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Downlink Scheduler Optimization in High-Speed Downlink Packet Access Networks Hussein Al-Zubaidy SCE-Carleton University 1125 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 Downlink Scheduler Optimization in High-Speed Downlink Packet Access Networks 21 August 2007 1 / 26

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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

    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 2 / 26

  • 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.

    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 3 / 26

  • 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.

    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 3 / 26

  • 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.

    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 3 / 26

  • 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.

    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 3 / 26

  • 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.

    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 4 / 26

  • 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.

    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 4 / 26

  • 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.

    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 4 / 26

  • 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.

    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 4 / 26

  • 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.

    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 5 / 26

  • 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.

    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 5 / 26

  • 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.

    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 5 / 26

  • Problem Definition and Model Description Problem Definition and Conceptualization

    HSDPA Scheduler Model (Downlink)

    User 1

    PDUs

    SDU

    User L

    Scheduler Transceiver

    UE1

    Channel State Monitor/Predictor

    UEL

    RNC

    Node-B

    RLC

    RNC

    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 6 / 26

  • Problem Definition and Model Description Problem Definition and Conceptualization

    FSMC Model for HSDPA Downlink Channel

    0 1 M-1

    P01

    P10

    P00

    P11

    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 7 / 26

  • 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.

    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 8 / 26

  • Problem Definition and Model Description Model Description and Basic Assumptions

    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} .

    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 9 / 26

  • Problem Definition and Model Description Model Description and Basic Assumptions

    Basic AssumptionsFSMC State Space

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

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

    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 10 / 26

  • 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), 1(t), 2(t), . . . , L(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,

    Li=1

    ai (s) 15

    c, and ai (s)

    xi (t)

    i (t)c

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

    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 11 / 26

  • 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), 1(t), 2(t), . . . , L(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,

    Li=1

    ai (s) 15

    c, and ai (s)

    xi (t)

    i (t)c

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

    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 11 / 26

  • 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), 1(t), 2(t), . . . , L(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,

    Li=1

    ai (s) 15

    c, and ai (s)

    xi (t)

    i (t)c

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

    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 11 / 26

  • 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), 1(t), 2(t), . . . , L(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,

    Li=1

    ai (s) 15

    c, and ai (s)

    xi (t)

    i (t)c

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

    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 11 / 26

  • 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), 1(t), 2(t), . . . , L(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,

    Li=1

    ai (s) 15

    c, and ai (s)

    xi (t)

    i (t)c

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

    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 11 / 26

  • 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

    aiic L

    i=1

    (xi x) 1{xi=B} (3)

    where we defined the fairness factor () 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.

    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 12 / 26

  • 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,. . ., xL,

    1,. . .,

    L|x1,. . ., xL,1,. . .,L,a1,. . .,aL)

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

    x i = min([xi yi ]+ + z i ,B

    )= min

    ([xi aiic]+ + z i ,B

    )(4)

    Using the independence of the channel state and queue sizes

    Pss(a) =L

    i =1

    (Pxix i (i , ai ) Pi

    i

    )(5)

    where Pii is the Markov transition probability of the FSMC.

    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 13 / 26

  • 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,. . ., xL,

    1,. . .,

    L|x1,. . ., xL,1,. . .,L,a1,. . .,aL)

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

    x i = min([xi yi ]+ + z i ,B

    )= min

    ([xi aiic]+ + z i ,B

    )(4)

    Using the independence of the channel state and queue sizes

    Pss(a) =L

    i =1

    (Pxix i (i , ai ) Pi

    i

    )(5)

    where Pii is the Markov transition probability of the FSMC.

    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 13 / 26

  • 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,. . ., xL,

    1,. . .,

    L|x1,. . ., xL,1,. . .,L,a1,. . .,aL)

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

    x i = min([xi yi ]+ + z i ,B

    )= min

    ([xi aiic]+ + z i ,B

    )(4)

    Using the independence of the channel state and queue sizes

    Pss(a) =L

    i =1

    (Pxix i (i , ai ) Pi

    i

    )(5)

    where Pii is the Markov transition probability of the FSMC.

    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 13 / 26

  • Problem Definition and Model Description State Transition Probability

    State Transition Probability cont.

    Pxix i (i , ai )=

    1 if x i =xi =B & aii = 0,

    qi if xi =xi =B & 0 < aiic ui ,

    qi if xi =B & xi < B & W 1 B,

    qi if xi

  • Problem Definition and Model Description Value Function

    Value Function

    Infinite-horizon MDP.

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

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

    The optimal policy is characterized by

    V (s) = maxaA

    [R(s, a) + sS

    Pss(a)V(s)] (7)

    where, V (s) = sup V(s), attained when applying the optimal

    policy .

    The model was solved numerically using Value Iteration.

    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 15 / 26

  • Problem Definition and Model Description Value Function

    Value Function

    Infinite-horizon MDP.

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

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

    The optimal policy is characterized by

    V (s) = maxaA

    [R(s, a) + sS

    Pss(a)V(s)] (7)

    where, V (s) = sup V(s), attained when applying the optimal

    policy .

