1. Wireless Packet Scheduling With Soft Deadlines Aditya Dua and Nicholas Bambos Department of Electrical Engineering Stanford University ICC 2007

2. Outline Introduction Model Construction Problem Formulation Proposed Algorithm Simulation Conclusions

3. Introduction Next-generation cellular wireless communication networks aim to provide a variety of QoS-sensitive packet-based services to downlink users. The problem of downlink scheduling is that the single transmitter at the BS is shared amongst multiple downlink user.

4. Intrduction In early works, each packet is associated with a hard deadline, i.e., a packet is dropped if not successfully transmitted by its designated deadline. The soft deadline mean a packet which violates its deadline is not dropped (which is the case with hard deadlines), but is penalized for doing so.

5. Motivation However, due to contention for the shared wireless link and fluctuations in wireless channel quality, the users cannot always be strictly in the deadline constraint. For instance, in the case of video streaming, dropped packets lead to playout freezes and, hence, user annoyance. Moreover, some packets are inherently more important than others (a peculiarity of multimedia encoders) and therefore must be prioritized for scheduling by the BS.

6. Motivation If the user has received excess service, we say that she is leading. potentially cause buffer overflows at the receiver starvation of delay tolerant traffic If the user has received less than her desired share of Service, we say that the she is lagging. degradation of multimedia quality

7. Goal Our goal is to design a scheduling policy that minimizes QoS degradation due to missed deadlines or received excess service and also treats all users fairly.

8. Model Construction BS Q1Q1 QiQi QNQN MS 1 MS i MS N scheduler … … … … T

9. Definitions QiQi 100100100 … The target profile for user i :Denote the packets ideally have departed for user i at time-slot t t To describe the service received ideally by different users, we associate with each user a sequence called the service trace, which specifies the inter-packet deadline (IPD) constraints for that user. IPD

10. Definitions MS i 010100100 … The Service trace for user i t To describe the service received actually by different users, we associate with each user a sequence called the service trace. :Denote the packets actually have departed for user i at time-slot t

11. Definitions is the number of deviation for user i before time-slot t : the number of packets which should ideally have departed from Q i by time-slot t Quantify the distortion

12. Definitions Both lags and leads are undesirable

13. Definitions : the success probability for user i at time-slot t To quantify the wireless channel quality in a time slot by the probability of a successful transmission of a packet over the channel.

14. Problem Formulation We will optimize the performance of the system over a finite horizon of T time-slots. To facilitate exposition, we assume that all queues contain T or more packets at time 0.

15. Problem Formulation : the cost for user i with deviations k Since distortion of target profiles is undesirable, deviations are associated with a “cost”. φ i (0) = 0 (since zero deviation is desirable) φ i (k) is non-negative and increasing for both k 0 (since both lags and leads are undesirable)

16. Problem Formulation φ i (0) = 0 (since zero deviation is desirable), φ i (k) is non-negative and increasing for both k 0 (since both lags and leads are undesirable)

17. Problem Formulation Remarks: The cost functions φ 1 (·),..., φ N (·) are not part of a “natural” description of the scheduling problem. The costs are imposed extraneously by the scheduler at the BS. Different cost functions to different users, the scheduler can provide differentiated QoS, enforce fairness etc.

18. Problem Formulation Let the state of the system in time-slot t be the vector The sum of deviation costs of all users in time-slot t.

19. Problem Formulation Define the action set Action i > 0 corresponds to scheduling Q i and action 0 corresponds to idling the system (no user is scheduled). A policy is a set of actions in time-slots 1,..., T. Π T =

20. Problem Formulation : denote the system state in time-slot t when policy Π T is employed. Our objective is to compute the optimal policy The system state

21. Problem Formulation If policy Π T schedules the ith user in time-slot t. The transmission is successful with probability (w.p.) and the state of Q i changes from to (since = 1). The transmission fails w.p. 1 − and the state of Qi changes from to (since = 1). e i as the configuration vector associated with action i

22. Problem Formulation : Denote the expected cost incurred by the optimal policy during time-slots t,..., T

23. Proposed Algorithm The myopic/greedy approach Here the author develop a heuristic algorithm based on solving the DP equations for a time-horizon of T = 1 time-slot. A greedy approach ignores future costs and an action is myopically or greedily chosen based on instantaneous cost Φ(·) alone. The greedy policy schedules user i in time-slot t

24. Proposed Algorithm Minimum Projection (MinProj) a special case of the greedy approach MinProj becomes a special case of assigning each user a quadratic cost function Reduce the greedy function

25. Proposed Algorithm The action in timeslot t is computed by finding the configuration vector ( from the set e 0 = 0, e 1,..., e N ) with the smallest projection on an affine transformation of the state d t. MinProj selects user in time-slot t such that

26. Proposed Algorithm is a diagonal matrix with as its ith diagonal entry the user with the smallest value is scheduled

27. Model Construction BS Q1Q1 QiQi QNQN MS 1 MS i MS N scheduler 0010 0101 1000 … … … … T 0010 0101 1000 T = ( 0, 0, 0, …, 0)

28. Model Construction = k 2 = 0= 0 = ( 0, 0, 0, …, 0) ( MinProj )

29. Model Construction BS Q1Q1 QiQi QNQN MS 1 MS i MS N scheduler 0010 0101 1000 … … … … T 0000 0101 1000 T = ( -1, 0, 0, …, 0)

30. Model Construction = k 2 = 1= 1 = ( -1, 0, 0, …, 0) ( MinProj )

31. Simulation N = 6. time-slot length of 2ms. φ i (k) = k 2 SNR γ was mapped to successful packet reception probability through the parametrized mapping p (γ) = 1− e −δγ ( δ = 0.4 ). Simulating the system for 20,000 time-slots.

32. Simulation Experiment A: The first three users (strong) had an average downlink SNR of 12dB, while the other three users (weak) had an average downlink SNR of 6dB.

33. Simulation Experiment B: the average downlink SNR for all users was set equal to 9dB. The IPDs of the first three users (light) were small and the other three users (heavy) were high

34. Conclusions This paper examined the problem of scheduling multiple users associated with target profiles across a shared wireless channel. The proposed policy, MinProj, significantly outperforms policies which exploit channel or deadline information alone.