Packet pacing in small buffer optical packet switched networks
Summary (4 min read)
Introduction
- The maturation of Wavelength Division Multiplexing (WDM) technology in recent years has made it possible to harness the enormous bandwidth potential of an optical fibre cost-effectively.
- As systems supporting hundreds of wavelengths per fibre with transmission rates of 10-40 Gbps per wavelength become available, electronic switching is increasingly challenged in scaling to match these transport capacities.
- The mechanism to achieve this, termed “pacing”, reduces the short-time-scale burstiness of arbitrary traffic, but without incurring significant delay penalties.
A. Loss for Real-Time Traffic
- The link rate is set at 10 Gbps, and packets have a constant size of 1250 bytes (this is consistent with earlier studies of slotted OPS systems).
- Fig. 1 shows the packet losses as a function of buffer size obtained from simulations of short range as well as long range dependent (LRD) input traffic at various system loads (the traffic model is detailed in section V).
- The plots illustrate that an OPS node with very limited buffering (say 10 to 20 packets) can experience significant losses even at low to moderate traffic loads, particularly with the LRD model which is more representative of real-world traffic.
- This may be unacceptable in a core network supporting real-time applications with stringent loss requirements.
B. Prior Work
- Some earlier works have proposed modifying traffic characteristics to improve performance in optical networks with limited buffers.
- ATM and IP networks have used rate-based shaping methods such as GCRA or leakybucket to protect the network against relatively longer-timescale rate fluctuations, while short-time-scale burstiness is expected to be absorbed by router buffers.
- This has been confirmed by studies in [22] and their earlier work in [23].
- Following on from their arguments in [24] showing that router buffer size need only be inversely proportional to the square-root of the number of TCP flows, they have recently shown in [25] that by making each TCP sender “pace” its packet injections into the network, a router buffer size of 10- 20 packets suffices to realise near-maximum TCP throughput performance.
- Another difference is that rather than pacing at the end-hosts, the authors focus on pacing at the edge of the optical network.
III. SYSTEM MODEL AND OFF-LINE OPTIMUM
- The packet pacer smoothes traffic entering the OPS network, and is therefore employed at the optical edge switches on their egress links connecting to the all-optical packet switching core.
- The objective of the pacer is to produce the smoothest output traffic such that each packet is released by its deadline.
- A feasible exit curve, namely one which is causal and satisfies the delay constraint, must lie in the region bounded above by the arrival curve A(t), and below by the deadline curve D(t).
- Current mechanims for smoothing consider one or a few video streams at end-hosts or video server; by contrast OPS edge nodes will have to perform the pacing on large traffic aggregates at extremely high data rates.
- The time-constraints for computing the optimal pacing patterns are also much more stringent – unlike video smoothing where a few frames (tens to hundreds of milliseconds) of delay is acceptable, OPS edge nodes will have buffer traffic for shorter time lest the buffering requirement becomes prohibitively expensive (at 10 Gbps, 1 msec of buffering needs 10 Mbits of RAM).
IV. EFFICIENT REAL-TIME PACING
- It is shown in [28] that an off-line pacer yields the smoothest output traffic satisfying the delay constraints if its service rate follows the shortest path lying between the arrival and deadline curves.
- In the on-line case, however, the packet arrival process is non-deterministic, and the arrival curve is not known beforehand.
- Upon each packet arrival, the deadline curve is augmented, and this may require a recomputation of the convex hull which defines the optimal exit curve.
A. Single Delay Class – Constant Amortised Cost Algorithm
- The authors first consider the case where all packets entering the pacer have identical delay constraints.
- This simplifies the hull update algorithm since each packet arrival augments the deadline curve at the end.
- At this stage the hull is convex and the backward scan can stop, resulting in the new hull.
- The algorithm of Fig. 4 has constant amortised computation cost per packet arrival, also known as Claim 1.
- A packet from the head of the pacer queue is released as soon as sufficient credits (corresponding to the packet size) are available, such credits being deducted when the packet departs the pacer.
B. Single Delay Class – Logarithmic Cost Algorithm
- In operation 2 the mid-point E of the right half is examined, and it is found that EH lies above the original hull, so the algorithm moves left, till it reaches point D in operation 3 that gives the desired tangent and final hull O-A-B-C-D-H. Fig. 7 depicts the update algorithm in pseudocode.
- Along with each vertex the authors also store pointers to its predecessor and successor on the boundary of its convex hull.
- The arrival of the new packet, which causes the deadline curve to be amended, results in appending a new vertex to the end of the hull.
- The search process is a binary search of the AVL tree, as described by Preparata [40, procedure TANGENT].
