A Scalable Frame-based Multi-Crosspoint Packet Switching Architecture

Transcription

1 A Scalable Frame-based ulti- Pacet Switching Architecture ie Li, Student ember, Itamar Elhanany, Senior ember Department of Electrical & Computer Engineering he University of ennessee noxville, Abstract Input-queued cell switches employing the oldestcell-rst (OCF) policy have been shown to yield low mean delay characteristics oreover, it has been proven that OCF is stable for admissible iid arrival trafc when executed with a scheduling speedup of However, an increase in lin rates and port densities directly leads to a decrease in pacet duration times, to a point where cell-by-cell switching is no longer considered practical o address this challenge, this paper studies framebased scheduling algorithms for a scalable combined input-output queued (CIOQ) switch architecture he latter is decomposed into independent subgroups, each employing multiple simple crosspoint switches A ey outcome of this decomposition is a substantial reduction of scheduling times Unlie many other schemes, which necessitate custom integrated circuits, the architecture proposed here utilizes commercially available crosspoint switches We present a Lyapunov-based stability analysis that dictates moderate conditions under which the switch is stable for all admissible trafc patterns By reconguring the crossbar switch once every several time slots, the timing constraints imposed on the scheduling algorithm are signicantly relaxed Simulation results are presented, demonstrating the merits of the approach, particularly in the presence of bursty trafc scenarios I IRODUCIO Recently, several novel architectures have been proposed for the design of pacet switches with large aggregate capacities and high-speed lin data rates Examples include the Parallel Pacet Switch (PPS) [], the Parallel Shared emory (PS) router [], and the Load-Balanced router [3] In theory, both the PPS and the PS can emulate a rst-come-rst-served output-queued (FCFS-OQ) pacet switch and support quality of service (QoS) guarantees evertheless, implementation of PPS and PS switches involves the design of intricate centralized schedulers, which inherently introduce scalability limitations It has been shown that the Load-Balancing architecture can guarantee 00% throughput for a broad class of trafc patterns and requires no scheduler However, the Load-Balancing architecture suffers from pacet reordering, a consequence of allowing multiple internal input-to-output paths for each ow oreover, it imposes frequent switch fabric recongurations [] hese two attributes introduce delay and scalability limitations, and consequently require the introduction of custom-designed VLSI components Input-queued (IQ) pacet switching architectures with virtual output queueing (VOQ) are commonly utilized in Internet routers as they offer pragmatic scalability while requiring moderate memory bandwidth A scheduling algorithm is needed for an IQ switch to dynamically determine the conguration of the crossbar by nding matchings between ingress and egress ports However, an increase in lin rates directly causes a decrease in pacet duration times to a point where cell-by-cell switching is no longer considered a practical approach his is true particularly for optical switch fabrics that employ slowly reconguring crossconnect elements he reconguration overhead for a typical optical switch fabric can be in the range of 0-00ns [] However, with -byte pacets and speeds of 0 bps, a reconguration time of a few nanoseconds is necessary for the cell-by-cell switching mechanism o address this issue, in a previous paper [], the authors have proposed a frame-based maximal weight matching (FW) algorithm with transfer speedup, in which scheduling decisions are issued in accordance with the W algorithm, however they are ept unchanged for a duration of consecutive time slots It has been proven that a CIOQ switch running the FW scheduling algorithm with a transfer speedup of is stable under admissible trafc for any frame size By reconguring the crossbar switch once every several time slots, we signicantly relax the timing constraints imposed on the scheduling algorithm In order to scale to high port densities, we propose a novel scalable pacet switching architecture which is straightforward to implement, as it employs a group of memoryless passive crosspoint switches he architecture is a CIOQ switch whereby an switch is partitioned into identical and independent switching groups, each hosting a pool of smaller crosspoint switches he motivation to employ such an architecture is to benet from the idea of partitioning one (large) crossbar into several small crosspoints [], so as to facilitate scalability and reduce the timing requirements from the scheduling algorithm he approach is characterized by offering a 00% throughput guarantee for a broad class of trafc patterns when employing the FW/OCF scheduling algorithm Pacet reordering need not be considered and switch fabric reconguration is infrequent Since the algorithm studied is frame-based, by reconguring the crossbar switch once every several time slots, the timing constraints imposed on crosspoint devices are signicantly relaxed II EERAL SWICH ARCHIECURE he proposed switch architecture is based on a design rst introduced in [] Consider an switch as shown in

