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Transcript of Distributed Rate Assignments for Broadband CDMA Networks Tara Javidi Electrical & Computer...
Distributed Rate Assignments for Broadband CDMA Networks
Tara JavidiElectrical & Computer Engineering
University of California, San Diego
Multi-Cell Single Hop CDMAMotivation
• Wideband CDMA network with variable rates
• Mobiles communicate directly with the base station
• Base stations are connected directly to the traditional IP network
Rate Assignment Problem
• Limited by congestion constraints in the wired network
• Limited by interference constraints in the wireless network
• Objective: Maximize the global network utility in a distributed adaptive manner
Philosophically Related WorksWired Networks
[1] F. Kelly. Mathematical Modeling of the Internet. B. Enquist and W. Schmid, editors. Mathematics Unlimited – 2001 and Beyond, pages 685-702. Springer-Verlaq, 2001.[2] J. Mo and J. Walrand. Fair End-to-End Window-Based Congestion Control. IEEE/ACM Transactions on Networking, 8(5):555-567, 2000.[3]S.H. Low and D.E. Lapsley. Optimization Flow Control I: Basic Algorithm and Convergence. IEEE/ACM Transactions on Networking, 7(6):861-874, 1999.
Wireless Networks
[3] T. Javidi Distributed Rate Assignment in Multi-sector CDMA. Global Telecommunications Conference, 2003.[4] M. Chiang and R. Man. Jointly Optimal Congestion Control and Power Control in Wireless Multihop Networks. Global Telecommunications Conference, 2003.[5] X. Lin and N.B. Shroff. The Impact of Imperfect Scheduling on Cross-Layer Rate Control in Wireless Networks. INFOCOM 2005.
Cross-Layer Design: One-Shot
• One-shot and joint design of a rate assignment protocol (merging MAC and transport layers)
• Wireless and wired networks generate feedback based on their respective system constraints
• This feedback allows for dynamic adaptation to slowly varying network conditions
Iterative Methods and Convergence
If the Lagrange multipliers are computed using a gradient projection method, the rate assignment
becomes an iterative algorithm that uses feedback from the network
Theorem: Given an appropriate choice of step-size, the distributed system will converge to the
solution to the primal problem (cross-layer optimal)
Related Work
[1] X. Lin and N.B. Shroff. Joint rate control and scheduling in multi-hop wireless networks. CDC’04
[2] M. Neely, E. Modiano, and C. Li. Fairness and Optimal Stochastic Control for Heterogeneous Networks. Infocom’05
+ Due to structure of the problem, we get truly distributed solutions (little overhead comm)
- Such solutions require a fundamental re-doing of the protocol stack in general and transport layer in particular
Cross-Layer Design: Modular
• MAC and transport layer protocols are separate • MAC chooses rate using feedback from wireless• The transport layer chooses rate based on end-end
feedback following a dual controller• Can this be optimal in a cross-layer sense?
• If no wired core, the answer is yes:[1] A. Eryilmaz and R. Srikant. Fair Resource Allocation in Wireless Using
Queue-based Scheduling and Congestion Control
Outline
• Motivation and Overview• One-Shot Rate Assignments• Modular Rate Assignments
• The Problem with Dual Methods• Practical Implementation & Cross-Layer
Coordination
• Observations, Conclusions, & Future Work
Notation
• CDMA uplink•dynamic power and spreading gain control
(distributed)
• Network Parameters•M: number of nodes: N of them wireless •L: number of sectors J: number of (wired) links • Cj: capacity of link j ψij: routing function
•W: chip bandwidth gil: channel power gain• K: acceptable interference b(i): mobile i’s sector
• Node Variables•Pi: transmit power for user i•αi: transmit rate for user i at MAC•xi: transmit rate for user i at transport
One-Shot Problem Formulation
subject to
Wired LinkCapacity
ROT-ControlledFeasible Rate Vector
Bench Mark: “cross-layer optimal”
Iterative Methods and Convergence
If the Lagrange multipliers are computed using a gradient projection method, the rate assignment
becomes an iterative algorithm that uses feedback from the network
Theorem: Given an appropriate choice of step-size, the distributed system will converge to the
solution to the primal problem (cross-layer optimal)
subject to
Modular Problem Formulation
Coordinate MAC and Transport Layers xi=αi
αi
αi
Dual Controller Fails
Question: What happens when we try to use the dual controller/gradient projection?
