Downlink Scheduler Optimization in High-Speed Downlink Packet Access Networks

Transcription

1 Downlink Scheduler Optimization in High-Speed Downlink Packet Access Networks Hussein Al-Zubaidy SCE-Carleton University 1125 Colonel By Drive, Ottawa, ON, Canada 21 August 2007 ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink Packet 21 August Access 2007 Networks () 1 / 26

2 Outline 1 Objective 2 Methodology 3 Problem Definition and Model Description 4 Case Study and Results 5 Conclusion and Future Work ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 2 / 26

3 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: ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 3 / 26

4 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 3 / 26

5 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 3 / 26

6 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 3 / 26

7 Methodology Methodology This work presents a different approach for scheduling in HSDPA. A declarative approach is used, Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 4 / 26

8 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. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 4 / 26

9 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 4 / 26

10 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 4 / 26

11 Problem Definition and Model Description Problem Definition and Conceptualization Problem Definition and Conceptualization The HSDPA downlink channel uses a mix of TDMA and CDMA: Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 5 / 26

12 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 5 / 26

13 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 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 5 / 26

14 Problem Definition and Model Description HSDPA Scheduler Model (Downlink) Problem Definition and Conceptualization PDUs User 1 UE 1 SDU Scheduler Transceiver RLC RNC RNC User L Channel State Monitor/Predictor Node-B UE L ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 6 / 26

15 Problem Definition and Model Description Problem Definition and Conceptualization FSMC Model for HSDPA Downlink Channel P 00 P 01 P M-1 P 10 ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 7 / 26

16 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, P ss (a), R(s, a)), where, T is the set of decision epochs, S and A are the state and action spaces, P ss (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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 8 / 26

17 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 (u i ) and delivered to Node-B at the beginning of the next TTI. Independent Bernoulli arrivals with parameter q i. Scheduler can assign c codes chunks at a time, where c {1, 3, 5, 15}. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks () 9 / 26

18 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 γ i (t). Channel state space is the set M = {0, 1,..., M 1}. user i channel can handle up to γ i (t) PDUs per code. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 10 () / 26

19 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) = (x 1 (t), x 2 (t),..., x L (t), γ 1 (t), γ 2 (t),..., γ L (t)) (1) ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 11 () / 26

20 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) = (x 1 (t), x 2 (t),..., x L (t), γ 1 (t), γ 2 (t),..., γ L (t)) (1) S = {X M} L is finite, due to the assumption of finite buffers size and channel states. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 11 () / 26

21 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) = (x 1 (t), x 2 (t),..., x L (t), γ 1 (t), γ 2 (t),..., γ L (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) = (a 1 (s), a 2 (s),..., a L (s)) (2) Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 11 () / 26

22 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) = (x 1 (t), x 2 (t),..., x L (t), γ 1 (t), γ 2 (t),..., γ L (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) = (a 1 (s), a 2 (s),..., a L (s)) (2) subject to, L i=1 a i (s) 15 c, and a xi (t) i(s) γ i (t)c Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 11 () / 26

23 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) = (x 1 (t), x 2 (t),..., x L (t), γ 1 (t), γ 2 (t),..., γ L (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) = (a 1 (s), a 2 (s),..., a L (s)) (2) subject to, L i=1 a i (s) 15 c, and a xi (t) i(s) γ i (t)c a i (t)c, number of codes allocated to user i at time epoch t. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 11 () / 26

24 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 L a i γ i c σ (x i x) 1 {xi =B} (3) i=1 i=1 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 12 () / 26

25 Problem Definition and Model Description State Transition Probability State Transition Probability P ss (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. P ss (a) = Pr(s(t + 1)=s s(t)=s, a(t)=a) = Pr(x 1,..., x L,γ 1,...,γ L x 1,..., x L,γ 1,...,γ L,a 1,...,a L ) Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 13 () / 26

26 Problem Definition and Model Description State Transition Probability State Transition Probability P ss (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. P ss (a) = Pr(s(t + 1)=s s(t)=s, a(t)=a) = Pr(x 1,..., x L,γ 1,...,γ L x 1,..., x L,γ 1,...,γ L,a 1,...,a L ) The evolution of the queue size (x i ) is given by x i = min ( [x i y i ] + + z i, B ) = min ( [x i a i γ i c] + + z i, B ) (4) Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 13 () / 26

