CprE 458/558: Real-Time Systems
Real-Time Networks – WAN
Packet Scheduling
CprE 458/558: Real-Time Systems (G. Manimaran)
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Scheduler
• Ensuring bandwidth (and delay), and buffer
guarantees to connections
• Determining the service order among packets from
different connections
• Scheduling algorithm has an associated admission
control that is used during channel setup
CprE 458/558: Real-Time Systems (G. Manimaran)
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Scheduler requirements
• Fairness – achieving fairness among competing flows
• Performance bounds for the guaranteed flows
• Efficiency -- schedulability
• Protection – guarantees of well-behaving flows are
protected from ill-behaving flows
• Flexibility – accommodating a diverse mix of traffic
class and rates
• Ease of implementation – high speed implementation
CprE 458/558: Real-Time Systems (G. Manimaran)
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Fairness and Max-Min Fairness
• Fairness
– Providing equal share of the resource to all the
flows
– The notion of fairness is obvious if all the flows
demand equal share of the resource
– Typically different flows exhibit varying resource
demands. The notion of Max-min fairness is
employed in such situations
CprE 458/558: Real-Time Systems (G. Manimaran)
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Max-Min Fairness
• Basic Idea: A fair share allocates
– a source with a small demand what it wants, and
evenly distributes unused resources to the big sources
• Formally, max-min fair share allocation is defined as:
– Resources are allocated in order of increasing demands
– No source gets a resource share larger than its demands
– Sources with unsatisfied demands get an equal share of the
resource
CprE 458/558: Real-Time Systems (G. Manimaran)
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Max-Min Fairness: Example
Four incoming flows with their
corresponding demands
2
2.6
4
Max-Min
Scheduler
Output Link
10
5
The max-min fairness allocation proceeds in several rounds
CprE 458/558: Real-Time Systems (G. Manimaran)
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Max-Min Fairness: Example (1)
• Round #1: Tentatively divide the resource (output
bandwidth) into four equal portions of size 10 / 4 = 2.5
• Allocation = [2.5, 2.5, 2.5, 2.5]
• Round #2: Deduct the excess resource allocation and
redistribute equally among others
CprE 458/558: Real-Time Systems (G. Manimaran)
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Max-Min Fairness: Example (2)
• Source 1’s demand is only 2.0 so deduct (2.5 - 2.0 =
0.5) and distribute the remaining amount of (0.5 / 3 =
0.167) to each of the rest three
• Allocation = [2.0, 2.67, 2.67, 2.67]
• Source 2’s demand is only 2.6 so deduct (2.67 - 2.6 =
0.07) and distribute the remaining amount of (0.07 / 2)
to each of the rest two
• Final Allocation = [2.0, 2.6, 2.7, 2.7]
CprE 458/558: Real-Time Systems (G. Manimaran)
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Working of the example
[2.5, 2.5, 2.5, 2.5]
Flow 1 has excess = 0.5
add (0.5 / 3) to each of
the rest
[2.0, 2.67, 2.67, 2.67]
Flow 2 has excess = 0.07
add (0.07 / 2) to each of the
rest
[2.0, 2.6, 2.7, 2.7]
CprE 458/558: Real-Time Systems (G. Manimaran)
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Max-Min Fairness: Example
Four incoming flows with their
max-min resource (bandwidth)
allocations / demands
2/2
2.6 / 2.6
2.7 / 4
Max-Min
Fairness
Resource Allocation
Output Link
10
2.7 / 5
CprE 458/558: Real-Time Systems (G. Manimaran)
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Weighted Max-Min Fairness
• A max-min weighted fairness share is as
follows
– Resources are allocated in order of increasing
demand, normalized by the weight
– No source gets a resource share larger than its
demand
– Sources with unsatisfied demands get resource
shares in proportion to their weights
CprE 458/558: Real-Time Systems (G. Manimaran)
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Weighted Max-Min Fairness: Example
Four incoming flows with their
corresponding demands
W1 = 2.5
4
W2 = 4
2
W3 = 0.5
10
W4 = 1.0
4
Max-Min
Scheduler
Output Link
16
The normalized weights are: [5, 8, 1, 2]
Now pretend as if the number of flows are (5 + 8 + 1 + 2) = 16 instead of just 4
CprE 458/558: Real-Time Systems (G. Manimaran)
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Working of the example
• Divide the capacity into 16 equal parts
– Flow 1’s share (capacity / 16) * 5 = (16 / 16) * 5 = 5
• Assign each flow an amount equal to its corresponding
normalized weight
• If there is excess allocation deduct it and redistribute it
for the rest in a weighted manner
CprE 458/558: Real-Time Systems (G. Manimaran)
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Working of the example
[5, 8, 1, 2]
Flow 2 has excess = 6
Flow 1 has excess = 1
[4, 2, 3.33, 6.66]
•We have to distribute excess “7” units among flows 3 and 4
•Their weights are 1 and 2 respectively
•Therefore, flow 3 will get an additional share of (7/3) * 1 and
flow 4 will get an additional share of (7/3) * 2
CprE 458/558: Real-Time Systems (G. Manimaran)
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Working of the example
[5, 8, 1, 2]
Flow 2 has excess = 6
Flow 1 has excess = 1
[4, 2, 3.33, 6.66]
Final Allocation [4, 2, 6, 4]
Flow 4 has excess = 2.66
allocate it to flow 3
CprE 458/558: Real-Time Systems (G. Manimaran)
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General Processor Sharing (GPS) or Fluid Flow Model
for achieving Max-min Fairness
Two incoming flows with their
resource demands
5
5
GPS
Resource Allocation
(Ideal, but Not practical)
Output Link
10
The schedule (ideal, but not realizable in networks)
0
5
CprE 458/558: Real-Time Systems (G. Manimaran)
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Max-Min fairness Approximation
Two incoming flows with their
resource demands
Packetized GPS
(Max-Min
Fairness
Approximation)
5
5
Output Link
10
The schedule
5 units of time
0
5 units of time
5
CprE 458/558: Real-Time Systems (G. Manimaran)
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A Simple Round Robin Scheduler
Cannot achieve max-min fairness
Four incoming flows
•Need to handle weighted flows
•Need to handle variable length packets
Round Robin
Scheduler
Output Link
The schedule
0
CprE 458/558: Real-Time Systems (G. Manimaran)
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Weighted Round Robin Scheduler
Normalized weights are as
follows:
[2, 3, 1, 1]
Four incoming flows with their
corresponding weights
10
15
5
Round Robin
Scheduler
Output Link
5
Cannot achieve max-min fairness
•Need to handle variable length packets
0
CprE 458/558: Real-Time Systems (G. Manimaran)
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