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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-Speed Downlink Packet Access NetworksHussein Al-Zubaidy
Email: [email protected]
Outline
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 HSDPA networks, 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 HSDPA networks, 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 HSDPA networks, 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 HSDPA networks, 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. A declarative approach is used,
Develop an analytic model for the HSDPA downlink scheduler.
A MDP based discrete stochastic dynamic programming model is used to model the system. This Model is a simplifying abstraction of the real scheduler which estimates system behavior under different conditions and describes the role 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. A declarative approach is used,
Develop an analytic model for the HSDPA downlink scheduler.
A MDP based discrete stochastic dynamic programming model is used to model the system. This Model is a simplifying abstraction of the real scheduler which estimates system behavior under different conditions and describes the role 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. A declarative approach is used,
Develop an analytic model for the HSDPA downlink scheduler.
A MDP based discrete stochastic dynamic programming model is used to model the system. This Model is a simplifying abstraction of the real scheduler which estimates system behavior under different conditions and describes the role 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. A declarative approach is used,
Develop an analytic model for the HSDPA downlink scheduler.
A MDP based discrete stochastic dynamic programming model is used to model the system. This Model is a simplifying abstraction of the real scheduler which estimates system behavior under different conditions and describes the role 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 allocated to 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 allocated to 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 allocated to 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)
Problem Definition and Model Description Problem Definition and Conceptualization
FSMC Model for HSDPA Downlink Channel
0 1 M-1
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 transition probability, and R(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 ) 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} .
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 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.
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), γ1(t), γ2(t), . . . , γL(t)) (1)
S = {X ×M}L is finite, due to the assumption of finite buffers size and channel states.
The action a(s) ∈ A is taken when in state s
a(s) = (a1(s), a2(s), . . . , aL(s)) (2)
subject to,
⌈ xi (t)
γi (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), γ1(t), γ2(t), . . . , γL(t)) (1)
S = {X ×M}L is finite, due to the assumption of finite buffers size and channel states.
The action a(s) ∈ A is taken when in state s
a(s) = (a1(s), a2(s), . . . , aL(s)) (2)
subject to,
⌈ xi (t)
γi (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), γ1(t), γ2(t), . . . , γL(t)) (1)
S = {X ×M}L is finite, due to the assumption of finite buffers size and channel states.
The action a(s) ∈ A is taken when in state s
a(s) = (a1(s), a2(s), . . . , aL(s)) (2)
subject to,
⌈ xi (t)
γi (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), γ1(t), γ2(t), . . . , γL(t)) (1)
S = {X ×M}L is finite, due to the assumption of finite buffers size and channel states.
The action a(s) ∈ A is taken when in state s
a(s) = (a1(s), a2(s), . . . , aL(s)) (2)
subject to,

