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Downlink Scheduler Optimization in High-SpeedDownlink Packet Access Networks

Hussein Al-Zubaidy

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

Email: [email protected]

21 August 2007

Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 Colonel By Drive, Ottawa, ON, Canada Email: [email protected] ()Downlink Scheduler Optimization in High-Speed Downlink Packet Access Networks21 August 2007 1 / 26

Outline

1 Objective

2 Methodology

3 Problem Definition and Model Description

4 Case Study and Results

5 Conclusion and Future Work


Objective

Objective

To devise a methodology to find the optimal scheduling regime in HSDPAnetworks, that controls the allocation of the time-code resources.

This resulting optimal policy should have the following properties:

Fair; Divide the resources fairly between all the active users.

Optimal Transmission: Maximizes the overall cell throughput.

Optimal Resource Utilization: Provide channel aware (diversity gain)and high speed resource allocation.


Objective

Objective







Objective

Objective







Objective

Objective







Methodology

Methodology

This work presents a different approach for scheduling in HSDPA. Adeclarative approach is used,

Develop an analytic model for the HSDPA downlink scheduler.

A MDP based discrete stochastic dynamic programming model is usedto model the system.This Model is a simplifying abstraction of the real scheduler whichestimates system behavior under different conditions and describes therole of various system components in these behaviors.It must be solvable.

Define an objective function.

Value iteration is then used to solve for optimal policy.


Methodology

Methodology







Methodology

Methodology







Methodology

Methodology







Problem Definition and Model Description Problem Definition and Conceptualization

Problem Definition and Conceptualization

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 allocatedto one or more users.















HSDPA Scheduler Model (Downlink)

User 1

PDUs

SDU

User L

Scheduler Transceiver

UE1

Channel State Monitor/Predictor

UEL

RNC

Node-B

RLC

RNC



FSMC Model for HSDPA Downlink Channel

0 1 M-1

P01

P10

P00

P11


Problem Definition and Model Description Model Description and Basic Assumptions

The Model

MDP based Model.

HSDPA downlink scheduler is modelled by the 5-tuple(T ,S ,A,Pss′(a),R(s, a)),where,

T is the set of decision epochs,S and A are the state and action spaces,Pss′(a)=Pr(s(t + 1)=s′|s(t)=s, a(s)=a) is the state transitionprobability, andR(s, a) is the immediate reward when at state s and taking action a.



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 ) anddelivered 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, wherec ∈ {1, 3, 5, 15} .



Basic Assumptions–FSMC State Space

The channel state of user i during slot t is denoted by γi (t).

Channel state space is the set M = {0, 1, . . . ,M − 1}.user i channel can handle up to γi (t) PDUs per code.


Problem Definition and Model Description State and Action Sets

State and Action Sets

The system state s(t) ∈ S is a vector and is given by

s(t) = (x1(t), x2(t), . . . , xL(t), γ1(t), γ2(t), . . . , γL(t)) (1)

S = {X ×M}L is finite, due to the assumption of finite buffers sizeand channel states.

The action a(s) ∈ A is taken when in state s

a(s) = (a1(s), a2(s), . . . , aL(s)) (2)

subject to,

L∑i=1

ai (s) ≤15

c, and ai (s) ≤

⌈xi (t)

γi (t)c

⌉ai (t)c , number of codes allocated to user i at time epoch t.








a(s) = (a1(s), a2(s), . . . , aL(s)) (2)

subject to,

L∑i=1

ai (s) ≤15

c, and ai (s) ≤

⌈xi (t)

γi (t)c









a(s) = (a1(s), a2(s), . . . , aL(s)) (2)

subject to,

L∑i=1

ai (s) ≤15

c, and ai (s) ≤

⌈xi (t)

γi (t)c









a(s) = (a1(s), a2(s), . . . , aL(s)) (2)

subject to,

L∑i=1

ai (s) ≤15

c, and ai (s) ≤

⌈xi (t)

γi (t)c

⌉

ai (t)c , number of codes allocated to user i at time epoch t.








a(s) = (a1(s), a2(s), . . . , aL(s)) (2)

subject to,

L∑i=1

ai (s) ≤15

c, and ai (s) ≤

⌈xi (t)

γi (t)c



Problem Definition and Model Description Reward Function

Reward Function

The reward must achieve the objective function

R(s, a) have two components corresponding to the two objectives

R(s, a) =L∑

i=1

aiγic − σ

L∑i=1

(xi − x̄) 1{xi=B} (3)

where we defined the fairness factor (σ) to reflect the significance offairness in the optimal policy.

