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

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

3. Traffic Arrivals
Peak rate
Frame size
Mean rate
Frame number

4. First-In-First-Out

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

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

7. 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

8. 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”

9. 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

10. 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

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

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

13. Plugging in …
Let:
FIFO SP
EDF

14. 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