2 roup # / roup # /+ / Stage Stage Switch pool # Switch pool # / / emory emory emory emory emory emory Output Output on in the following section From a crosspoint optimization perspective, since the highest number of inputs or outputs on any crosspoint device in the system is a ey scalability metric, we note that the maximal port count on any crosspoint is given by maxf; g: For example, if one wishes to design a -port switch (ie = ), where = ; = ; = 8; then maxf; g = ;suggesting that the switch can be realized using existing off-the-shelf crosspoint devices III FW/OCF SABILIY AALYSIS / roup # Switch pool # emory emory emory Output Fig Proposed switch architecture in which an CIOQ switch is equally partioned into independent groups employing multiple passive crosspoints switches gure, whereby input modules are equally partitioned into groups, each of which is independently connected to all outputs via a pool of non-blocing crosspoint switches It is assumed that each of the crosspoint switches is small to facilitate practical scalable switch implementations hroughout this paper we shall refer to a ow as the collection of all pacets with the same input and output index values We further let a group ow denote the set of all pacets from a given group destined to a unique output All pacets belonging to the same group ow will be buffered in the same memory module at their destination output For example, all pacets from group # that are destined to output will be buffered in memory of output : Hence, multiple memory modules must be maintained at each output to hold pacets from different group ows Clearly, the number of memory modules maintained at each output is, since for each output, there can be at most different group ows, each of which corresponds to one group We shall let all pacets from the same ow traverse through the same path, ie, we only consider single-path switching, discarding multipath scenarios that incur pacet reordering he core switching fabric comprises two stages of passive crosspoint switches he rst connects the ingress ports to the rest of the fabric, hosting a pool of crosspoint switches per group, where denotes the number of crosspoint switches in the second stage and is the maximal number of outputs that can be matched to a single input ote that = represents the common case in which each input can be matched to at most one output If > then a transfer speedup is required Each of the crosspoint switches in the second stage has inputs and outputs By placing an switch between the crosspoints pool and each input port, maximal trafc throughput is guaranteed, as will be elaborated In this section we derive the necessary conditions for the switch supporting a single class of service to be stable With reference to gure, let Q (t) denote the VOQ size at input i holding pacets destined to output j at time t Let us also dene the corresponding random arrival process, A (t) f0; g, with a mean (normalized) rate of pacet arrivals from input i to output j, E[A (t)] = Since the switch is equally partitioned into independent groups and each group supports its own non-blocing paths, stability analysis focused on any particular group can be easily extended to all other groups with minor modications, as will be described later hroughout this paper, we consider a simple FW/OCF scheduling algorithm pertaining to the group he algorithm consists of an iterative process whereby during each iteration the maximal weight among the currently contending set of nodes is found, and a match is registered between the corresponding input-output pairs An iteration example is depicted in gure Upon matching an input to an output, the respective input and output pair is removed from contending during subsequent iterations (shown in scenario of gure ) Alternatively, only the associated output is removed from future contention, as illustrated in scenario of gure, allowing other inputs from the same group to be matched to available outputs Assuming the weight matrix is not completely null, the number of iterations can range between and = Conguration of the crosspoints, determined by the FW/OCF algorithm, can be represented by a service matrix, S(t) = fs (t)g, where S (t) = if input i is matched to output j at time t, otherwise S (t) = 0: Based on the weights of the queues, a schedule is obtained which remains unchanged for consecutive time slots A new schedule will only occur at time t +, reected by S (t + ) Denition : Let g denote the trafc rate matrix for the g th group, as given by g th g = (g ) +; (g ) (g ) +; (g ) g ; +; (g ) +; +; +; (g ) g ; g ; () Denition : Let g (t) denote the weight matrix at time t, 3 7