The positive term of the reward maximizes the cell throughput.

The second term guarantees some level of fairness and reducesdropping probability.


Problem Definition and Model Description State Transition Probability

State Transition Probability

Pss′(a) denotes the probability that choosing an action a at time twhen in state s will lead to state s′ at time t + 1.

Pss′(a) = Pr(s(t + 1)=s′|s(t)=s, a(t)=a)

= Pr(x ′1,. . ., x′L,γ

′1,. . .,γ

′L|x1,. . ., xL,γ1,. . .,γL,a1,. . .,aL)

The evolution of the queue size (xi ) is given by

x ′i = min([xi − yi ]

+ + z ′i ,B)

= min([xi − aiγic]+ + z ′i ,B

)(4)

Using the independence of the channel state and queue sizes

Pss′(a) =L∏

i =1

(Pxix

′i(γi , ai ) Pγiγ

′i

)(5)

where Pγiγ′i

is the Markov transition probability of the FSMC.






= Pr(x ′1,. . ., x′L,γ

′1,. . .,γ

′L|x1,. . ., xL,γ1,. . .,γL,a1,. . .,aL)



+ + z ′i ,B)


)(4)


Pss′(a) =L∏

i =1

(Pxix


′i

)(5)

where Pγiγ′i







= Pr(x ′1,. . ., x′L,γ

′1,. . .,γ

′L|x1,. . ., xL,γ1,. . .,γL,a1,. . .,aL)



+ + z ′i ,B)


)(4)


Pss′(a) =L∏

i =1

(Pxix


′i

)(5)

where Pγiγ′i




State Transition Probability cont.

Pxix′i(γi , ai )=

1 if x ′i =xi =B & aiγi = 0,

qi if x ′i =xi =B & 0 < aiγic ≤ ui ,

qi if x ′i =B & xi < B & W 1 ≥ B,

qi if x ′i <B & x ′i = W 1,

1−qi if x ′i <B & x ′i = W 2,

0 otherwise.

(6)

whereW 1 = [xi − aiγic]+ + ui

W 2 = [xi − aiγic]+


Problem Definition and Model Description Value Function

Value Function

Infinite-horizon MDP.

Total expected discounted reward optimality criterion with discountfactor λ is used, where 0 < λ < 1.

The objective is to find the policy π among all policies, that maximizethe value function V π(s).

The optimal policy is characterized by

V ∗(s) = maxa∈A

[R(s, a) + λ∑s′∈S

Pss′(a)V ∗(s′)] (7)

where, V ∗(s) = supπ V π(s), attained when applying the optimalpolicy π∗.

The model was solved numerically using Value Iteration.



Value Function





V ∗(s) = maxa∈A

[R(s, a) + λ∑s′∈S

Pss′(a)V ∗(s′)] (7)





Value Function





V ∗(s) = maxa∈A

[R(s, a) + λ∑s′∈S

Pss′(a)V ∗(s′)] (7)





Value Function





V ∗(s) = maxa∈A

[R(s, a) + λ∑s′∈S

Pss′(a)V ∗(s′)] (7)





Value Function





V ∗(s) = maxa∈A

[R(s, a) + λ∑s′∈S

Pss′(a)V ∗(s′)] (7)




Case Study and Results Case Study: Two Users with 2-State FSMC

The Optimal Policy Structure

0,0 1,0 2,0

0,1

0,2

0 1

5

10

15

20

25

x2

0 1 5 10 15 20 25 x 1

2,1 3,0

1,2

0,3

1,1

(a) Symmetrical case

0,0 1,0 2,0

0,1

0,2

0 1

5

10

15

20

25

x2

0 1 5 10 15 20 25 x 1

2,1

3,0

1,2

0,3

1,1

(b) Pγ1 =0.8, Pγ2 =0.5.

0,0 1,0 2,0

0,1

0,2

0 1

5

10

15

20

25

x2

0 1 5 10 15 20 25 x 1

2,1

3,0

1,2

0,3

1,1

(c) P(z1 = 5) = 0.8 andP(z2 =5)=0.5.

The Optimal Policy for Two Symmetrical Users, Different Channel Quality, Different Arrival Probability



Heuristic Policy

We studied the optimal policy structure by running a wide range ofscenarios, we noticed the following trends

The policy is a switch-over.

