Chengzhi Li and Edward W. Knightly Schedulability Criterion and Performance Analysis of Coordinated Schedulers

Edward W. Knightly Rice University Background: Priority Scheduling Each packet has a priority index Scheduler selects smallest priority index pkt first Examples: WFQ, VC, EDF, SCED … Index assignment scheme  Service discipline Arrival Index L/r Arrival Index FIFO index = arrival_time Virtual Clock index = max(arrival_time, prev_index) + L/r

Edward W. Knightly Rice University Earliest Deadline First Scheduler services packet with smallest – deadline = arrival_time + delay_bound EDF is optimal for a single server Arrival Index

Edward W. Knightly Rice University Multiple Nodes: Sub-Optimality Over multiple nodes, EDF is not optimal –Locally optimal rules do not achieve global optimum (best end-to-end performance)  … Can do better

Edward W. Knightly Rice University Multiple Nodes: Issue 2, Traffic Distortion l Traffic can become more bursty downstream –Arrivals previously in now in l Consequence: difficult to analyze and efficiently support multi-node QoS Node j Node j+1 t + It arrivals

Edward W. Knightly Rice University Existing Solutions to Distortion Problem 1. Reshape traffic (Ex. Rate Controlled EDF) Hold packets until conform to original pattern 2. Isolate flows (Ex. Weighted Fair Queueing) Limit distortion by limiting sharing (e.g., guaranteed rate) l Problems –Utilization impact of isolation/non-work-conserving –Scalability issues with per-flow operations Node j Node j+1 t + It

Edward W. Knightly Rice University Our Approach: CNS Coordinated Network Scheduling [LiKn00] Virtual Coordination among servers –Server computes priority index as a function of upstream index –Ex. Downstream index = upstream index + constant –Target at end-to-end service Implications –Late packets have increased priority downstream –Early packets have priorities reduced downstream CNS is a general framework that includes –FIFO+ –Coordinated EDF (CEDF) –Coordinated Jitter Controlled Virtual Clock (CJVC)

Edward W. Knightly Rice University CNS Definition CNS is a work conserving scheduler that selects the packet with the smallest priority index first Indexes are given by: Recursive Priority Index Assignment

Edward W. Knightly Rice University Main Contribution End-to-end deterministic analysis of CNS –Characterize downstream priority index distortion vs. traffic pattern distortion using Essential Traffic Envelope –Exploit coordination property –Allow local (per-node) violations provided e2e satisfied –Devise end-to-end schedulability condition Show that CNS outperforms WFQ –Devise an index assignment scheme –If WFQ can schedule a set of flows, so can CNS

Edward W. Knightly Rice University Traffic Envelopes l Envelopes characterize arrivals as a function of interval length –Max and deterministic [Cr92, KWLZ95] –Statistical [QK99] l Recall: traffic distortion problem  envelopes distorted time t + It E *( I ) = 3

Edward W. Knightly Rice University New Concept: Essential Traffic Envelope l Essential traffic impedes a packet’s ability to meet a deadline –Ex. with FIFO, it’s pkts arriving earlier l Approach: bound traffic with a deadline range vs. an arrival time range (ETE vs. TE) Arrival Index Essential Traffic

Edward W. Knightly Rice University Illustration: First Hop (EDF and CNS) l 1st hop: priority indexes are the same in CNS and EDF l Suppose that the third packet is seriously delayed due to cross traffic Packet Arrival Event Packet Departure Event Packet Priority Index

Edward W. Knightly Rice University Second Hop Without Coordination (EDF) l At the second hop, the priority indexes depend on the (local/late) arrival times in EDF l Traffic distortion is large and propagates downstream Packet Arrival Event Packet Departure Event Packet Priority Index

Edward W. Knightly Rice University Second Hop With Coordination (CNS) Illustration of Essential Traffic Smoothing l 2 nd hop: the priority indexes are independent of the (local/late) arrival times in CNS l Departures are narrowly distorted (without reshaping) l Theory tightly bounds distortion of essential traffic Packet Arrival Event Packet Departure Event Packet Priority Index

Edward W. Knightly Rice University End-to-End Schedulability Condition l Allow local violations (ex. missed per-node deadlines) –…contrast to all previous deterministic work l Bound Essential Traffic Envelope downstream l Derive an end-to-end delay bound Schedulability Condition for all coordinated schedulers (CEDF, CJVC, GEDF, FIFO+, …)  CEDF, FIFO+, … not previously derived  CJVC bound tighter than previous results

Edward W. Knightly Rice University Index Assignment Coordinated scheduling achieves the same end-to-end delay bound as WFQ l Recall: indexes can be delay targets or L/r rate assignments l Result: under CJVC-like rate assignment and leaky bucket constrained flows Same WFQ bounds, yet scalable (unlike WFQ and RC-EDF), work conserving (unlike RC-EDF), … CNS is no worse than WFQ. But can be much better!

Edward W. Knightly Rice University A Simple Priority Index Assignment At Ingress Servers At Downstream Servers Coordinated scheduling achieves the same end-to-end delay bound as WFQ  Also scalable, work conserving If flow traffic is bounded by

Edward W. Knightly Rice University Simulation Study Simplified CNS priority index assignment schemes: –Constant local delay assignment scheme (5 msec and 15 msec respectively) Path for target trafficPath for background traffic Server 1Server 2Server 3Server 4Server 5Server 6

Edward W. Knightly Rice University CNS vs. EDF (Pareto on-off) With 300 flows, reduction in delay form 120 msec to 50 msec On rate: 64 kbps Mean of on period: 312 msec Mean of off period: 325 msec Parato shape: 1.9

Edward W. Knightly Rice University CNS vs. WFQ (Pareto on-off) With 300 flows, delay reduced from 170 to 50 msec On rate: 64 kbps Mean of on period: 312 msec Mean of off period: 325 msec Pareto shape: 1.9

Edward W. Knightly Rice University Conclusions Proposed a shedulability criterion for CNS Derived a general end-to-end delay bound for CNS Proved CNS can outperform WFQ and EDF

Edward W. Knightly Rice University Example Recursive Priority Index Assignments (CEDF) t+5 t+5+5 t t target packet t = arriving time of target packet at ingress router vs. local arrival time + 5

Edward W. Knightly Rice University A Numerical Example  CNS can be better! CNSWFQ D1 = 4L/CD1<=4L/C  r1=C, r2=r3=0 D2 = 3L/C r2 = 0  D2 >= 4L/C D3 = 3L/C r3 = 0  D3 >= 4L/C flow 3 Server 1 flow 1 flow 2 Server 2 CC flow 2