27 Problem Definition and Model Description State Transition Probability State Transition Probability P ss (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. P ss (a) = Pr(s(t + 1)=s s(t)=s, a(t)=a) = Pr(x 1,..., x L,γ 1,...,γ L x 1,..., x L,γ 1,...,γ L,a 1,...,a L ) The evolution of the queue size (x i ) is given by x i = min ( [x i y i ] + + z i, B ) = min ( [x i a i γ i c] + + z i, B ) (4) Using the independence of the channel state and queue sizes L ( ) P ss (a) = P xi x i (γ i, a i ) P γi γ i where P γi γ i i =1 is the Markov transition probability of the FSMC. (5) ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 13 () / 26

28 Problem Definition and Model Description State Transition Probability cont. State Transition Probability where 1 if x i =x i =B & a i γ i = 0, q i if x i =x i =B & 0 < a i γ i c u i, P xi x i (γ q i if x i =B & x i < B & W 1 B, i, a i )= q i if x i <B & x i = W 1, 1 q i if x i <B & x i = W 2, 0 otherwise. W 1 = [x i a i γ i c] + + u i W 2 = [x i a i γ i c] + (6) ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 14 () / 26

29 Value Function Problem Definition and Model Description Value Function Infinite-horizon MDP. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink Packet 21 August Access 2007 Networks 15 () / 26

30 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. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 15 () / 26

31 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). Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 15 () / 26

32 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 [R(s, a) + λ P ss (a)v (s )] (7) a A s S where, V (s) = sup π V π (s), attained when applying the optimal policy π. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 15 () / 26

33 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 [R(s, a) + λ P ss (a)v (s )] (7) a A s S where, V (s) = sup π V π (s), attained when applying the optimal policy π. The model was solved numerically using Value Iteration. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 15 () / 26

34 Case Study and Results The Optimal Policy Structure Case Study: Two Users with 2-State FSMC x 1 0 0,0 1,0 2, x 1 0 0,0 1,0 2,0 3,0 1 0,1 5 1,1 2,1 3,0 0,1 5 1,1 2,1 0,2 0,2 10 1,2 10 1, ,3 20 0, x2 25 x2 (a) Symmetrical case (b) P γ1 =0.8, P γ2 = x 1 0 0,0 1,0 2,0 1 0,1 5 1,1 2,1 0,2 3,0 10 1, ,3 25 x2 (c) P(z 1 = 5) = 0.8 and P(z 2 =5)=0.5. The Optimal Policy for Two Symmetrical Users, Different Channel Quality, Different Arrival Probability ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 16 () / 26

35 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. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 17 () / 26

36 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 (w i ) is a function of the difference of the two channel qualities and that of the arrival probabilities: w 1 = f ([ P γ ] +, [ P z ] + ) (8) w 2 = f ([ P γ ] +, [ P z ] + ) (9) where P γ =P(γ 1 =1) P(γ 2 =1) and P z =P(z 1 =u) P(z 2 =u). Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 17 () / 26

37 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 (w i ) is a function of the difference of the two channel qualities and that of the arrival probabilities: w 1 = f ([ P γ ] +, [ P z ] + ) (8) w 2 = f ([ P γ ] +, [ P z ] + ) (9) where P γ =P(γ 1 =1) P(γ 2 =1) and P z =P(z 1 =u) P(z 2 =u). The intermediate regions has almost a constant width that equals 2c. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 17 () / 26

38 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 (w i ) is a function of the difference of the two channel qualities and that of the arrival probabilities: w 1 = f ([ P γ ] +, [ P z ] + ) (8) w 2 = f ([ P γ ] +, [ P z ] + ) (9) where P γ =P(γ 1 =1) P(γ 2 =1) and P z =P(z 1 =u) P(z 2 =u). The intermediate regions has almost a constant width that equals 2c. a 1 (respectively a 2 ) is increasing in x 1 (respectively x 2 ). ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 17 () / 26

39 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 (w i ) is a function of the difference of the two channel qualities and that of the arrival probabilities: w 1 = f ([ P γ ] +, [ P z ] + ) (8) w 2 = f ([ P γ ] +, [ P z ] + ) (9) where P γ =P(γ 1 =1) P(γ 2 =1) and P z =P(z 1 =u) P(z 2 =u). The intermediate regions has almost a constant width that equals 2c. a 1 (respectively a 2 ) is increasing in x 1 (respectively x 2 ). f () is increasing in P γ and decreasing in P z. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 17 () / 26

40 Case Study and Results Heuristic Policy Structure Heuristic (dotted line) vs. optimal policy; c = x 1 0 0, x 1 0 0,0 1 1,0 5 1, ,1 20 0, x2 25 x2 (d) Symmetrical case (e) P γ1 =0.8, P γ2 = x ,0 1, , x2 (f) P(z 1 = 5) = 0.8 and P(z 2 =5)=0.5. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 18 () / 26