The weight (wi ) is a function of the difference of the two channelqualities and that of the arrival probabilities:

w1 = f ([−∆Pγ ]+, [−∆Pz ]+) (8)

w2 = f ([∆Pγ ]+, [∆Pz ]+) (9)

where∆Pγ =P(γ1 =1)− P(γ2 =1) and ∆Pz =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 |∆Pγ | and decreasing in |∆Pz |.



Heuristic Policy




w1 = f ([−∆Pγ ]+, [−∆Pz ]+) (8)

w2 = f ([∆Pγ ]+, [∆Pz ]+) (9)







Heuristic Policy




w1 = f ([−∆Pγ ]+, [−∆Pz ]+) (8)

w2 = f ([∆Pγ ]+, [∆Pz ]+) (9)







Heuristic Policy




w1 = f ([−∆Pγ ]+, [−∆Pz ]+) (8)

w2 = f ([∆Pγ ]+, [∆Pz ]+) (9)







Heuristic Policy




w1 = f ([−∆Pγ ]+, [−∆Pz ]+) (8)

w2 = f ([∆Pγ ]+, [∆Pz ]+) (9)






Case Study and Results Heuristic Policy Structure

Heuristic (dotted line) vs. optimal policy; c = 15

0,0

0 1 5

10

15

20

25

x2

1,0

0,1

0 1 5 10 15 20 25 x 1

(d) Symmetrical case

0,0

0 1 5

10

15

20

25

x2

1,0

0 1 5 10 15 20 25 x 1

0,1

(e) Pγ1 =0.8, Pγ2 =0.5.

0,0

0 1 5

10

15

20

25

x2

1,0

0,1

0 1 5 10 15 20 25 x 1

(f) P(z1 = 5) = 0.8 andP(z2 =5)=0.5.


Case Study and Results Heuristic Policy Structure

Heuristic (dotted line) vs. optimal policy; c = 5

0,0 1,0 2,0

0,1

0,2

0 1

5

10

15

20

25

x2

0 1 5 10 15 20 25 x 1

2,1

3,0

1,2

0,3

1,1

(g) Symmetrical case

0,0 1,0 2,0

0,1

0,2

3,01,1

2,1

1,2

0,3

0 1 5 10 15 20 25 x 10 1

5

10

15

20

25

x2

(h) Pγ1 =0.8, Pγ2 =0.5.

0,0 1,0 2,0

0,1

0,2

3,01,1

2,1

1,2

0,3

0 1 5 10 15 20 25 x 10 1

5

10

15

20

25

x2

(i) P(z1 = 5) = 0.8 andP(z2 =5)=0.5.


Case Study and Results Performance Evaluation

Performance Evaluation: The Effect of Policy Granularity

0.2 0.4 0.6 0.8 1 1.2 1.40

5

10

15

20

25

30

35

40

45

Offered Load (Rho)

Ave

rage

Que

ue L

engt

h (P

DU

s)

User1 (c=15)User2 (c=15)User1 (c=5)User2 (c=5)User1 (c=3)User2 (c=3)

(j) on Average Queue Length

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.20

0.05

0.1

0.15

0.2

0.25

Offered Load (Rho)

Ave

rage

Dro

p P

roba

bilit

y

Two actions (c=15)Four actions (c=5)Six actions (c=3)

(k) on Average Drop Probability

Where ρ =∑

i Pzi ui/rπ is the offered load and rπ is the measured systemcapacity under π. P(γ1 =1)=0.8 and P(γ2 =1)=0.5.


Case Study and Results Performance Evaluation

Heuristic Policy Evaluation

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100002

2.5

3

3.5

4

4.5

5

5.5

6

6.5

7

Time slots

Thr

ough

put (

PD

Us/

mse

c)

alpha=0.63, beta=0.12

Round Robin Heuristic MDP

Rho = 1.2

Rho = 0.8

Rho = 0.5

(l) System Throughput for different ρ;P(γ1 =1)=0.8 and P(γ2 =1)=0.5.

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

2

4

6

8

10

12

14

16

18

20

Time slots

Del

ay (

mse

c)

alpha=0.63, beta=0.12, Pz1=0.8, Pz2=0.5, u=10

Round Robin User1 User2 Heuristic User1 User2 Optimal (MDP) User1 (c=5)User2 (c=5)

(m) Queueing Delay Performance;P(γ2 = 1) = 0.5, q1 = 0.8, q2 = 0.5and u = 10.


Conclusion and Future Work Conclusion

Conclusion

The optimal policy can be described as share the codes in proportionto the weighted queue length of the connected users.

