Open Issues in Router Buffer Sizing

Open Issues in Router Buffer Sizing Amogh Dhamdhere Constantine Dovrolis College of Computing Georgia Tech

Outline • Motivation and previous work • The Stanford model for buffer sizing • Important issues in buffer sizing • Simulation results for the Stanford model • Summary and future work NTG Seminar

Motivation • Router buffers are crucial elements of packet networks • Absorb rate variations of incoming traffic • Prevent packet losses during traffic bursts • Increasing the router buffer size: • Can increase link utilization (especially with TCP traffic) • Can decrease packet loss rate • Can also increase queuing delays • So the million dollar question is: How much buffer should a router have ? NTG Seminar

Motivation (cont’) • Some recent results suggest that small buffers are sufficient to achieve full utilization • The loss rate is not considered ! • Other results propose larger buffers to achieve full utilization and a bounded loss rate • Why these contradictory results ? • Different assumptions, applicability of these models ? • Is there a single answer to the buffer sizing problem ? • NO ! • Is that answer a very small buffer ? • NO ! NTG Seminar

Previous work • Approaches based on queuing theory (e.g. M|M|1|B) • Assume a certain input traffic model, service model and buffer size • Loss probability for M|M|1|B system is given by p=ρB(1- ρ)/(1- ρB+1) • TCP is not open-loop; TCP flows react to congestion • There is no universally accepted Internet traffic model • Morris’ Flow Proportional Queuing (Infocom ’00) • Proposed a buffer size proportional to the number of active TCP flows (B = 6*N) • Did not specify which flows to count in N • Objective: limit loss rate • High loss rate causes unfairness and poor application performance NTG Seminar

Previous work (cont’) • BSCL (Dhamdhere et al. Infocom 2005) • Proposed a buffer sizing formula to achieve full utilization and a bounded loss rate • Applicable to congested edge links • Proposes a buffer proportional to the number of active large flows • Can lead to a large queuing delay ! NTG Seminar

Stanford Model - Appenzeller et al. • Objective: Find the minimum buffer size to achieve full utilization of target link • Assumptions: • Most traffic is from “long” TCP flows • Long flows are in congestion avoidance for most of their lifetime (follow the TCP throughput equation) • The number of flows is large enough that flows are independent and unsynchronized • Aggregate window size distribution tends to normal • Queue size distribution also tends to normal NTG Seminar

Stanford Model (cont’) • Buffer for full utilization is given by B = CT / √N • N is the number of “long” flows at the link • CT: Bandwidth delay product • If link has only short flows, buffer size depends only on offered load and average flow size • Flow size determines the size of bursts during slow start • For a mix of short and long flows, buffer size is determined by number of long flows • Small flows do not have a significant impact on buffer sizing • Resulting buffer can achieve full utilization of target link • Loss rate at target link is not taken into account NTG Seminar

Stanford Model (cont’) • More recent results (Wischik, McKeown et al. ’05) • Sacrifice some utilization to make buffers smaller • Of the order of 20 packets • If TCP sources are “paced”, even smaller buffers are sufficient • O(log W) where W is the TCP window size • Pacing makes the sources less bursty • Pacing can occur automatically, due to slow access links and fast backbone links Don’t want to sound like a broken record, but… WHAT ABOUT THE LOSS RATE ? NTG Seminar

What are the objectives ? • Network layer vs. application layer objectives • Network’s perspective: Utilization, loss rate, queuing delay • User’s perspective: Per-flow throughput, fairness etc. • Stanford Model: Focus on utilization & queueing delay • Can lead to high loss rate (> 10% in some cases) • BSCL (Infocom ’05) : Both utilization and loss rate • Can lead to large queuing delay • Buffer sizing scheme that bounds queuing delay • Can lead to high loss rate and low utilization • A certain buffer size cannot meet all objectives • Which problem should we try to solve? NTG Seminar

Saturable/congestible links • A link is saturable when offered load is sufficient to fully utilize it, given large enough buffer • A link may not be saturable at all times • Some links may never be saturable • Advertised-window limitation, other bottlenecks, size-limited • Small buffers are sufficient for non-saturable links • Only needed to absorb short term traffic bursts • Stanford model is targeted at backbone links • Backbone links are usually not saturable due to over-provisioning • Edge links are more likely to be saturable • But N may not be large for such links • Stanford model requires large N NTG Seminar

Which flows to count ? • N: Number of “long” flows at the link • “Long” flows show TCP’s saw-tooth behavior • “Short” flows do not exit slow start • Does size matter? • Size does not indicate slow start or congestion avoidance behavior • If no congestion, even large flows do not exit slow start • If highly congested, small flows can enter congestion avoidance • Should the following flows be included in N ? • Flows limited by congestion at other links • Flows limited by sender/receiver socket buffer size • N varies with time. Which value should we use ? • Min ? Max ? Time average ? NTG Seminar

Which traffic model to use ? • Traffic model has major implications on buffer sizing • Early work considered traffic as exogenous process • Not realistic. The offered load due to TCP flows depends on network conditions • Stanford model considers mostly persistent connections • No ambiguity about number of “long” flows (N) • N is time-invariant • In practice, TCP connections have finite size and duration, and N varies with time • Open-loop vs closed-loop flow arrivals NTG Seminar

