1. Intro to Deterministic Analysis
left-continuous

2. Deterministic network calculus:
Theory for obtain worst-case (=deterministic) network performance
Developed in the 1990s (Rene Cruz)
Bounds of interest:
Delay at a switch
Backlog at a switch
Traffic at output of switch
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3. Components of a Packet Switch
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4. Modeling a packet switch
Model with input and output buffers
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5. Modeling a packet switch
Model with input and output buffers
Simplified model (only output buffers)
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6. A path of network switches
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7. Model of a switch Buffering takes place only at the output.
(Neglect processing delay)
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8. Packet arrivals Store and Forward:
Packet arrives to buffer only after all bytes of the packet have been received
An arrival to the buffer appears instantaneous
Multiple packets can arrive at the same time
Scheduling Algorithms:
FIFO
Priority
Round-Robin
Earliest-Deadline-First
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9. Modeling Traffic Arrivals
We write arrivals as functions of time:
A(t) : Arrivals until time t, measured in bits
There are a number of choices to be made:
Continuous time or Discrete time domain
Discrete sized or fluid flow traffic
Left-continuous or right-continuous
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10. Continuous time vs. Discrete time Domain
Continous time: t is a non-negative real number
Discrete time: Time is divided in clock ticks
t = 0,1,2, ….
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11. Discrete-sized vs. Fluid flow
Traffic arrives in multiples of bits
Traffic arrives like a fluid
It is often simpler to view traffic as a fluid flow, that allows discrete sized bursts
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12. Left-continuous vs. right-continuous
With instantaneous (discrete-sized) arrivals in a continuous time domain, the arrival function A is a step function
There is a choice to draw the step function:
© Jörg Liebeherr, 2006
ECE 1545

13. Left-continuous vs. right-continuous
A(t) considers arrivals in (0,t]
A(t) considers arrivals in [0,t) (Note: A(0) = 0 !)
We will use a left-continuous arrival function
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14. Arrivals of packets to a buffered link
Backlog at the buffered link

15. Arrival and departure functions

16. Backlog Backlog Link rate of output is C
Packet length is up to L bits long
Assumptions:
Scheduler is work-conserving
(always transmitting when there is a backlog)
Infinite Buffers
Backlog
slope C
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ECE 1545

17. Definitions:
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ECE 1545

18. Dealing with instantaneous arrivals
If we have an instantaneous arrival, then the arrival function is a step function.
Need to decide which time the arrival takes place.
We assume that the arrival occurs at time t+
This leads to a left-continuous arrival function.
© Jörg Liebeherr, 2006
ECE 1545

19. © Jörg Liebeherr, 2006
ECE 1545