41 Case Study and Results Heuristic Policy Structure Heuristic (dotted line) vs. optimal policy; c = x 1 0 0,0 1,0 2,0 1 0,1 1,1 3, x 1 0 0,0 1,0 2,0 1 3,0 0,1 1,1 5 0,2 0,2 2,1 10 2, ,2 15 1,2 20 0,3 20 0, x2 x2 (g) Symmetrical case (h) P γ1 =0.8, P γ2 = x 1 0 0,0 1,0 2,0 1 0,1 1,1 5 0,2 2,1 3,0 10 1, ,3 25 x2 (i) P(z 1 = 5) = 0.8 and P(z 2 =5)=0.5. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 19 () / 26

42 Case Study and Results Performance Evaluation Performance Evaluation: The Effect of Policy Granularity Two actions (c=15) Four actions (c=5) Six actions (c=3) Average Queue Length (PDUs) User1 (c=15) User2 (c=15) User1 (c=5) User2 (c=5) User1 (c=3) User2 (c=3) Average Drop Probability Offered Load (Rho) (j) on Average Queue Length Offered Load (Rho) (k) on Average Drop Probability Where ρ = i P z i u i /r π is the offered load and r π is the measured system capacity under π. P(γ 1 =1)=0.8 and P(γ 2 =1)=0.5. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 20 () / 26

43 Case Study and Results Heuristic Policy Evaluation Performance Evaluation Throughput (PDUs/msec) alpha=0.63, beta=0.12 Rho = 1.2 Rho = 0.8 Rho = 0.5 Round Robin Heuristic MDP Time slots (l) System Throughput for different ρ; P(γ 1 =1)=0.8 and P(γ 2 =1)=0.5. Delay (msec) alpha=0.63, beta=0.12, Pz1=0.8, Pz2=0.5, u=10 Round Robin User1 User2 Heuristic User1 User2 2 Optimal (MDP) User1 (c=5) User2 (c=5) Time slots (m) Queueing Delay Performance; P(γ 2 = 1) = 0.5, q 1 = 0.8, q 2 = 0.5 and u = 10. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 21 () / 26

44 Conclusion Conclusion and Future Work Conclusion The optimal policy can be described as share the codes in proportion to the weighted queue length of the connected users. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink Packet 21 August Access 2007 Networks 22 () / 26

45 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. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 22 () / 26

46 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. Hussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 22 () / 26

47 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink hussein@sce.carleton.ca Packet 21 August Access 2007 Networks 22 () / 26

48 Contributions Conclusion and Future Work 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 thedownlink samescheduler wireless Optimization link. in This High-Speed model Downlink resulted Packet Access in Networks a static ussein Al-Zubaidy[8ex] SCE-Carleton University1125 Colonel By Drive, Ottawa, ON, Canada hussein@sce.carleton.ca 21 August () / 26

49 Future Work Conclusion and 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink Packet 21 August Access 2007 Networks 24 () / 26

50 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink Packet 21 August Access 2007 Networks 24 () / 26

51 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. ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink Packet 21 August Access 2007 Networks 24 () / 26

52 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 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 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 H. Al-Zubaidy, J. Talim and I. Lambadaris, Determination of Optimal Policy for Code Allocation in High Speed Downlink Packet Access ussein Al-Zubaidy[8ex] SCE-Carleton University1125 DownlinkColonel Scheduler By Optimization Drive, Ottawa, inon, High-Speed Canada Downlink Packet 21 August Access 2007 Networks 24 () / 26

53 Conclusion and Future Work with Multi-State Channel Model. Crete Island, Greece, Oct Future Work ACM/IEEE MSWiM 2007 Chania, H. Al-Zubaidy, J. Talim and I. Lambadaris, Dynamic Scheduling in High Speed Downlink Packet Access Networks: Heuristic Approach. MILCOM07, Orlando, USA, Oct H. Al-Zubaidy, I. Lambadaris, J. Talim, Downlink Scheduler Optimization in High-Speed Downlink PacketAccess Networks. 26th Annual IEEE Conference on Computer Communications INFOCOM 2007, May 2007, Anchorage, Alaska, USA. The 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 iscussion [8ex] Hussein Zubaidy [4ex] hussein/ Thank You () 25 / 26

54 Conclusion and Future Work Future Work Thank You Discussion Hussein Zubaidy hussein/ iscussion [8ex] Hussein Zubaidy [4ex] hussein/ Thank You () 25 / 26

55 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 Network Controller (RNC) PDU Protocol data unit LQF Longest Queue First iscussion [8ex] Hussein Zubaidy [4ex] hussein/ Thank You () 26 / 26