This document discusses packet scheduling for quality of service (QoS) management in multi-service networks. It describes common performance bounds like maximum delay and delay jitter. First-come first-served scheduling is discussed along with its limitations. Priority queuing and max-min fair sharing are presented as alternatives to provide traffic isolation and fair resource sharing. The concept of a scheduler's schedulable region for efficient admission control is also introduced.

1. Packet Scheduling
for QoS management
TELCOM2321 – CS2520
Wide Area Networks
Dr. Walter Cerroni
University of Bologna – Italy
Visiting Assistant Professor at SIS, Telecom Program
Slides partly based on Dr. Znati’s material

2. 2
Multi-service network
• Single network infrastructure carrying traffic from different
services (data, voice, video...) in an integrated way
• Different quality of service requirements to be met

3. 3
Performance bounds
• Deterministic
– holding for every packet sent on a connection
• Statistical
– probability that a packet violates the bound is less
than a specified value
– one-in-N bound, no more than one packet in N
consecutive packets violates the bound
• Common performance bounds
– minimum bandwidth
– maximum loss
– maximum delay
– maximum delay jitter

4. 4
Performance bounds: Delay jitter
• Delay jitter bound requires that the network limit
the difference between the largest and the
smallest delays experienced by packets
delayprob.densityfunction
delay
propagation
delay
jitter
average
delay
worst-case
delay

5. 5
Performance bounds: Delay jitter
• Delay jitter bound is useful for audio/video playback,
where receiver can compensate delay variations
– delaying the first packet by the delay-jitter bound in an elasticity
buffer
– playing back packets at a constant rate from the buffer
Time
CBR playback
at the client
playback
buffer delay
variable
network delay
CBR streaming
at the source
Cumulativedata
reception
at the client
buffered
data

6. 6
Performance bounds: Delay jitter
• Playback buffer delay must be appropriate
– if too short, it will cause losses
– if too large, it will affect interactivity
Time
Cumulativedata
loss
too large e2e delay

7. 7
The role of the network
• The network should have enough resources
available to be able to satisfy the performance
bounds required by the application
– admission control
– congestion control
• The network should efficiently manage the
resources available in order to guarantee a
quality of service acceptable to the application
– packet scheduling at intermediate nodes

8. 8
Packet scheduling
• Packets are queued at intermediate nodes
– store and forward
• The server on each queue must
– decide which packet to service next
– manage the queue of backlogged packets
• The server uses a scheduling discipline to
– fairly share the resources
– provide performance guarantees
• Trade-off between
– traffic isolation
• circuit switching: guaranteed dedicated resources
– resource sharing
• packet switching: complete resource sharing

9. 9
Scheduling policy requirements
• A scheduler should be
– not too expensive in terms of required hardware
– scalable
• the number of operations to implement a discipline should be
as independent as possible of the number of scheduled
connections
– fair
• it should allocate a fair share of the link capacity and output
queue buffer to each connection
– protective
• the misbehavior of one source should not affect the
performance received by other sources

10. 10
The simplest scheduler: FCFS or FIFO
• First Come First Served or First In First Out
• Packets are served in the same order as they arrive
• Most commonly used scheduling discipline
• Example
– M/G/1 queue: Poisson arrivals, generic service time
• Stability condition on server utilization
• Probability of idle server state
queue server
arrival rate departure rate
average
service time

11. 11
M/G/1: Average waiting time
• Each packet arriving at the queue
– is served immediately, if server is idle
• waiting time = 0 with probability
– must wait for the packet currently being served to finish its
service, if server is busy
• waiting time = residual service time with prob.
• average residual service time:
– must wait also for all packets previously queued to finish their
service, if queue is not empty
• waiting time = sum of service times for each queued packet
• average number of packets in the queue (Little’s theorem):
• Average waiting time

12. 12
M/G/1: Average waiting time
• Solving for :
– the average waiting time depends on arrival rate, server
utilization (i.e. load) and service time distribution
• Exponential services: M/M/1
• Deterministic services: M/D/1

13. 13
Limitations of FCFS
• All packets are serviced the same way
• No consideration for delay sensitivity
– small packets must wait for long packets to be serviced
• Unfair
– connections with large packets usually receive better services by
getting higher percentage of server time
• Not protective
– greedy connections are advantaged over friendlier connections
– an excessively active connection may cause other connections
implementing congestion control to back off more than required
• The cause is complete resource sharing without traffic
isolation
– isolation through separate queues for different traffic flows or
classes sharing the same bandwidth

14. 14
Separate queues
• Flow with arrival rate and average service time
• server utilization due to flow packets
• Stability condition:
...

