This document discusses priority queuing, which assigns different priority levels to packets in a queue to address impatient customers. It describes how priority can be determined by packet headers, source/destination addresses, ports, or other criteria. The document outlines preemptive and non-preemptive priority queuing, provides state transition diagrams and performance measures, and gives an example comparing FCFS, preemptive priority, and non-preemptive priority queuing for a router handling video and audio packets.

1. Priority Queuing
Done by:
Shahad H. Zwayen

3. FCFS queuing discipline

4. M/M/1 with FCFS queuing discipline

5. Impatient Customers! (problem)

6. Solution??

7. Priority Queuing

8. A packet's priority class may depend on:
1. Explicit marking that it carries in its packet
header (e.g. ToS) bits in an IPv4 packet)
2. Its source or destination IP address.
3. Its destination port number.
4. Other criteria

9. M/M/1 system with dual priority

10. PQ types:
1- preemptive
2- non preemptive

11. Preemptive scheduling discipline

12. Preemptive priority queuing (2- classes)
Class 1
Class 2
𝜆
𝜇
𝜇
𝜆1
𝜆2

13. State transition diagram

14. Performance measures
𝐸 𝐿1 =
𝜌1
1 − 𝜌1
𝐸 𝐿2 =
𝜌2
(1 − 𝜌1)(1 − 𝜌1 − 𝜌2)

15. Non-preemptive scheduling discipline

16. Non-preemptive PQ:

17. Non-preemptive performance measures

18. Example:
Let as consider a router forwarding two types of
packets Video and audio.
For 𝜆 𝑉𝑖𝑑𝑒𝑜= 0.2, 𝜆 𝑎𝑢𝑑𝑖𝑜 = 0.6 and the processing
time = 1 sec.

19. Solving ….
𝜌 𝑣𝑖𝑑𝑒𝑜 = 𝜆 𝑉𝑖𝑑𝑒𝑜/𝜇
𝜌 𝑣𝑖𝑑𝑒𝑜 = 0.2
𝜌 𝑎𝑢𝑑𝑖𝑜 = 𝜆 𝑎𝑢𝑑𝑖𝑜/𝜇
𝜌 𝑎𝑢𝑑𝑖𝑜 = 0.6
𝜌𝑡𝑜𝑡𝑎𝑙 = 0.8

20. In case of all packets are processed in
order of arrival
𝐸 𝑆 =
1
1 − 0.8
= 5 𝑠𝑒𝑐
𝐸 𝐿 𝐹𝐶𝐹𝑆 =
0.8
1 − 0.8
= 4

21. In case of video packets have absolute
priority over audio packets (Preemptive)
𝐸 𝑆 𝑣𝑖𝑑𝑒𝑜 =
1
1 − 0.2
= 1.25 𝑠𝑒𝑐
𝐸 𝐿 𝑣𝑖𝑑𝑒𝑜 =
0.2
1 − 0.2
= 0.25

22. Performance measures for audio packets
𝐸 𝐿 𝑎𝑢𝑑𝑖𝑜 =
0.6
(1 − 0.2)(1 − 0.2 − 0.6)
=
0.6
0.16
= 3.75
𝐸 𝑆 𝑎𝑢𝑑𝑖𝑜 =
1
(1 − 0.2)(1 − 0.2 − 0.8)
= 6.25 𝑠𝑒𝑐

23. In case of video packets have Non-Preemptive
priority over audio packets

24. REFERENCES
• Queueing Systems, Ivo Adan and Jacques Resing,
March 26, 2015.
• Analysis of M/M/n/K Queue with Multiple
Priorities, Sanjay K. Bose, 2002.
• IJCIT, Multiple Services Scheduling with Priority-
Queuing Model, Peng Ke, YuanXiang Li and
FuChuan Ni, ISSN 2218-5224.
• Multi-server queueing systems with multiple
priority classes, Mor Harchol-Balter, Takayuki
Osogami, Alan Scheller-Wolf, Adam Wierman.

25. Thank you

26. Comments?