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), γ1(t), γ2(t), . . . , γL(t)) (1)
S = {X ×M}L is finite, due to the assumption of finite buffers size and channel states.
The action a(s) ∈ A is taken when in state s
a(s) = (a1(s), a2(s), . . . , aL(s)) (2)
subject to,
⌈ xi (t)
γi (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
R(s, a) have two components corresponding to the two objectives
R(s, a) = L∑
(xi − x) 1{xi=B} (3)
where we defined the fairness factor (σ) to reflect the significance of fairness in the optimal policy.
The positive term of the reward maximizes the cell throughput.
The second term guarantees some level of fairness and reduces dropping 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 t when 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
The evolution of the queue size (xi ) is given by
x ′i = min ( [xi − yi ]
+ + z ′i ,B )
) (4)
Using the independence of the channel state and queue sizes
Pss′(a) = L∏
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 t when 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
The evolution of the queue size (xi ) is given by
x ′i = min ( [xi − yi ]
+ + z ′i ,B )
) (4)
Using the independence of the channel state and queue sizes
Pss′(a) = L∏
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 t when 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
The evolution of the queue size (xi ) is given by
x ′i = min ( [xi − yi ]
+ + z ′i ,B )
) (4)
Using the independence of the channel state and queue sizes
Pss′(a) = L∏
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 (γi , ai )=
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.
W 2 = [xi − aiγic]+
Problem Definition and Model Description Value Function
Value Function
Infinite-horizon MDP.
Total expected discounted reward optimality criterion with discount factor λ is used, where 0 < λ < 1.
The objective is to find the policy π among all policies, that maximize the value function V π(s).
The optimal policy is characterized by
V ∗(s) = max a∈A
[R(s, a) + λ ∑ s′∈S
Pss′(a)V ∗(s′)] (7)
where, V ∗(s) = supπ V π(s), attained when applying the optimal policy π∗.
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 discount factor λ is used, where 0 < λ < 1.
The objective is to find the policy π among all policies, that maximize the value function V π(s).
The optimal policy is characterized by
V ∗(s) = max a∈A
[R(s, a) + λ ∑ s′∈S
Pss′(a)V ∗(s′)] (7)
where, V ∗(s) = supπ V π(s), attained when applying the optimal policy π∗.
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 discount factor λ is used, where 0 < λ < 1.
The objective is to find the policy π among all policies, that maximize the value function V π(s).
The optimal policy is characterized by
V ∗(s) = max a∈A
[R(s, a) + λ ∑ s′∈S
Pss′(a)V ∗(s′)] (7)
where, V ∗(s) = supπ V π(s), attained when applying the optimal policy π∗.
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 discount factor λ is used, where 0 < λ < 1.
The objective is to find the policy π among all policies, that maximize the value function V π(s).
The optimal policy is characterized by
V ∗(s) = max a∈A
[R(s, a) + λ ∑ s′∈S
Pss′(a)V ∗(s′)] (7)
where, V ∗(s) = supπ V π(s), attained when applying the optimal policy π∗.
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 discount factor λ is used, where 0 < λ < 1.
The objective is to find the policy π among all policies, that maximize the value function V π(s).
The optimal policy is characterized by
V ∗(s) = max a∈A
[R(s, a) + λ ∑ s′∈S
Pss′(a)V ∗(s′)] (7)
where, V ∗(s) = supπ V π(s), attained when applying the optimal policy π∗.
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
2,1 3,0
2,1
3,0
1,2
0,3
1,1
0,0 1,0 2,0
2,1
3,0
1,2
0,3
1,1
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 of scenarios, we noticed the following trends
The policy is a switch-over.
The weight (wi ) is a function of the difference of the two channel qualities 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 |.
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 of scenarios, we noticed the following trends
The policy is a switch-over.
The weight (wi ) is a function of the difference of the two channel qualities 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 |.
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 of scenarios, we noticed the following trends
The policy is a switch-over.
The weight (wi ) is a function of the difference of the two channel qualities 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 |.
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 of scenarios, we noticed the following trends
The policy is a switch-over.
The weight (wi ) is a function of the difference of the two channel qualities 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 |.
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 of scenarios, we noticed the following trends
The policy is a switch-over.
The weight (wi ) is a function of the difference of the two channel qualities 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 |.
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                                                   
(d) Symmetrical case
0,1
     0,0                                                   
(f) P(z1 = 5) = 0.8 and P(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    
     
2,1
3,0
1,2
0,3 
1,1 
2,1
1,2
0,3
 
   
     
