Dynamic Scheduling in High-Speed Downlink Packet Access Networks:

Heuristic Approach

Hussein Al-Zubaidy, Jerome Talim, Ioannis Lambadaris

SCE-Carleton University1125 Colonel By Drive, Ottawa, ON, Canada

Email: {hussein, jtalim, ioannis.lambadaris}@sce.carleton.ca

Objective

• 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.

Methodology

• 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.

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.

HSDPA Downlink Scheduler and FSMC Channel Models

Basic Assumptions

• 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.

The Optimal Policy Structure (c = 5)

P(γi =1)=0.5 and P(zi =5)=0.5 for all i{1, 2}

P(γ1=1)=0.8, P(γ2=1)=0.5 and P(zi =5)=0.5

P(γ1=1) = P(γ2=1)= 0.5 and P(z1=5)= 0.8, P(z2=5)= 0.5

Legend: a1, a2 : means a1 ( a2 ) code chunks allocated to user 1 ( user 2 )

Heuristic Policy ( 2 users)

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 |.

Weight Function Approximation

Following these observations, we approximated w1

and w2 as follows

][7.0][5.11ˆ

][7.0][5.11ˆ

2

1

z

z

PPw

PPw

Where [e]+ = max (e, 0)

Extended Heuristic Policy

Define the following:– I = {1, 2, . . . , L} the set of all the users in the cell,

– x = (x1, x2, . . . , xL) ∈ NL is a vector representing the instantaneous queue length of all L users in the cell,

– wij is the pairwise weight function of user i relative to user j

– rij = wijxi; The weighted queue length of user i w.r.t. user j.

– {r∗i : i ∈ I} are the vectors ri with their components ordered in descending order,

– m(i) is the order of the ith element of the vector v ordered according to the rule θ∗ such that

Ordering Rule

• θ = (θ1, θ2, . . . , θL), where θi is the location of component i of the vector rθ under the permutation θ.

• Let θ∗ be a permutation such that rθ∗=r∗

• By definition, m(i) = θ∗i , where θ∗i is given by

Weight Function (wij )

The pairwise weight function is given by

where ∆Pijγ = P(γi = 1)−P(γj = 1), ∆Pij

z = P(zi = u)− P(zj =u), u is the patch size and [e]+ = max (e, 0). Now,

Users Ordering and Service Urgency

• define r = (h1, h2, . . . , hL) to be the vector of all local maxima of all ri ∈ WL, where

hi = maxj∈I rij = r∗i,[1].• r∗ is the vector r ordered according to θ∗

which represents the ordered vector of the global weighted queue size of the L users.

• define ψ =(ψ1, ψ2, . . . , ψL) ∈ {0, 1}L to be the connectivity state vector at each TTI, i.e., ψi = 1{γi≥1}.

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 user i 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, k such that

The Heuristic Code Allocation Policy

• divide the 3 code chunks between users i, j, k as follow:– if hi = hj = hk then (ai, aj, ak) = (1, 1, 1)

– else if hi > hk and hj > hk then

– else if hi, hk > hj then

– else if hj, hk > hi then

Heuristic Policy Structure (2-user; c = 15)

P(γi =1)=0.5 and P(zi =5)=0.5 for all i{1, 2}

P(γ1=1)=0.8, P(γ2=1)=0.5 and P(zi =5)=0.5

P(γ1=1) = P(γ2=1)= 0.5 and P(z1=5)= 0.8, P(z2=5)= 0.5

Heuristic Policy Structure (2-user; c = 5)

P(γi =1)=0.5 and P(zi =5)=0.5 for all i{1, 2}

P(γ1=1)=0.8, P(γ2=1)=0.5 and P(zi =5)=0.5

P(γ1=1) = P(γ2=1)= 0.5 and P(z1=5)= 0.8, P(z2=5)= 0.5

Performance Evaluation

System throughput for different loading conditions.

Queuing delay performance when q1 = 0.8, q2 = 0.5 and u = 10.

Conclusion

• 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.

Thank you

Q & A

Hussein Al Zubaidy

www.sce.carleton.ca/~hussein/