15. 15
Priority queuing
• priority classes
• Class with arrival rate and average service time
• Class 1 has highest priority, then class 2, then class 3, ...
• Low-priority packets are serviced only when there are no
packets of higher priority waiting to be serviced
– FCFS within the same class
– arrivals of high-priority packets do not stop current service of low-
priority packets (non-preemptive)

16. 16
M/G/1 with priorities: Average waiting time
• Each class packet arriving at the queue
– is served immediately, if server is idle
• waiting time = 0 with probability
– must wait for the packet currently being served to finish its
service, if server is busy
• average residual service time:
– must wait for all packets of class previously queued to
finish their service
• average number of class packets in the queue:
each requiring average service time
– must wait also for all packets of class that have been
received during its waiting time to finish their service
• average number of class packets arrived during class packet
waiting time:
each requiring average service time

17. 17
M/G/1 with priorities: Average waiting time
• Average class waiting time
• Solving for
• Same expression in recursive format (Cobham’s formula)

18. 18
Example: 2 classes
Assuming identical exponential services for both classes and
we get

19. 19
Example: 2 classes
0
2
4
6
8
10
12
14
16
18
20
0 0.2 0.4 0.6 0.8 1
no priorities

20. 20
Limitations of priority queuing
• Effective only when high priority traffic is a small part of
the total traffic
– efficient admission control and policing may be required
• Not protective
– a misbehaving source at a higher priority level can increase delay
at lower priority levels
• Unfair
– starvation of low-priority queues in case of heavy high-priority
traffic
• More sophisticated scheduling disciplines are required
– better traffic isolation
– fairer resource sharing

21. 21
Conservation Law
• Traffic isolation while sharing resources is limited by the
conservation law
• The sum of the mean queuing delays received by the set
of multiplexed connections, weighted by their share of the
link's load, is independent of the scheduling discipline
• In other words, a scheduling discipline can reduce a
particular connection's mean delay, compared with
FCFS, only at the expense of another connection
• Valid if server is idle only when queues are empty
– work-conserving schedulers

22. 22
Non-Work Conserving Schedulers
• A non-work conserving scheduler may idle even when
packets are currently waiting for service
• A non-work conserving scheduler can reduce delay jitter
if packets are only serviced at their eligibility times
– packets are serviced no faster than the allowed rate
– in case of exceeding bursts, non-eligible packets are retained
– introducing idle time makes the traffic more predictable
– bursts do not build up within the network
• A(k), arrival time for k-th packet
• E(k), eligibility time for k-th packet
• XMIN, inverse of the highest allowed packet rate
• E(k+1) = max { E(k) + XMIN, A(k+1) }
• Bandwidth wasted during forced idle times
• Jitter reduced at the cost of increased average delay

23. 23
Max-Min fair share
• Resources should be shared in a fair way, especially
when they are not sufficient to satisfy all requests
• Max-Min fair share
– bandwidth allocation technique that tries to maximize the
minimum share for non-satisfied flows
• Basic principles
– resources are allocated in order of increasing demands
– users with relatively small demands are satisfied
– no user gets a resource share larger than its demand
– users with unsatisfied demands get an equal share of unused
resources

24. 24
Max-Min fair share
1. Order demands d1, d2, ..., dN such that d1 ≤ d2 ≤ ... ≤ dN
2. Compute the initial fair share of the total capacity C:
FS = C / N
3. For each demand dk such that dk ≤ FS allocate the
requested bandwidth
4. Compute the remaining bandwidth R and the number of
unsatisfied demands M
5. Repeat steps 3 and 4 using the updated fair share
FS = R / M until no demand left is ≤ FS
6. Allocate the current FS to remaining demands

25. 25
Max-Min fair share: Example
1. Demands: d1 = 23, d2 = 27, d3 = 35, d4 = 45, d5 = 55
2. Bandwidth: C = 155
3. FS = 155 / 5 = 31
4. d1 and d2 satisfied, M = 3
5. Bandwidth left: R = 155 – (23 + 27) = 105
6. FS = 105 / 3 = 35
7. d3 satisfied, M = 2
8. R = 105 – 35 = 70
9. FS = 70 / 2 = 35
10. d4 and d5 not satisfied they get 35

26. 26
Scheduling and admission control
• Given a set of currently admitted connections and a
descriptor for a new connection request, the network
must verify whether it is able to meet performance
requirements of new connection
• It is also desirable that the admission policy does not
lead to network underutilization
• A scheduler define its “schedulable region” as the set of
all possible combinations of performance bounds that it
can simultaneously meet
– resources are finite, so a server can only provide performance
bounds to a finite number of connections
• New connection requests are matched with the
schedulable region of relevant nodes

27. 27
Scheduling and admission control
• Schedulable region is a technique for efficient admission
control and a way to measure the efficiency of a
scheduling discipline
– given a schedulable region, admission control consists of
checking whether the resulting combination of connection
parameters lies within the scheduling region or not
– the larger the scheduling region, the more efficient the scheduling
policy
No. of class 1
requests
No. of class 2
requests
(C1,C2)
(C1MAX,0)
schedulable
region
(0,C2MAX)