1. OPTIMAL LINEAR-TIME QOS- BASED SCHEDULING FOR WIMAX Arezou Mohammadi, Selim G. Akl, Firouz Behnamfar School of Computing, Queen’s University CCECE 2008

2. Outline Introduction Motivation and Goal Proposed algorithm Simulation Conclusions

3. Introduction In this paper, author proposed two scene. For a service provider that covers a library data transmission is as important as voice. In an area such as the downtown of a city voice transmission might be more important than data. The bandwidth allocation issue related four types of service and two types of bandwidth allocation methods which is defined by 802.16 std.

4. Introduction Unsolicited grant service (UGS) UGS is designed to support real-time service flows that generate fixed size packets on a periodic basis. (VoIP) Real-time polling service (rtPS) rtPS is designed to support real-time traffic with variable size packets on a periodic basis. (video) Non-real-time polling service (nrtPS) nrtPS is used for non real-time applications that require variable size grant on a regular basis. (FTP) Best Effort (BE) service BE consumes the remaining bandwidth by a contention-based bandwidth request mechanism. (Email transmission)

5. Introduction Two types of bandwidth allocation methods are defined in the 802.16 standard: Grant Per Connection (GPC) With the GPC method, BS allocates grants to end users on a connection basis. Grant Per Subscriber Station (GPSS). With the GPSS method, grants are allocated on a SS basis, and packet scheduling is handled by SSs.

6. Motivation and Goal In this work, we focus on the GPS method BS responsible for handling all of the bandwidth allocation The problem of maximizing the number of data packets to be sent through an uplink subframe become a big issue. In a city UL bandwidth (slots) MS 1 UGS MS 2 UGS MS 3 rtPS MS 4 nrtPS MS 5 BE ms1ms2ms3

7. Motivation and Goal In this work, we focus on the GPS method BS responsible for handling all of the bandwidth allocation The problem of maximizing the number of data packets to be sent through an uplink subframe is a big issue. In a library UL bandwidth (slots) MS 1 UGS MS 2 UGS MS 3 rtPS MS 4 nrtPS MS 5 BE ms1ms2ms4ms5

8. Motivation and Goal We aim at modeling the problem as Knapsack problem and optimize the number of packets with various QoS requirements.

9. Proposed algorithm Assumption The service provider can choose a suitable modulation and coding scheme for data flows. There are a set of n data packets that are accepted by the admission controller and are waiting to be served

10. Proposed algorithm Definitions d i : the deadline for packet i l i : the length for packet i (number of slots) q i : the QoS class for packet i

11. Proposed algorithm Maximizing the total number of packets Subject to C is the uplink subframe bandwidth (number of slots)

12. Proposed algorithm The problem, which is formally defined as in the model, is a 0-1 Knapsack problem, which is an NP-hard problem. Subject to

13. Proposed algorithm The Knapsack problem can be solved in pseudo-polynomial time using dynamic programming, with a run time of O(n). i12345 V i ( )10111 Wi(li)Wi(li)21345 C = 5slots

14. Proposed algorithm W=12345 i=000000 101 {v 1 } 20 30 2 {v 1, v 3 } 401 {v 1 } 2 {v 1, v 3 } 501 {v 1 } 2 {v 1, v 3 } V[ i, w ] i12345 V i ( )10111 W i (l i )21345 C = 5slots {v 2 } {v 3 } V[2,3]=max(v[1,3],0+v[1,2])=1

15. Proposed algorithm Theorem 1: The algorithm provided here is a globally optimal uplink scheduling algorithm for any given consecutive number of frames. Sketch of the proof: We use induction to prove our claim. The algorithm is optimal for one subframe. We prove that it is optimal for subframe K + 1, if it is optimal for subframe K. Then, using contradiction, we prove the inductive step of the induction.

16. Proposed algorithm Maximizing the number of UGS packets : the ith packet

17. Proposed algorithm

18. Simulation Randomly generation l i 0< l i < 200 n = 20~200

19. Simulation

21. Conclusions In this paper, we presented two models to describe uplink scheduling in WiMAX systems. We showed that the 0-1 Knapsack problem is reducible to the problems described here. Therefore, we present an optimal algorithm for each model of the application, with a running time of O(n), where n is the number of packets to be sent.