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Introduction
Network architecture concerns the definition,
and, perhaps more importantly, the placement and connection of
functionalities in a network. An architecture determines which functional
module or physical element performs a specific task, and how the various
components are connected together. In large and complex communication
networks, architectural decisions are often more important than the details
of resource location algorithms themselves, and are harder to change. Yet,
network architectural principles have remained as fuzzy notions based on
heuristics and intuitions, or at best a “reverse-engineering” of a design
after the fact. The time is ripe for building a scientific foundation for a
clean slate design of network architectures and to guide the evolution from
existing network architectures to new ones. This is the overarching vision
of the proposed project.
Optimization theory is a powerful tool for
designing architectures and providing the algorithmic structures for
communication networks. Starting with fair resource allocation as the goal,
dual decomposition theory provides a powerful tool to assign
functionalities to various network entities, to define signaling
requirements, and to design network management and resource allocation
algorithms, all of which are important components of a network
architecture. In this project, our goal is to develop an analytical
foundation for deriving alternative architectures and studying the
robustness of these architectures to various algorithmic choices.
Thus, far we have made progress on a number
of specific fronts described below.
Alternative network
architectures
A key step in deriving network architectures
using an optimization formulation is to appropriately formulate resource
constraints so that flow balance is maintained which also ensures network
stability. One way to represent the resource constraints is to make sure
that the ingress rates are less than the egress rates on any path from any
source to its destination. This seems natural since queues are maintained
to buffer packets in the direction from sources to destinations. In [1], we
reversed the direction of the constraints which allows the resulting
architecture to be interpreted as a control plane for the flow of signaling
information from destinations to sources. The actual data is still sent
from sources to destinations, but it allows destinations to send
appropriate feedback signals to the sources to regulate the rate of
transmission. The solution also has the added benefit of identifying a new
architectural component called “shadow queues” which provides some degree
of control over QoS. The QoS-control aspects of the solutions are currently
being investigated.
Signaling and feedback in
network architectures
Network architecture can be viewed as a
functional decomposition of various network tasks (components of the architecture
such as routing, scheduling/MAC, etc.) along with the associated interfaces
between these components. These components can span over multiple nodes and
network feedback drives the interactions and dynamics of these various
components. In the context of a wireless network, the amount of feedback
available drives architectural choices and decompositions over wireless
networks, and drives network algorithm design.
In this study [4],
we have developed a systematic framework for understanding the role that
feedback delay plays in network algorithm design (routing and scheduling)
and the associated capacity region of the wireless network.
In our study, we considered two network
architectures. First, we studied a network with a centralized controller
and with heterogeneous delays from each of the nodes to the controller and
with arbitrary topology (thus, the central controller has NSI (Network
State Feedback) with different delays from different nodes). Next, we
considered a decentralized architecture, where each node makes a decision
based on its current channel and queue state along with homogeneous delayed
NSI from other nodes.
For each of the cases (with additional flow
restrictions for the decentralized case), we first characterized the
optimal network throughput region and showed that the throughput region
shrinks with increase in delay. Thus, feedback delay impacts decomposition
choices, and the results have quantified (under certain restrictions on
network flows and channels, please see [4])
the best throughput that can be achieved as a function of network state
delay. Next, we developed novel channel and queue length based routing and
scheduling algorithms that achieve the above throughput region.
Network algorithms and
complexity
Power control is an essential component of a
wireless network architecture, and function decomposition choices among
power control, scheduling, routing and congestion control can fundamentally
affect network throughput, delay performance and robustness.
In [3],
we studied the problem of distributed power control in the context of
utility maximization and throughput optimality over a wireless ad hoc
network. This problem has received increasing attention over the recent
past where the focus has been on developing joint congestion control,
routing and scheduling algorithms using a (stochastic) network utility
maximization framework.
