 7

8 The possible modification We will give a concise description of the MiMa-algorithm. Step 1. Initially, matrix T is introduced. Step 2. A vector-column, which consists of the number of conflicts in each row (row conflict weights) is calculated. Step 3. A vector-row, which consists of the number of conflicts in each column (column conflict weights), is calculated too. Step 4. In the vector-row we choose the maximal element which determines the column with the most conflicts. Step 5. In the vector-column we choose the maximal element which determines the row with the most conflicts. Step 6. If there is a request Step 7. If there is goto Step 2, else Stop. The output of the algorithm depends on the choices in Step 4 and Step 5. The possible modifications with respect to the original MiMa-algorithm ( choose the Maximal element for Step 4, choose the Maximal element for Step 5) are three: Variant 1: choose the Maximal el. for Step 4, choose the minimal el. for Step 5. Variant 2: choose the minimal el. for Step 4, choose the Maximal el. for Step 5. Variant 3: choose the minimal el. for Step 4, choose the minimal el. for Step 5. We will work with the first variant. 8

9 Model of Uniform Load Traffic We will use a type of matrices T for uniform traffic with the following properties: easy generation for any size of the switch (n x n); generation should not depend on the type of hardware, compiler and operation system; their exact, optimal, non-conflict schedule should be known. Matrix T describes unidirectional packet flow - from input lines to output lines. Family of patterns S-Pattern i : S-Pattern 1 S-Pattern i The S-Pattern i imposes a limit on the buffer size of the input line to i.k requests. 9

10 Computer simulation of a throughput The transition from a GN-model to executive program is performed as in [16]. The source code has been tested by means of the program packet Vfort (free access from Institute of mathematical modeling of Russian Academy of Sciences). The source code is compiled by the PC with Intel E8400 2x3.0 GHz, 2 GB RAM. The resulting executive code is executed in the DOS-console under Windows XP SP2. For simulations we will use a simple pattern model for i.i.d. Bernoulli uniform load traffic, which includes a family of patterns denoted below as S-i, i=1,2, [14]. Requests represent packets with the same size. The index i shows values of element in the traffic matrix. The optimal schedule for S-1 requires k opt = 1.n switchings of the crossbar matrix for n x n switch. The optimal schedule for S-i requires k opt = i.n switches of the crossbar matrix for n x n switch. The throughput is computed by dividing the result of optimal solution by the result of the simulated solution: if the Mima-algorithm gives the schedule with k r switchings, then the throughput will be k opt / k r. 10

11 throughput for S-1 Fig. left presents the results from computer simulation of the modified MiMaalgorithm with input data S-1. Sizes of the crossbar matrix from 2x2 (n=2) to 130x130 (n=130) are simulated. For comparison Fig.4 (right) presents the results from computer simulation of the original MiMa-algorithm with input data S-1. B A Throughput of modified MiMa Throughput of original MiMa 11

12 Comparison of throughput for S-1 The most important thing is that the dependence of the THR on n is worse at the modified algorithm it tends to 100% slower. It reaches 100% at n equal to power of 2 in both cases. In order to clarify the results in figure left is showed THR, аnd in figure right-hand number of solutions k r depending on the size n, for both variants of the algorithm. B A Comparison of throughput for S-1 Comparison of k r for S-1 The results from computer simulation of the modified MiMa-algorithm with input data pattern S-2 to pattern S-10 are similar. 12

13 throughput for S-10 Fig.7 shows the differences between throughput results from the computer simulation of the modified variant for S-1 and S-10. Fig.8 shows the differences between throughput results from the computer simulation of the original variant of algorithm for S-1 and S-10. Throughput of modified MiMa for S-1, S-10 Throughput of original MiMa for S-1, S-10 It is shown that at S-10 the efficiency is better in both variants. 13

14 calculating the boundary Fig. left shows the differences between throughput results from the computer simulation of the modified and original variants of algorithm for input data S-10. Fig.right displays k r depending on the n, for both variants of the algorithm.again, the original variant is better. Comparison of throughput for S-10 Comparison of k r for S-10 The results from computer simulations of the modified MiMa-algorithm with input data patterns bigger than S-10 (i>10) are similar to the previously displayed. The original MiMa- algorithm shows obviously better results 14

15 Conclusion and Future Work In this paper a model of algorithm for computing a non-conflict schedule is suggested. This is a version of our MiMa-algorithm with a new selection of the initial element of the traffic matrix. The results from computer simulations of a modified MiMaalgorithm using uniform traffic are presented. It is shown that the original MiMa-algorithm yields better results with respect to the throughput of the crossbar switch in comparison to the modified version. In a future work we intend to examine the other two modifications of our MiMa-algorithm to confirm the conclusion about the benefits of the original MiMa. 15

16 References [1] Kang, K., K. Park, L. Sha, Q. Wang. Design of a crossbar VOQ real-time switch with clock-driven scheduling for a guaranteed delay bound. Real-Time Systems, January 2013, V. 49, Issue 1, pp [2] Cisco Nexus 5548P Switch Architecture. /prod/ collateral/ switches/ps9441/ps9670/ps11215/white_paper_c pdf [3] Chen, T., J. Mavor, Ph. Denyer, D. Renshaw. Traffic routing algorithm for serial superchip system customisation. IEE Proc., Jan 1990, Vol. 137, No.1. pp [4] Anderson T., Owicki S., Saxe J. and C.Thacker. High speed switch scheduling for local area networks. ACM Trans.Com.Syst., 1993, vol. 11, no.4, pp [5] McKeown N. The islip Scheduling Algorithm for Input-Queue Switches.IEEE/ACM Trans. Networking, April 1999, Vol. 7, no.2, pp [6] Chang, H.J., G. Qu, S.Q. Zheng. Performance of CTC(N) Switch under Various Traffic Models. Springer, LNEE, 2012, Vol. 126, pp [7] Atanassov, K. Generalized Nets and System Theory. Akademic Press Prof. M.Drinov, Sofia, Bulgaria, [15] Tashev, T., V. Monov. Large-Scale Simulation of Non-Uniform Load Traffic in Studying the Throughput of a Crossbar Packet Switch. In: Large-Scale Scientific Computing. Springer Berlin Heidelberg, LNCS, vol. 8353, (in press) 16

17 Acknowledgments Acknowledgments The research work reported in the paper is partly supported by the project AComIn "Advanced Computing for ", grant , funded by thefp7 Capacity Programme (Research Potential of Convergence Regions). Thank you! 17