Answer: The dual controller fails to converge to solution of the optimization problem
We need to maximize a function that is strictly concave over all the primal variables
Modular Utility Functions
if i is a wired user
if i is a wireless user
A New Modular Problem Formulation
subject to
Economic Interpretation of the Dual
Price forLink j
Price forSector l
Individual ProfitMaximization
(Transport Layer)
Cross-LayerCoordination Signal
Iterative Methods and Convergence
If the Lagrange multipliers are computed using a gradient projection method, the rate assignment
becomes an iterative algorithm that uses feedback from the network
Theorem: Given an appropriate choice of step-size, the distributed system will converge to the
solution to the primal problem (cross-layer optimal)
Wired Network Prices• Individual Lagrange multipliers are generated
using gradient projection
• This has a well known physical interpretation: queuing delay!
• Aggregate price qi can be interpreted as end-to-end queuing delay, which can be measured by each user
if
if
Wireless Network Prices
• Individual Lagrange multipliers are generated using
gradient projection
• We can construct a signaling mechanism under which the
aggregate price pi becomes closely related to forward link
SINR on the pilot signal
• Again, individual Lagrange multipliers are
generated using gradient projection
• These equations are similar to the equations
representing delay in queues!
if
if
if
if
Cross-Layer Coordination Signal
• Each equality is broken into two inequalities• For each inequality two multipliers computed
Cross Layer Coordination Signal
• Two imaginary queues whose associated delays are υi
+ and υi-
• Queue 1 is our MAC-layer buffer, and Queue 2 is our token bucket
• Token bucket is not used to regulate service rate, but to keep track of the mismatch between transport and MAC layer rates
The Role of the New Buffers
• Non-zero delay in the MAC-layer buffer corresponds to a wireless bottleneck• The “price” from the actual link prevents the transport layer from
out-running the MAC layer
• Non-zero delay in the token bucket corresponds to a wired bottleneck• The “price” from the token bucket prevents the MAC layer from
out-running the transport layer
• Generally only one of the queues is nonempty (i.e. only one of the constraints is active) at a time
• Without the use of a token bucket, the solution will converge but not to the desired equilibrium when wired bottle-neck
Transport Layer Profit Maximization
• Information about the interference levels in the wireless network is now incorporated into the end-to-end queuing delay (qi+υi
+) minus the token bucket delay (υi
-)
• Allows the transport layer to take interference levels into account without any major modification of current protocols• add the token bucket delay to the propagation delay
Mac Layer Profit Maximization
• Wireless sources now receive “credit” for long data queues (i.e. large νi
+) and are penalized for long token buckets (i.e. large νi
-)
• Prioritize wireless users based on their backlog • (De)Prioritize wireless users based on received
service so far
Simulations
Dynamical Behavior
• Convergence• Since we wish to interpret the Lagrange multipliers as delay, the
step size must be chosen as Δt/C• Convergence is dependent upon the step size being “small
enough,” hence the algorithm being run “fast enough”
• Nested Feedback Loops• Decoupling of the MAC and transport layer allows for the
corresponding feedback loops to be run at different time scales – aid in convergence and/or robustness?
• Interaction of three separate feedback loops (MAC, transport, and power control) plays a significant role in dynamic situations
• Choice of parameters σ and K play an important role
Future Work
• Provide a stability analysis• Use the concept of Markov chain stability for queue
lengths
• Understand the impact of realistic arrival statistics on the system• How does statistical multiplexing impact the transient
behavior of the system?
• Determine whether these results can be extended to other MAC protocols• Does the addition of the MAC-layer queue and token
bucket provide sufficient coordination for other MAC schemes?