Typically, the approach in literature
consists of formulating the network resource allocation problem as a convex
optimization problem (by approximating the wireless physical layer), and
cross-layer architectures either are based on primal-dual algorithms for
convex optimization (please see [3]
for references) and/or by means of a per-time-slot scheduling combined with
a queue length based backpressure algorithm (based on the work by Tassiulas
and Ephremides). In either case, it is now understood that a key difficulty
is in the distributed scheduling aspect (either for utility maximization or
for queue stability). In wireless networks, the transmission rate of each
link is dependent on the transmission decision (schedule) at other nodes as
well as their actual transmit power levels (for transmitting nodes). This
dependency between the capacity of links and transmission schedule is
typically non-convex. Thus solving the scheduling problem at each time slot
is difficult and acts as a bottle neck for the cross-layer optimization
based architecture. A popular approach to address this is to suitably
approximate the physical layer model in order to render it convex (see work
by M. Chiang and collaborators).
In our study, we took a different approach
where we did not approximate the physical layer interactions across nodes.
Instead, we used a message-passing approach in order to to solve the
non-convex scheduling/power-control problem in a distributed fashion with
polynomial complexity. We first considered a K-hop interference model, and
described a message passing algorithm that finds an optimal power
allocation (schedule) in the case of line networks with a time complexity
(in number of nodes N) that grows as N for line networks. Further, we
showed that this algorithm, when combined with appropriate congestion-control
and routing algorithms results in throughputoptimality and utility
maximization over wireless networks. We further studied a complete physical
interference model, where our algorithms provide -optimal solutions. Our
results also extend to grid networks.
Exploiting convexity
As discussed above, power control is widely
recognized as a key architectural component to improve data rates in
wireless networks. However, much of the research in infrastructure-less
wireless networks focuses on link scheduling only while assuming that the
power levels of the nodes are fixed. Typically power control is performed
with the goal of reaching an equilibrium set of power levels which remains
constant. However, the set of achievable data rates, i.e., the capacity
region, with fixed power levels is a non-convex region which can be
convexified by allowing long-term power variations. Scheduling can be
viewed as a convexification procedure but one where only two power levels
are allowed, zero and the maximum power. We have recently characterized the
conditions on the network parameters under which the capacity region of the
network can be convex even if fixed power levels are used. In other words,
when these conditions are satisfied, then scheduling is not required. The
advantage of convex capacity regions is that they allow the gradient
procedures of convex optimization to be used to design simple distributed
algorithms. However, the conditions under which convexity holds may be
limited and thus, one of our long-term goals is divide the network into
regions such that a combination of simple power control and simple
scheduling rules will be nearly optimal.
The Impact of static
architectural design on user QoS in dynamic networks
As mentioned earlier, architectures are often
derived using a static network model, where the number of users is fixed.
To verify the robustness of these models, it is important to develop a
methodology to study the impact of such architectural design on user-QoS
when the number of users is dynamic. Towards this end, we considered
connection-level models of resource allocation in the Internet, where files
arrive into the network according to a Poisson process and the size of each
file is exponentially distributed [2] [7]. In [7], we
study how the stability region of the network (i.e., the set of offered
loads for which the number of active users in the network remains finite)
is affected by the congestion controller. Previous works in the literature
typically adopt a time-scale separation assumption, which assumes that,
whenever the number of users in the system changes, the data rates of the
users are adjusted instantaneously to the optimal rate allocation computed
by the global utility maximization problem. Under this assumption, it has
been shown that such rate assignment policies can achieve the largest
possible stability region. In this work, we remove this time-scale
separation assumption and show that the largest possible stability region
can still be achieved by a large class of congestion control algorithms. A
second assumption that is also made in prior work is that the packets of a
source (or user) are offered to each link along its path instantaneously,
rather than passing through one queue at a time. We show that connection
level stability is again maintained when this assumption is removed,
provided that a back-pressure scheduling algorithm is used jointly with the
appropriate congestion controller. In [2],
for a simple symmetric three-link star network, we derived the optimal
resource allocation policy which minimizes the expected number of files
waiting in the system. The performance of the optimal policy is then
compared with the performance of a static optimization-based policy called
proportional fairness. We showed that the expected number of files under
proportional fairness is at most 1.5 times more than the expected number
under the optimal policy in a heavy-traffic regime.