    The model was solved numerically using Value Iteration.

    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 15 / 26

  • Problem Definition and Model Description Value Function

    Value Function

    Infinite-horizon MDP.

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

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

    The optimal policy is characterized by

    V (s) = maxaA

    [R(s, a) + sS

    Pss(a)V(s)] (7)

    where, V (s) = sup V(s), attained when applying the optimal

    policy .

    The model was solved numerically using Value Iteration.

    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 15 / 26

  • Problem Definition and Model Description Value Function

    Value Function

    Infinite-horizon MDP.

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

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

    The optimal policy is characterized by

    V (s) = maxaA

    [R(s, a) + sS

    Pss(a)V(s)] (7)

    where, V (s) = sup V(s), attained when applying the optimal

    policy .

    The model was solved numerically using Value Iteration.

    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 15 / 26

  • Problem Definition and Model Description Value Function

    Value Function

    Infinite-horizon MDP.

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

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

    The optimal policy is characterized by

    V (s) = maxaA

    [R(s, a) + sS

    Pss(a)V(s)] (7)

    where, V (s) = sup V(s), attained when applying the optimal

    policy .

    The model was solved numerically using Value Iteration.

    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 15 / 26

  • 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) P1 =0.8, P2 =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

    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 16 / 26

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

    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 ([P ]+, [Pz ]+) (8)w2 = f ([P ]

    +, [Pz ]+) (9)

    whereP =P(1 =1) P(2 =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 |P | and decreasing in |Pz |.

    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 17 / 26

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

    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 ([P ]+, [Pz ]+) (8)w2 = f ([P ]

    +, [Pz ]+) (9)

    whereP =P(1 =1) P(2 =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 |P | and decreasing in |Pz |.

    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 17 / 26

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

    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 ([P ]+, [Pz ]+) (8)w2 = f ([P ]

    +, [Pz ]+) (9)

    whereP =P(1 =1) P(2 =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 |P | and decreasing in |Pz |.

    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 17 / 26

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

    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 ([P ]+, [Pz ]+) (8)w2 = f ([P ]

    +, [Pz ]+) (9)

    whereP =P(1 =1) P(2 =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 |P | and decreasing in |Pz |.

    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 17 / 26

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

    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 ([P ]+, [Pz ]+) (8)w2 = f ([P ]

    +, [Pz ]+) (9)

    whereP =P(1 =1) P(2 =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 |P | and decreasing in |Pz |.

    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 17 / 26

  • Case Study and Results Heuristic Policy Structure

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

    0,0

    015

    10

    15

    20

    25

    x2

    1,0

    0,1

    01 5 10 15 20 25 x1

    (d) Symmetrical case

    0,0

    015

    10

    15

    20

    25

    x2

    1,0

    01 5 10 15 20 25 x1

    0,1

    (e) P1 =0.8, P2 =0.5.

    0,0

    015

    10

    15

    20

    25

    x2

    1,0

    0,1

    01 5 10 15 20 25 x1

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

    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 18 / 26

  • 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

    01

    5

    10

    15

    20

    25

    x2

    01 5 10 15 20 25 x1

    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

    01 5 10 15 20 25 x101

    5

    10

    15

    20

    25

    x2

    (h) P1 =0.8, P2 =0.5.

    0,0 1,0 2,0

    0,1

    0,2

    3,01,1

    2,1

    1,2

    0,3

    01 5 10 15 20 25 x101

    5

    10

    15

    20

    25

    x2

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

    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 19 / 26

  • 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 =

    i Pzi ui/r is the offered load and r is the measured system

    capacity under . P(1 =1)=0.8 and P(2 =1)=0.5.

    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 20 / 26

  • 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 ;P(1 =1)=0.8 and P(2 =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(2 = 1) = 0.5, q1 = 0.8, q2 = 0.5and u = 10.

    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 21 / 26

  • 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.

    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 22 / 26

  • 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.

    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 22 / 26

  • 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.

    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 22 / 26

  • 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.

    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 22 / 26

  • 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].

    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 23 / 26

  • 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.

    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 24 / 26

  • 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.

    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 24 / 26

  • 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.

    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 24 / 26

  • Conclusion and 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

    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 24 / 26

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

  • Conclusion and Future Work Future Work

    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

  • Conclusion and Future Work Future Work

    Thank You

    Discussion

    Hussein Zubaidy

    www.sce.carleton.ca/hussein/

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

  • Conclusion and Future Work Acronyms

    Acronyms

    HSDPAHigh Speed Downlink Packet Access.

    3GPPThird Generation Partnership Project

    MDPMarkov Decision Process

    TDMATime Division Multiple Access

    CDMACode Division Multiple Access

    TTITransmission Time Interval (2 ms)

    FSMCFinite State Markov Channel

    SDUService Data Unit

    RLCRadio Link Control Protocol located at Radio NetworkController (RNC)

    PDUProtocol data unit

    LQFLongest Queue First

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