Dynamic Scheduling in High-Speed Downlink Packet Access Networks: Heuristic Approach

1. Dynamic Scheduling in High-Speed Downlink Packet Access Networks: Heuristic Approach Hussein Al-Zubaidy, Jerome Talim, Ioannis Lambadaris SCE-Carleton University 1125 Colonel By Drive, Ottawa, ON, Canada Email: {hussein, jtalim, ioannis.lambadaris}@sce.carleton.ca

2. To develop a heuristic approach to find the near-optimal packet scheduling policy in HSDPA networks. This approach should have the following characteristics: Computationally efficient. The resulted heuristic policy should perform close to the optimal one. Objective

3. Develop an MDP-based model for the HSDPA downlink scheduler. Solve the model numerically (using value iteration) to find the optimal packet scheduling policy. Study the structure of the optimal policy for the two users case. Develop a heuristic policy based on the collected information. Extend the policy to any number of users. Methodology

4. Problem Definition The HSDPA downlink channel uses a mix of TDMA and CDMA: • Time is slotted into fixed length 2 ms TTIs. • During each TTI, there are 15 available codes that may be allocated to one or more users.

5. HSDPA Downlink Scheduler and FSMC Channel Models

6. L active users in the cell. Finite buffer with size B per user for each of the L users. Error free transmission. SDUs are segmented by RLC into a fixed number of PDUs (ui) and delivered to Node-B at the beginning of the next TTI. Independent Bernoulli arrivals with parameter qi . Scheduler can assign c codes chunks at a time, where c {1, 3, 5, 15} . The channel state of user i during slot t is denoted by γi(t). user i channel can handle up to γi(t) PDUs per code. Basic Assumptions

7. The Optimal Policy Structure (c = 5) P(γ1=1)=0.8, P(γ2=1)=0.5 and P(zi =5)=0.5 P(γi =1)=0.5 and P(zi =5)=0.5 for all i{1, 2} Legend: a1, a2: means a1 ( a2) code chunks allocated to user 1 ( user 2 ) P(γ1=1) = P(γ2=1)= 0.5 and P(z1=5)= 0.8, P(z2=5)= 0.5

8. We studied the optimal policy structure by running a wide range of scenarios, we noticed the following trends: The optimal policy is a multi-threshold Weighted LQF. The weight (wi) is a function of the difference of the two channel qualities and that of the arrival probabilities: w1 = f ([−ΔPγ]+, [−ΔPz]+); w2 = f ([ΔPγ]+, [ΔPz]+) where ΔPγ=P(γ1=1) − P(γ2=1) and ΔPz=P(z1=u) − P(z2=u). The intermediate regions has almost a constant width that equals 2c. a1(respectively a2) is increasing in x1 (respectively x2). f ( ) is increasing in | ΔPγ | and decreasing in | ΔPz |. Heuristic Policy ( 2 users)

9. Weight Function Approximation Following these observations, we approximated w1and w2 as follows Where [e]+ = max (e, 0)

10. Extended Heuristic Policy Define the following: • I = {1, 2, . . . , L}the set of all the users in the cell, • x = (x1, x2, . . . , xL) ∈ NLis a vector representing the instantaneous queue length of all Lusers in the cell, • wijis the pairwise weight function of user irelative to user j • rij= wijxi; The weighted queue length of user iw.r.t. user j. • {r∗i: i ∈ I} are the vectors riwith their components ordered in descending order, • m(i) is the order of the ithelement of the vector vordered according to the rule θ∗such that

11. Ordering Rule • θ = (θ1, θ2, . . . , θL), where θiis the location of component iof the vector rθunder the permutation θ. • Let θ∗ be a permutation such that rθ∗=r∗ • By definition, m(i) = θ∗i, where θ∗iis given by

12. Weight Function (wij ) The pairwise weight function is given by where ∆Pijγ= P(γi= 1)−P(γj= 1), ∆Pijz= P(zi= u)− P(zj=u), uis the patch size and [e]+ = max (e, 0). Now,

13. define r = (h1, h2, . . . , hL) to be the vector of all local maxima of all ri ∈ WL, where hi= maxj∈Irij= r∗i,[1]. r∗is the vector rordered according to θ∗ which represents the ordered vector of the global weighted queue size of the Lusers. define ψ =(ψ1, ψ2, . . . , ψL) ∈ {0, 1}Lto be the connectivity state vector at each TTI, i.e., ψi= 1{γi≥1}. Users Ordering and Service Urgency

14. The Heuristic Code Allocation Policy 1) Case (c = 15): At each TTI, do the following • find r∗and hence m(i) for all i ∈ I, • serve useri such that 2) Case (c = 5): At each TTI, do the following • order the weighted queue size for all users and find r∗ • select users i, j, ksuch that

15. The Heuristic Code Allocation Policy • divide the 3 code chunks between users i, j, kas follow: • if hi= hj= hk then (ai, aj, ak) = (1, 1, 1) • else if hi > hk and hj > hk then – else if hj, hk > hi then – else if hi, hk > hj then

16. Heuristic Policy Structure (2-user; c = 15) P(γ1=1)=0.8, P(γ2=1)=0.5 and P(zi =5)=0.5 P(γi =1)=0.5 and P(zi =5)=0.5 for all i{1, 2} P(γ1=1) = P(γ2=1)= 0.5 and P(z1=5)= 0.8, P(z2=5)= 0.5

17. Heuristic Policy Structure (2-user; c = 5) P(γ1=1)=0.8, P(γ2=1)=0.5 and P(zi =5)=0.5 P(γi =1)=0.5 and P(zi =5)=0.5 for all i{1, 2} P(γ1=1) = P(γ2=1)= 0.5 and P(z1=5)= 0.8, P(z2=5)= 0.5

18. Performance Evaluation System throughput for different loading conditions. Queuing delay performance when q1 = 0.8, q2 = 0.5 and u = 10.

19. Studied the optimal packet scheduling policy for the HSDPA downlink scheduler. From critical observations we conjectured that the policy is of threshold type and is multimodular in x1 and x2. Present an extended heuristic policy for code allocation in HSDPA system. The devised heuristic policy performs very close to the optimal policy regardless of the system loading. It provided extreme reduction in computation time. Conclusion

20. Thank you Q & A Hussein Al Zubaidy www.sce.carleton.ca/~hussein/