3 Current Contention List +, +, g, + + g L +, L +, O L g, Denition 7: Let denote the maximal number of matches allowed to be made for each input port during a single scheduling period he buffer dynamics under the FW/OCF algorithm dictate that for Q (t) > aximal Weight Found L +, + +, L +, + +, O L g g g,, Scenario Scenario L L +, + +, +, + +, L L +, + +, +, + +, O O L g g g L g g g,,,, Fig Example of an iteration at group g, for the FW/OCF scheduling algorithm Each element represents a weighted request for service Scenario represents a single input/output matching, while Scenario pertains to the case where more than one input from the same group is matched to an output such that g (t) = (g ) +; (g ) (g ) +; (g ) g ; +; (g ) +; +; +; (g ) g ; g ; () where (t) is the waiting time of the HoL cell in queue (i; j) at time t Denition 3: Let the queue occupancy vector for the g th group be dened as h i Q g (t) = Q (g ) +;(t); Q (g ) +;(t); :::; Q g ; (t) : (3) Denition : An arrival process is said to be strictly admissible iff P i= and P j= Denition : he (aggregate) weight of the FW/OCF algorithm at time t is given by W (t) = D = g (t); S 3 7 (t)s (t) () E (t) where S (t) denotes the matching congurations determined by the scheduling algorithm at time t Denition : Let (m) (t) denote the inter-arrival time between two consecutive cells, m and m +, both of which are stored in queue (i; j), and correspondingly, let (t) = (t); m = ; ; :::; Q (t)g maxf (m) (t + ) = (t) + S (t) m= (m) (t); () where is the internal transfer speedup, while for Q (t) (t + ) (t) + Q (t) (t) + () (t) + from which we can write (t + ) (t) (7) " # + for Q (t) >, and S (t) m= (m) (t) (t) (t + ) (t) + (t) (8) + (t) for Q (t) he term S (t) expresses the consecutive transmissions that may occur during a single frame interval ext, we construct a discrete-time quadratic Lyapunov function, L(t) [7], such that L(t) = (t) [8][9][]: As an expression of a time slot lag, we write L(t + ) L(t) = (t + ) (t) : (9) By partitioning the above into the case of Q (t) < and Q (t) ; we obtain the following: E [L(t + ) L(t)jQ(t)] (0) P " h + S (t) E (m) (t)i #! (t) m= + P E + (t) P S (t) (t) + P ( + ) ( + ) + (t) [ S (t)] h D Ei h g ; g (t)i S (t); g (t) + C g where C = ( + ), is a constant In order to prove that the algorithm yields a stable queueing system, we show that beyond a given threshold of maximal weight there is a negative drift in the state of the system athematically speaing, from inequality D (0), an appropriate value E for, such that h g ; g (t)i < Sg (t); g (t), guarantees that the algorithm is stable Hence, we focus

4 our attention on the two basic scenarios described above, as illustrated in gure : Scenario : For each matching generated, its respective input and output pair is removed from contending during subsequent iterations heorem : For scenario, an switch running the FW/OCF scheduling algorithm with a transfer speedup of is stable under admissible iid trafc for any frame size, Proof: Without loss of generality, assume that following o n (g ) a round of matching, V OQ sl, where s + ; :::; g and l[; :::] is selected It then follows that all of the elements in row s and column l of the weight matrix are removed from future contention By decomposing < g ; g > < S g ; g > into each round, we have g j= sj + (g ) i= + il For any admissible trafc pattern, we now that sj and g (g ) j= i= + il, from which we deduct that sj + g (g ) j= i= + il Hence, = is sufcient to guarantee stability Scenario : For each matching generated, only the associated output is removed from future contentions In this case, we remove the restriction of only one VOQ being matched per ingress port, such that there can now be up to VOQs matched per ingress port We extend the stability analysis devised thus far to address scenario, ie the case in which up to > VOQs can be matched in each ingress port during every schedule (note that is a xed number, although in each schedule different input ports may have variant number of actual matches, but the number of matches can not exceed ) A schedule here comprises of multiple rounds/iterations, each of which produces one input-output matching As such, a schedule round may have at most rounds/iterations per group heorem : In the case of scenario, an switch running the FW/OCF scheduling algorithm with transfer speedup of > += is stable under admissible iid trafc for any frame size Proof: Let us rst briey review the matching process At the beginning of each schedule interval, the VOQ with largest weight is selected; later all VOQs with the same output as that chosen are removed from subsequent contention rounds ext, the scheduler chooses the VOQ with the largest weight value among those in the current contention list, and then removes all VOQs with same output as the one chosen he scheduler also checs to see if the number of matches along the same input has reached : If so, then it removes all VOQs in the same input from future contention his process is repeated until no more matchings can be made Without loss of generality, assume that a schedule produces a total of matches in a given interval/frame Hence, there are rounds/iterations, each of which corresponds to precisely one match Further, suppose that during the th round/iteration, where f; ; :::; g, V OQ i ;j, which has the largest weight value among those in the current contending list, is selected by the scheduler oreover, we let I, J denote the set of all possible input and output indices for the current contention list, respectively; for example, clearly, (g ) (g ) if = ; I = f + ; + ; :::; g g and J = f; ; :::; g: If the number of matches (including the most recent one) at the same input, eg input i I, is, then all VOQs in the current contention list, with the same output and input as the selected one, are removed from future rounds Let W i ;j ; W