Delays in Packet Networks Getting a Grip on Delays in Packet Networks Jorg Liebeherr Dept. of ECE University of Toronto

Packet Switch Fixed-capacity links Variable delay due to waiting time in buffers Delay depends on Traffic Scheduling

Traffic Arrivals Peak rate Frame size Mean rate Frame number

First-In-First-Out

Static Priority (SP) Blind Multiplexing (BMux): All “other traffic” has higher priority

Earliest Deadline First (EDF) Benchmark scheduling algorithm for meeting delay requirements

Traffic Description Traffic arrivals in time interval [s,t) is Cumulative arrivals A Traffic arrivals in time interval [s,t) is Burstiness can be reduced by “shaping” traffic

Shaped Arrivals Traffic is shaped by an envelope such that: Flow 1 . C Flow N Flows are shaped Regulated arrivals Buffered Link Traffic is shaped by an envelope such that: Popular envelope: “token bucket”

What is the maximum number of shaped flows with delay requirements that can be put on a single buffered link? Link capacity C Each flows j has arrival function Aj envelope Ej delay requirement dj

Delay Analysis of Schedulers Consider a link scheduler with rate C Consider arrival from flow i at t with t+di: Limit (Scheduler Dependent) Deadline of Tagged arrival Arrivals from flow j Tagged arrival Tagged arrival departs by if

Delay Analysis of Schedulers Arrivals from flow j with FIFO: Static Priority: EDF:

Schedulability Condition We have: Therefore: An arrival from class i never has a delay bound violation if Condition is tight, when Ej is concave

Plugging in … Let: FIFO SP EDF

Numerical Result (Sigmetrics 1995) C = 45 Mbps MPEG 1 traces: Lecture: d = 30 msec Movie (Jurassic Park): d = 50 msec EDF Static Priority (SP) Peak Rate strong effective envelopes Type 1 flows