The impact of suboptimal
algorithms in network architectures
Protocol components in the current network
architecture are often designed to attain certain optimality goals, with
the hope that, when these optimal components work together, the overall
network performance will also be optimized. However, for many network
settings, due to either the scale of the network; the constraint on the
response time of the algorithms; or the inherent non-convexity in the
system, such optimal solutions can be difficult to attain. In this project,
we explore architectural choices that are robust to sub-optimality in each
individual component. We argue that there is a need to shift our attention
from optimal but complicated solutions, to easily implementable designs
that are suboptimal but still possess good performance bounds. In the first
year of the project, we studied the rate-allocation component of the
network architecture, and investigated the following questions related to
suboptimal components. (1) We investigated the robustness of the network
architecture by studying how much sub-optimality the rate-allocation
component can exhibit while the overall network architecture can still
achieve satisfactory user-level performance. (2) We investigated how to
tradeoff suboptimal rate-allocation with other performance measures, e.g.,
throughput and link utilization.
Our findings in [5]
demonstrate that it is possible to design an overall network architecture
that is robust to suboptimal components. In particular, we show that even
when the transport layer only computes suboptimal rate allocation, under
suitable conditions the system can still achieve good user-level
performance (in terms of achieving the largest connection-level stability
region). Specifically, when the ratio of the utility gap (caused by a
suboptimal rate allocation algorithm) to the maximum utility approaches
zero as queue length tends to infinity, the maximum connection-level
stability region can be retained. When the utility gap is in proportion to
the maximum utility, only a reduced stability region can be achieved, in
which case we provide a lower bound for the achievable stability regions.
Not only that these results demonstrate how to characterize and design
network architectures that are robust to suboptimal (but potentially
simpler and easier-to-implement) rate control, they also allow the network
designer to intentionally under-optimize a given design objective, with the
goal to improve other performance measures of the network.
As mentioned earlier, the computational and
communication burden to support optimal MAC layer resource allocation
algorithms can be quite prohibitive. Thus it important to investigate the
performance of simpler but provably efficient sub-optimal solutions when
designing new communication architectures. To that end, we have recently
developed new analytic results for characterizing the performance limits of
the Greedy Maximal Scheduling (GMS) algorithm [9] [10] [11]. The
study of GMS is extremely important for a variety of reasons: (1) It has
been empirically shown to perform as well as the optimal solution; (2) GMS
results in a significant complexity reduction over the optimal solution;
(3) Intelligently designed constant time distributed scheduling solutions
can be proven to approach the performance of GMS. These new results are a
significant improvement over previously known bounds and answer the
long-standing mystery as to why the observed performance of GMS is so much
better than what the original bounds would indicate. Part of this work
resulted in the IEEE INFOCOM 2008 best paper award [9].
An analytical foundation for
wireless networks supporting delay-sensitive applications
Optimization has been used as a powerful tool
to understand and design new wireless network architectures and algorithms.
In particular, new cross-layer control algorithms that deviate from the
traditional layered architecture have been shown to substantially improve
the overall capacity and throughput of the network. However, current
optimization approaches to network design often cannot take into account
the delay requirements of the applications. A key difficulty is that the
stochastic dynamics of these cross-layer control algorithms are too complex
to characterize using available analytical tools. In this project, we
studied new analytical techniques that can characterize the
delay-performance of complex cross-layer network algorithms. We focused on
queue-length-based MAC scheduling algorithms in the first year of the
project. Such techniques can then be used to compare the delay-performance
of different architectural choices, and help us to design better network
architectures for supporting delay-sensitive applications.
In our recent work [6], we develop a new
unified theory that combines large-deviations with Lyapunov stability to
characterize the Quality-of-Service parameters (such as delay-violation and
queue-overflow probabilities) of complex queue-length-based scheduling
algorithms. A desirable feature of this unified theory is that it can be
readily applied to any control algorithms that have a Lyapunov function.