i ; :::; W ;j i denote the weight values of ;j the st nd,, matching of the input, which were selected by the scheduler during rounds th ; th ; :::; th, respectively Clearly W i ;j W i W ;j i ; hence W ;j i ;j (W i +W ;j i +:::+W ;j i ) Furthermore, let ;j I ; :::; I = I denote the set of all possible input indices for the contending list during rounds th ; th ; :::; th J ; :::; J, respectively; and let = J denote the set of all possible output indices for the contending list using similar round notation We thus have i ;jw i ;j W i ;j () jj and (W i ;j + W i ;j W i ;j ); ii + ii W W i ;j + W i ;j W i ;j ; hence, ii + ii + jj i ;jw i ;j W ii =I ii =I (+ )(W i ;j + W i ;j W i ;j ) () (3) Alternatively, if the number of matches (including the new one) at the same input is ; we have W ii + ii W i ;j + W i ;j W i ;j ii =I < ( + )(W i ;j + W i ;j W i ;j ) () his represents a general result for every round/iteration herefore, by decomposing < g ; g > < S g ; g > into each round according to inequalities (3) and (), we conclude that < g ; g > ( + ) < S g; g >;which implies that > + = is a sufcient condition to guarantee stability

5 0 mbs= mbs= mbs=8 mbs= 8 = = = =8 3 ean cell delay (cell times) 30 0 ean cell delay (cell times) ormalized offer load ormalized offer load Fig 3 Average cell delay as a function of the mean burst size (BS) for a xed frame size of 8 cells he FW/OCF algorithm can issue at most match per ingress port Fig Average cell delay when arrivals are Bernoulli iid with uniform distribution for different frame sizes () he FW algorithm issues up to matches per ingress port IV SIULAIO RESULS In order to evaluate the performance of the FW/OCF algorithm under the multi-crosspoints based architecture proposed, three sets of simulations were carried out In all cases, a switch was considered with a transfer speedup of : he switch was partitioned into independent switching groups, each of which supported 3 ingress ports In the rst three sets of simulations = (ie the transfer speedup is ) he rst set of simulations was targeted at examining the impact of bursty trafc on the delay characteristics A twostate arov-modulated (O/OFF) process was employed [0], whereby bursts are uniformly distributed across the outputs Figure 3 shows the average delay as a function of the mean burst sizes (BS) for a xed frame size of 8 pacets An inverse relationship between the BS and the average delay is observed Since the FW scheduling discipline is inherently correlated, bursty trafc better utilizes the transmission intervals In the second set of simulations, the FW/OCF algorithm was allowed to mae up to matches per ingress port and the transfer speedup is correspondingly dropped to he arrival process was Bernoulli iid with uniformly distributed destination distribution Figure depicts the average delay measured for different frame sizes and shows that despite the relaxed switching times and distributed passive crosspoint switches, the overall performance is ept high V COCLUSIOS his paper presents a novel scalable multi-crosspoints based pacet switching architecture coupled with a frame-based scheduling algorithm for routers with large port densities and high-speed line rates It has been shown that the architecture can guarantee 00% throughput for a broad class of trafc scenarios By equally partitioning an CIOQ switch into multiple independent switching groups, the timing requirements from the FW/OCF algorithm are substantially reduced oreover, by reconguring the crosspoint switches once every several time slots, it is possible to signicantly relax the timing constraints imposed on the scheduling algorithm Compared with other architectures targeting high end routers, the proposed multi-crosspoints based architecture is scalable, easy to implement, and does not entail complex pacet processing or reordering Acnowledgements his wor has been partially supported by the Department of Energy research contract DE-F0-0ER07 REFERECES [] RZSIyer and ceown, Analysis of the parallel pacet switch architecture, IEEE/AC ransactions on etworing, vol, no, pp 3 3, 003 [] R Iyer and ceown, Routers with a single stage of buffering, AC Computer Communication Review SICO '0, pp, 00 [3] C Chang, D Lee, and Y Jou, Load balanced Birhoff-von eumann switches, High Performance Switching and Routing, 00 IEEE Worshop, pp 7 80, 00 [] Ieslassy, he load-balanced router, PhD hesis, Stanford University, 00 [] Li and IElhanany, Stability of a frame-based maximal weight matching algorithm with transfer speedup, IEEE Communications Letters, vol 9, no 0, pp 9 9, 00 [] SYam and DSung, Decomposed corssbar switches with multiple input and output buffers, IEEE LOBECO 00, vol, pp, 00 [7] J Dai and B Prabhaar, he throghput of data switches with and without speedup, IEEE IFOCO 000, pp, arch 000 [8] A eittiul and ceown, A practical scheduling algorithm to achieve 00% throughput ininput-queued switches, in IFOCO '98, vol, San Francisco, CA, USA, ar/apr 998, pp [9] P umar and S eyn, Stability of queueing networs and scheduling policies, IEEE ransactions on Automatic Control, vol 0, no, pp 0, February 99 [0] I Elhanany and B atthews, On the performance of output queued cell switches with non-uniformly distributed bursty arrivals, IEE Proceedings on Communications, vol 3, no, pp 0 0, 00