1. Admission Control and Scheduling for QoS Guarantees for Variable-Bit-Rate Applications on Wireless Channels I-H. Hou and P.R. Kumar Department of Computer Science University of Illinois 報告人：李宗穎 Proc. of ACM MobiHoc, pages 175–184, 2009

2. 2 Outline Introduction A model for QoS with Probabilistic Arrival Example for Application Necessary Condition for Feasibility Scheduling Policies Implementation and Simulation

3. 3 Introduction Two major issues concerning QoS over wireless admission control scheduling describe the QoS requirements by four criteria traffic pattern channel reliability delay bound throughput bound

4. 4 A model for QoS with Probabilistic Arrival (1/7) QoS requirements that generalizes a model that has been proposed in [5] [5] I-H. Hou, V. Borkar, and P. R. Kumar. A theory of QoS for wireless. To appear in Proc. of INFOCOM 2009.

5. 5 A model for QoS with Probabilistic Arrival (2/7) Clients generate jobs for the server to accomplish, and during each time slot, the server can attempt exactly one job The time slots are grouped into intervals, with each interval containing τ time slots Unfinished jobs are discarded at the end of an interval, so a delay bound of τ time slots is imposed on all jobs

6. 6 A model for QoS with Probabilistic Arrival (3/7) Don’t restrict attention only to clients that generate one job during each interval Clients generate jobs according to a probability mass function and exactly every client in S generates a job in an interval is R(S)

7. 7 A model for QoS with Probabilistic Arrival (4/7) Because wireless channels are unreliable, the job gets delivered with probability p n, which is called the reliability for client n Each client n requires a long-term average throughput of q n delivered jobs per interval

8. 8 A model for QoS with Probabilistic Arrival (5/7) Definition 1. Let Ht be the set of all possible histories of the system up to time slot t. A scheduling policy is a function η: H t  {1, 2,…, N, ψ} with the interpretation at time slot t + 1, the server attempts to transmit the job from client n if η(h t ) = n or idles if η(h t ) = ψ

9. 9 A model for QoS with Probabilistic Arrival (6/7) Definition 2. A set of clients is said to be fulfilled by a scheduling policy η if the long-term average throughput of each client n is at least q n jobs per interval with probability 1 q n the timely throughput bound of client n

10. 10 A model for QoS with Probabilistic Arrival (7/7) Definition 3. A set of clients is said to be feasible if there exists a scheduling policy η that fulfills it Definition 4. An optimal scheduling policy is a policy that fulfills every feasible set of clients

11. 11 Video Stream MPEG alternates between three coding modes (I,P,B) that require different numbers of bits per frame a higher bit rate implies a higher arrival probability, and can be converted into a timely throughput bound, and captured by the parameter q n

12. 12 VoIP Stream VoIP traffic involves both uplink traffic and downlink traffic This paper consider audio codecs that generate CBR traffic, such as ITU-T G.711 The job generation time for clients may be offset a set of three clients {1, 2, 3} client {1 (1,3,5…) 2 (2,4,6…) 3 (1,4,7…)} R(1, 3) = R(2, 3) = 1/2

13. 13 Real Time Surveillance there may be sensor nodes for monitoring heart activity, blood pressure, and body temperature Paper assume each client generates jobs periodically, with the differing frequencies of job generation reflecting the importance of the corresponding data

14. 14 Necessary Condition for Feasibility (1/6) Paper extend some Lemma to a necessary condition in [5] for a set of clients to be feasible to the more general model with variable traffic arrival patterns [5] I-H. Hou, V. Borkar, and P. R. Kumar. A theory of QoS for wireless. To appear in Proc. of INFOCOM 2009.

15. 15 Necessary Condition for Feasibility (2/6) LEMMA 1. The long-term average timely throughput of a client n is at least q n jobs per interval if and only if the server, on average, attempts jobs from that client w n = q n /p n times per interval

16. 16 Necessary Condition for Feasibility (3/6) LEMMA 2. A set of N clients is feasible only if Σ N w n ≦ τ Since the length of an interval is τ time slots and the server can attempt jobs at most once in each time slot

17. 17 Necessary Condition for Feasibility (4/6) LEMMA 3. γ n be the random variable denoting the number of attempts the server needs to make for a job from client n Prob{γ n = t} = p n (1 - p n ) t-1 (Geometric dist.) Delay Bound Guarantee ?

18. 18 Necessary Condition for Feasibility (5/6) LEMMA 4. E[L S ]: expected number of idle time slots in interval R(S): an interval occurs with probability

19. 19 Necessary Condition for Feasibility (6/6) LEMMA 5. A set of clients is feasible only if holds for every subset S It may seem that the condition for a strict subset S of {1,2,…,N} is redundant, and that we only need to evaluate the condition for all clients

20. 20 Example interval length τ = 3, and two clients Client 1  p 1 =0.5 q 1 =0.876 R{1}=1 Client 2  p 2 =0.5 q 2 =0.45 R{2}=1 So We can calculate following value w 1 = 1.76 ; w 2 = 0.9 I {1} = I {2} = 1.25 ; I {1,2} = 0.25 w 1 = 1.76 > 1.75 = τ – I {1} (unfeasible!!) w 1 + w 2 = 2.66 > 2.75 = τ – I {1,2} (feasible)

21. 21 largest time-based debt first policy DEFINITION 6. Let u n (t) denote the number of attempts that the server has made for jobs from client n up to time slot t. The time-based debt for client n is defined to be w n t - u n (t)

22. 22 largest weighted-delivery debt first policy DEFINITION 7. Let c n (t) denote the number of jobs for client n accomplished by the server up to time slot t. The weighted delivery debt for client n is defined to be [q n t - c n (t)]/p n

23. 23 Largest Debt First Policy

24. 24 VoIP traffic Group A : 60ms, 21.3kbits/s, 99% delivery ratio Subgroup {A 1, A 2, A 3 }, A i begin i, i+3, i+6… Group B : 40ms, 32kbits/s, 80% delivery ratio Subgroup {B 1, B 2 }, B j begin j, j+2… Feasible set  6 clients in each subgroup A i, 5 clients in each subgroup B j (infeasible B j =6) The channel reliability of the n th client in each subgroup is (60 + n)%

25. 25 Timely throughput insufficiency for VoIP traffic

26. 26 MPEG Video Streaming Group A:0.765 packet/interval, 90% delivery ratio Group B:0.34 packet/interval, 80% delivery ratio Feasible set  4 clients in each subgroup A i, 4 clients in each subgroup B j (infeasible A j =5) The channel reliability of the n th client in each subgroup is (60 + n)%

27. 27 Timely throughput insufficiency for video streaming

28. 28 Conclusion Paper have analytically addressed the problem of providing QoS support for heterogeneous VBR traffic flows over unreliable wireless channels Paper have also addressed implementation issues under IEEE 802.11, and implemented the two scheduling policies in ns-2