Traffic model (cont’) • Open-loop TCP traffic: • Flows arrive randomly with average size S, average rate l • Offered load lS, link capacity C • Offered load is independent of system state (delay, loss) • The system is unstable if lS > C • Closed-loop TCP traffic: • Each user starts a new transfer only after the completion of previous transfer • Random think timebetween consecutive transfers • Offered load depends on system state • The system can never be unstable NTG Seminar

Why worry about loss rate? • The Stanford model gives very small buffer if N is large • E.g., CT=200 packets, N=400 flows: B=10 packets • What is the loss rate with such a small buffer size? • Per-flow throughput and transfer latency? • Compare with BDP-based buffer sizing • Distinguish between large and small flows • Small flows that do not see losses: limited only by RTT • Flow size: k segments • Large flows depend on both losses & RTT: NTG Seminar

Simulation setup • Use ns-2 simulations to study the effect of buffer size on loss rate for different traffic models • Heterogeneous RTTs (20ms to 530ms) • TCP NewReno with SACK option • BDP = 250 packets (1500 B) • Model-1: persistent flows + mice • 200 “infinite” connections – active for whole simulation duration • mice flows - 5% of capacity, size between 3 and 25 packets, exponential inter-arrivals NTG Seminar

Simulation setup (cont’) • Flow size distribution for finite size flows: • Sum of 3 exponential distributions: Small files (avg. 15 packets), medium files (avg. 50 packets) and large files (avg. 200 packets) • 70% of total bytes come from the largest 30% of flows • Model-2: Closed-loop traffic • 675 source agents • Think time exponentially distributed with average 5 s • Time average of 200 flows in congestion avoidance • Model-3: Open-loop traffic • Exponentially distributed flow inter-arrival times • Offered load is 95% of link capacity • Time average of 200 flows in congestion avoidance NTG Seminar

Simulation results – Loss rate • CT=250 packets, N=200 for all traffic types • Stanford model gives a buffer of 18 packets • High loss rate with Stanford buffer • Greater than 10% for open loop traffic • 7-8% for persistent and closed loop traffic • Increasing buffer to BDP or small multiple of BDP can significantly decrease loss rate Stanford buffer NTG Seminar

Why the different loss rate trends ? • Open loop traffic: • The offered load does not depend on the buffer size • Possible to decrease loss rate to zero with sufficient buffer size • Loss rate decreases quickly with buffer size • Closed loop traffic: • Larger buffer leads to smaller loss rate, flows complete faster, and new flows arrive faster • Loss rate decreases slowly with buffer size NTG Seminar

Per-flow throughput • Transfer latency = flow-size / flow-throughput • Flow throughput depends on both loss rate and queuing delay • Loss rate decreases with buffer size (good) • Queuing delay increases with buffer size (bad) • Major tradeoff: Should we have low loss rate or low queuing delay ? • Answer depends on various factors • Which flows are considered: Long or short ? • Which traffic model is considered? NTG Seminar

Persistent connections and mice • Application layer throughput for B=18 (Stanford buffer) and larger buffer B=500 • Two flow categories: Large (>100KB) and small (<100KB) • Majority of large flows get better throughput with large buffer • Large difference in loss rates • Smaller variability of per-flow throughput with larger buffer • Majority of short flows get better throughput with small buffer • Lower RTT and smaller difference in loss rates NTG Seminar

Why the difference between large and small flows ? • Persistent flows: Larger buffer is better • Mice flows: Smaller buffer is better • Reason: Different effect of packet loss • Persistent flows: • Large congestion window halved due to packet loss • Take longer to reach original window = Decreased throughput • Mice flows: • Congestion windows never become very large • Quickly return to original window, especially with a smaller buffer • For persistent flows, the tradeoff is in favor of low loss rate, while for mice it is in favor of low queuing delay NTG Seminar

Variability of per-flow throughputs • Large buffer reduce the variability of throughput for persistent flows • Two reasons: • All RTTs increased by a constant (the queuing delay) • Smaller loss rate decreases the chance of a flow getting “unlucky” and seeing repeated losses • In our simulations, the RTT increase accounts for most of the variability reduction • Why is variability important ? • For N persistent connections, we have a zero-sum game • If one flow gets high throughput, some other must be losing NTG Seminar

Closed-loop traffic • Per-flow throughput for large flows is slightly better with larger buffer • Majority of small flows see better throughput with smaller buffer • Similar to persistent case • Smaller difference in per-flow loss rate • Reason: Loss rate decreases slowly with buffer size NTG Seminar

Open-loop traffic • Both large and small flows get much better throughput with large buffer • Significantly smaller per-flow loss rate with larger buffer • Reason: Loss rate decreases very quickly with buffer size NTG Seminar

Summary and Future Work • The buffer size required at a router depends on multiple factors: • The provisioning objective • The model which the input traffic follows • The nature of flows that populate that link (large vs small) • Very small buffers proposed in recent work can cause a large loss rate and harm application performance • Most work so far has focused on network layer performance • What is the optimal buffer when some application layer performance metric is considered ? NTG Seminar

Thank You ! NTG Seminar

Open Issues in Router Buffer Sizing