This is important because many cross-layer algorithms have been analyzed
and designed with a Lyapunov function approach. Hence, our results provide
immediate solutions for the delay-performance of this class of algorithms.
For example, we show that for a large class of Lyapunov functions, a
scheduling algorithm that minimizes the drift of the Lyapunov function Must
also be optimal in minimizing the overflow probability of a suitably-chosen
norm of the queue-length. In particular, we show that the back pressure
algorithm and the max-weighted-rate-sum algorithm, both commonly used in
the literature for cross-layer throughput-optimization, are optimal in
minimizing the overflow probability of the sum of the square of queues. In
future work, we will extend this approach to the entire cross-layer
protocol stack, and develop comprehensive techniques to analyze and design
network architectures for better delay-performance.
We have also embarked on an investigation to
study the expected delay analysis of scheduling schemes for wireless
networks. We consider a class of wireless networks with general
interference constraints on the set of links that can be served
simultaneously at any given time. We restrict the traffic to be single-hop,
but allow for simultaneous transmissions as long as they satisfy the
underlying interference constraints. We begin by proving a system level
lower bound on the delay performance of any scheduling scheme for this
system. We then analyze a large class of throughput optimal policies which
have been studied extensively in the literature. The delay analysis of
these systems has been limited to asymptotic behavior in the heavy traffic
regime and order results. We obtain a tight upper bound on the delay
performance for these systems. We use the insights gained by the upper and
lower bound analysis to develop an estimate for the expected delay of these
networks operating under the well-known Maximum Weighted Matching (MWM)
scheduling policy. We show via simulations that the estimate is accurate
and that the MWM policy is close to being delay-optimal for arbitrary loads
within the capacity region. Preliminary results have been reported in [8].
Improved Routing Architectures
Link-state routing with hop-by-hop forwarding
is widely used in the Internet today. The current versions of these
protocols, like OSPF, split traffic evenly over shortest paths based on
link weights. However, optimizing the link weights for OSPF to the offered
traffic is an NP-hard problem, and even the best setting of the weights can
deviate significantly from an optimal distribution of the traffic. In our
recent work[15] [20][31], we
propose a new link-state routing protocol, PEFT[31], that
splits traffic over multiple paths with an exponential penalty on longer
paths. Unlike its predecessor, DEFT, our new protocol provably achieves
optimal traffic engineering while retaining the simplicity of hop-by-hop
forwarding. A gain of 15% in capacity utilization over OSPF is demonstrated
using the Abilene topology and traffic traces. The new protocol also leads
to significant reduction in the time needed to compute the best link
weights. Both the protocol and the computational methods are developed in a
new conceptual framework, called Network Entropy Maximization, where a
specific notion of entropy is used to identify the traffic distributions
that are not only optimal but also realizable by link-state routing. This
constructive proof that link-state routing can achieve optimal traffic
engineering also highlights a new mentality in the design of Internet: the
level of difficulty of a network management problem may be taken as a
indicator that some of the earlier assumptions need to be perturbed to make
the problem tractable in the first place.
Architectural foundation for
adaptive network virtualization
Network virtualization has emerged as a
powerful way to allow multiple network architectures, each customized to a
particular application or user community, to run on a common substrate.
Each virtual network could run its own protocols to make efficient use of
its share of the underlying resources. However, running multiple virtual
networks in parallel raises several key questions: Can each of the network
architectures be designed completely independently, without regard for the
other virtual networks that would run in parallel with them? How should the
shared resources, such as link bandwidth, be divided between the multiple
virtual networks, and on what timescale? How does the resulting system
compare to a single monolithic design that tries to meet the needs of the
multiple applications? To answer these questions, our work draws on recent
advances in using optimization theory to "derive'' network protocols [17]. The key insight
underlying our work is that primal decomposition essentially corresponds to
network virtualization, with the ability to dynamically vary the share of
the resources allocated to each virtual network. The beauty of primal
decomposition is that the two child problems can now be solved
independently to generate two separate protocol designs, each customized to
the
corresponding traffic class, while ensuring that the resulting solutions
collectively maximize the original joint objective.