2,1
1,2
0,3 
 
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 1.4 0
5
10
15
20
25
30
35
40
45
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 1.2 0
0.05
0.1
0.15
0.2
0.25
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 system capacity under π. P(γ1 =1)=0.8 and P(γ2 =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 10000 2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
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 10000 0
2
4
6
8
10
12
14
16
18
20
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 = 0.5 and 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 proportion to the weighted queue length of the connected users.
The suggested heuristic policy has a reduced constant time complexity (O(1)) as compared to the exponential time complexity needed in the determination of the optimal policy.
The performance of the resulted heuristic policy matches very closely to the optimal policy.
The results also proved that RR is undesirable in HSDPA system due to 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 proportion to the weighted queue length of the connected users.
The suggested heuristic policy has a reduced constant time complexity (O(1)) as compared to the exponential time complexity needed in the determination of the optimal policy.
The performance of the resulted heuristic policy matches very closely to the optimal policy.
The results also proved that RR is undesirable in HSDPA system due to 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 proportion to the weighted queue length of the connected users.
The suggested heuristic policy has a reduced constant time complexity (O(1)) as compared to the exponential time complexity needed in the determination of the optimal policy.
The performance of the resulted heuristic policy matches very closely to the optimal policy.
The results also proved that RR is undesirable in HSDPA system due to 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 proportion to the weighted queue length of the connected users.
The suggested heuristic policy has a reduced constant time complexity (O(1)) as compared to the exponential time complexity needed in the determination of the optimal policy.
The performance of the resulted heuristic policy matches very closely to the optimal policy.
The results also proved that RR is undesirable in HSDPA system due to 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 HSDPA system were developed.
2 The HSDPA downlink scheduler was modeled by MDP, then Dynamic Programming is used to find the optimal code allocation policy in each TTI (refer to [1] and [2]).
3 A heuristic approach was developed and used to find the near-optimal heuristic policy for the 2-user case. This work was presented in [3].
4 An optimal policy for code allocation in HSDPA system using FSMC was investigated and the optimal policy structure and the effect of the increased number of channel model states on the optimal policy structure and model accuracy was studied and presented in [4].
5 An extension of the heuristic approach for any finite number of users was derived analytically, using the information about the optimal policy structure and Order Theory, and presented in [5].
6 An analytic model was developed, using stochastic modeling, to find the average service rate and server share allocation policy for a group of users sharing the same wireless link. This model resulted in a static server share allocation policy and is used as a baseline for the dynamic 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 function characteristics, such as monotonicity, multi-modularity, and the switch-over behavior that we noticed before.
Relax the assumption of error free transmission and extend the model to take into account retransmissions.
Study the effect of using different arrival process statistics using simulation 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 function characteristics, such as monotonicity, multi-modularity, and the switch-over behavior that we noticed before.
Relax the assumption of error free transmission and extend the model to take into account retransmissions.
Study the effect of using different arrival process statistics using simulation 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 function characteristics, such as monotonicity, multi-modularity, and the switch-over behavior that we noticed before.
Relax the assumption of error free transmission and extend the model to take into account retransmissions.
Study the effect of using different arrival process statistics using simulation 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 in High 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-optimal scheduling.pdf)
H. Al-Zubaidy, J. Talim and I. Lambadaris, Optimal Scheduling Policy Determination for High Speed Downlink Packet Access. The IEEE International Conference on Communications (ICC 2007), Glasgow, Scotland, June 2007.
H. Al-Zubaidy, J. Talim and I. Lambadaris, Heuristic Approach of Optimal Code Allocation in High Speed Downlink Packet Access Networks. The Sixth International Conference on Networking (ICN 2007), Martinique, April 2007.
H. Al-Zubaidy, J. Talim and I. Lambadaris, Determination of Optimal Policy 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
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 in High Speed Downlink Packet Access Networks: Heuristic Approach. MILCOM07, Orlando, USA, Oct 2007.
H. Al-Zubaidy, I. Lambadaris, J. Talim, Downlink Scheduler Optimization in High-Speed Downlink PacketAccess Networks. The 26th Annual IEEE Conference on Computer Communications INFOCOM 2007, May 2007, Anchorage, Alaska, USA.
H. Al-Zubaidy, I. Lambadaris and J. Talim, Service Rate Determination For Group Of Users With Random Connectivity Sharing A Single Wireless Link. The Seventh IASTED International Conferences 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 [8ex] Hussein Zubaidy [4ex] www.sce.carleton.ca/∼hussein/ ()Thank You 25 / 26
Conclusion and Future Work Acronyms
Acronyms
3GPP–Third Generation Partnership Project
MDP–Markov Decision Process
TTI–Transmission Time Interval (2 ms)
FSMC–Finite State Markov Channel
SDU–Service Data Unit
RLC–Radio Link Control Protocol located at Radio Network Controller (RNC)
PDU–Protocol data unit
LQF–Longest Queue First