The suggested heuristic policy has a reduced constant timecomplexity (O(1)) as compared to the exponential time complexityneeded in the determination of the optimal policy.

The performance of the resulted heuristic policy matches very closelyto the optimal policy.

The results also proved that RR is undesirable in HSDPA system dueto the poor performance and lack of fairness.



Conclusion







Conclusion







Conclusion






Conclusion and Future Work Contributions

Contributions

1 A novel approach and a methodology for scheduling in HSDPAsystem were developed.

2 The HSDPA downlink scheduler was modeled by MDP, then DynamicProgramming is used to find the optimal code allocation policy ineach TTI (refer to [1] and [2]).

3 A heuristic approach was developed and used to find the near-optimalheuristic policy for the 2-user case. This work was presented in [3].

4 An optimal policy for code allocation in HSDPA system using FSMCwas investigated and the optimal policy structure and the effect ofthe increased number of channel model states on the optimal policystructure and model accuracy was studied and presented in [4].

5 An extension of the heuristic approach for any finite number of userswas derived analytically, using the information about the optimalpolicy structure and Order Theory, and presented in [5].

6 An analytic model was developed, using stochastic modeling, to findthe average service rate and server share allocation policy for a groupof users sharing the same wireless link. This model resulted in a staticserver share allocation policy and is used as a baseline for thedynamic policies. This work is presented in [7].


Conclusion and Future Work Future Work

Future Work

Prove analytically some of the optimal policy and value functioncharacteristics, such as monotonicity, multi-modularity, and theswitch-over behavior that we noticed before.

Relax the assumption of error free transmission and extend the modelto take into account retransmissions.

Study the effect of using different arrival process statistics usingsimulation obviously.



Future Work






Future Work






H. Al-Zubaidy, J. Talim and I. Lambadaris, Optimal Scheduling inHigh Speed Downlink Packet Access Networks. Technical Report no.SCE-06-16, System and Computer Engineering, Carleton University.(Available at http://www.sce.carleton.ca/ hussein/TR-optimalscheduling.pdf)

H. Al-Zubaidy, J. Talim and I. Lambadaris, Optimal Scheduling PolicyDetermination for High Speed Downlink Packet Access. The IEEEInternational Conference on Communications (ICC 2007), Glasgow,Scotland, June 2007.

H. Al-Zubaidy, J. Talim and I. Lambadaris, Heuristic Approach ofOptimal Code Allocation in High Speed Downlink Packet AccessNetworks. The Sixth International Conference on Networking (ICN2007), Martinique, April 2007.

H. Al-Zubaidy, J. Talim and I. Lambadaris, Determination of OptimalPolicy for Code Allocation in High Speed Downlink Packet Access


http://www.sce.carleton.ca/~hussein/TR-optimal scheduling.pdf

http://www.sce.carleton.ca/~hussein/TR-optimal scheduling.pdf


with Multi-State Channel Model. ACM/IEEE MSWiM 2007 Chania,Crete Island, Greece, Oct 2007.

H. Al-Zubaidy, J. Talim and I. Lambadaris, Dynamic Scheduling inHigh Speed Downlink Packet Access Networks: Heuristic Approach.MILCOM07, Orlando, USA, Oct 2007.

H. Al-Zubaidy, I. Lambadaris, J. Talim, Downlink SchedulerOptimization in High-Speed Downlink PacketAccess Networks. The26th Annual IEEE Conference on Computer CommunicationsINFOCOM 2007, May 2007, Anchorage, Alaska, USA.

H. Al-Zubaidy, I. Lambadaris and J. Talim, Service RateDetermination For Group Of Users With Random Connectivity SharingA Single Wireless Link. The Seventh IASTED InternationalConferences on Wireless and Optical Communications (WOC 2007),Canada, May 2007.

Discussion [8ex] Hussein Zubaidy [4ex] www.sce.carleton.ca/∼hussein/ ()Thank You 25 / 26


Thank You

Discussion

Hussein Zubaidy

www.sce.carleton.ca/∼hussein/


Conclusion and Future Work Acronyms

Acronyms

HSDPA–High Speed Downlink Packet Access.

3GPP–Third Generation Partnership Project

MDP–Markov Decision Process

TDMA–Time Division Multiple Access

CDMA–Code Division Multiple Access

TTI–Transmission Time Interval (2 ms)

FSMC–Finite State Markov Channel

SDU–Service Data Unit

RLC–Radio Link Control Protocol located at Radio NetworkController (RNC)

PDU–Protocol data unit

LQF–Longest Queue First