C. General Poly-Logarithmic Cost Algorithm
- The authors now consider the general case where arriving packets may have arbitrary delay constraints.
- The idea behind the algorithm is that for an incoming packet with arbitrary deadline, the original deadline curve is split into two parts, corresponding to the left and right of the new arrival’s deadline.
- The convex hulls for each of the parts is independently computed, after the deadline curve to the right has been shifted up to account for the new packet arrival.
- The authors vertices are stored in the leaves of a search tree T structure which is capable of supporting concatenable-queue operations, such as the 2-3 tree [41, sections 4.12], with the value of time used as the search key.
- The division is a recursive process detailed in [41, section 4.12].
V. PERFORMANCE EVALUATION FOR A SINGLE FLOW
- Having addressed the feasibility of pacing at high data rates, the authors demonstrate the utility of pacing in OPS systems with small buffers.
- This section evaluates via analysis and simulation the impact of pacing on traffic burstiness and loss for a single flow, while the next section evaluates via simulation loss performance for several flows in realistic network topologies.
A. Traffic Models
- The authors apply their pacing technique to Poisson and long range dependent (LRD) traffic models (both of which were introduced in section II-A); the Poisson model is selected for its simplicity and ease of illustration of the central ideas, while the LRD model is chosen since it is believed to be more reflective of traffic in real networks.
- Fig. 10 shows for Poisson and LRD traffic the burstiness β(s) versus time-scale s (in µsec) on loglog scale observed in simulation for pacing delay d of 0 (i.e. no pacing), 10µsec, 100µsec, 1msec, and 10msec, also known as 1) Simulation Results.
- At very long time-scales (beyond the delay budget d of the pacer), burstiness is again invariant to pacing.
VI. SIMULATION STUDY OF NETWORKS
- The previous section considered the impact of pacing on burstiness and loss at a single node.
- First, unlike the single-link scenario considered earlier in which all traffic was smoothed by the 11 one pacer, traffic will now be paced locally and independently by each ingress point of the OPS core – though globally suboptimal, this is the only feasible practical option.
- For both topologies the authors quantify the core packet loss as a function of contention resolution resources (optical buffers and wavelength converters) for various end-to-end delay penalties (incurred via pacing at the edge).
- The cumulative distribution of packet size is shown in Fig. 16, with distinct steps at 40 (the minimum packet size for TCP), 1500 (the maximum Ethernet payload size), as well as at 532 and 576 from TCP implementations that don’t use path MTU discovery.
- The benefits of pacing are again clear: for say 60 wavelengths per fibre, pacing delays of less than a millisecond are able to reduce loss by more than one order of magnitude.
VII. CONCLUSIONS
- Emerging optical packet switched (OPS) networks will likely have very limited contention resolution resources usually implemented in the form of packet buffers or wavelength converters.
- This can cause high packet losses and adversely impact end-to-end performance.
- Pacing dramatically reduces traffic burstiness for a bounded and controllable penalty in end-to-end delay.
- The authors showed via simulation of realistic OPS network topologies that pacing can reduce losses by orders of magnitude, at the expense of a small and bounded increase in end-to-end delay.
- The authors also intend to compare their traffic pacing at the optical edge to pacing TCP traffic at end-hosts [25].
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Citations
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Cites background from "Packet pacing in small buffer optic..."
...…et al., 2006, Beheshti et al., 2006, Prasad et al., 2007, Vishwanath and Sivaraman, 2008, Vishwanath et al., 2009a,b, Vishwanath and Sivaraman, 2009, Sivaraman et al., 2009, LeGrange et al., 2009, Vishwanath et al., 2011), to fit the all-fiber networks which is the fastest type of high-speed…...
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...Sivaraman et al. [ 17 ] show the impact of small buffers on real-time and TCP traffic and identify short timescale burstiness as the major contributor of degradation....
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References
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...Proof: Our proof method follows the technique outlined for amortized analysis in [ 39 ] that assigns a dollar cost to each unit of computation....
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"Packet pacing in small buffer optic..." refers methods in this paper
...The tree is then divided about so that all the leaves to the left of and itself are in one 2‐3 tree and all the leaves to the right of are in a second 2‐3 tree . The division is a recursive process detailed in [ 41 ], Section IV.[12]....
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"Packet pacing in small buffer optic..." refers background in this paper
...To support data traffic efficiently, various optical sub-wavelength switching methods such as in [2], [3] have been proposed, of which optical packet switching (OPS) [4] is particularly attractive....
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Frequently Asked Questions (2)
Q2. What have the authors stated for future works in "Packet pacing in small buffer optical packet switched networks" ?
Their future work targets a deeper study of TCP performance, particularly when mixed with real-time traffic [ 16 ], [ 17 ].