Architectural foundation for
content delivery over the Internet
Despite the widespread use of P2P
technologies for video streaming in the Internet today, the fundamental
limit of the highest achievable rate through any P2P method (tree, mesh,
push, or pull-based peering) remains unknown until several recent papers.
In some of these papers [28]
[29], we establish a taxonomy of 16 variants of the P2P streaming capacity
problem, and develop a tree-based peering construction that is proved to
achieve the capacity in 8 of the 12 cases where capacity is unknown before.
During the process, a suite of combinatorial graph-theoretic algorithms
have been developed. Furthermore, practical scheduling algorithms for
wireless P2P systems are developed. We have also examined the interaction
between Content Delivery Networks and Internet Service Provider. We show
that the current practice of separation between server selection by CDN and
traffic engineering by ISP can reach a Nash equilibrium, but a suboptimal
one. Sharing information between the two entities about their individual
optimization may not always improve efficiency either. But deploying a Nash
bargaining solution, a joint optimum can be achieved and both efficiency
and fairness improved. These ongoing studies will continue to deepen our
understanding on the ``horizontal'' axis of architectural choices: how much
of content sharing should be carried out by peers and how much by servers,
as well as on the "vertical'' axis: how much sharing of information
and control should be allowed between those who operate the network and
those who distribute content?
Architecture for Network Service
Availability
Service availability is one of the most
closely scrutinized metrics in offering network services. It is important
to cost-effectively provision a managed and differentiated network with
various service availability guarantees under a unified architecture. In
particular, demands for availability may be elastic and such elasticity can
be leveraged to improve cost-effectiveness. In [19], we
establish the framework of provisioning elastic service availability
through network utility maximization, and propose an optimal and
distributed solution using differentiated failure recovery schemes.First,
we develop a utility function with configurable parameters to represent the
satisfaction perceived by a user upon service availability as well as its
allowed source rate. Second, adopting Quality of Protection and shared path
protection, we transform optimal provisioning of elastic service
availability into a convex optimization problem. The desirable service
availability and source rate for each user can be achieved using a
price-based distributed algorithm. Finally, we numerically show the
tradeoff between the throughput and the service availability obtained by
users in various network topologies. This investigation quantifies several
engineering implications. For example, indiscriminately provisioning
service availabilities for different kinds of users within one network
leads to noteworthy sub-optimality in total network utility. The profile of
bandwidth usage also illustrates that provisioning high service
availability exclusively for critical applications leads to significant
waste in bandwidth resource.
Stability of NUM based
Architecture under Noisy Feedback
While NUM-decomposition-based derivation of
protocol stacks provides a unifying and fresh angle to design network
architecture, the robustness of this approach under various stochastic
dynamics, at session, packet, channel, and topology levels all need to be
carefully examined. State-of-the-art has been reviewed in our recent survey
article [18].
In particular, robustness with respect to probabilistic packet loss and
noisy feedback has been characterized, for both impacts on stability and
rate of convergence [16]. We
show that under mild sufficient conditions, protocol stacks designed based
on primal and dual decompositions of NUM remain stable despite common types
of packet loss and imperfect feedback.
Collaboration
There has been much cross-institutional
interaction among the team members through student visits and post-doctoral
scholars. In addition, we have regular phone calls as well as
video-conferences between PIs and students to discuss collaborative
research.
Dr. Lei Ying (currently an Assistant
Professor at Iowa State University) graduated from the University of
Illinois at Urbana-Champaign in 2007 where his Ph.D. was supervised by R.
Srikant. He then was a post-doctoral scholar and worked with S. Shakkottai
at UT Austin. He has collaborated with both the PIs and joint publications
between Ying, Srikant and Shakkottai are under preparation. Ying has also
recently collaborated with N. Shroff on themes related to this project. Lin
and Shroff are collaborating with Shroff’s postdoctoral researcher Dr. Joo
on the performance of cross-layer architectures with imperfect control.
Chiang, Srikant and students are collaborating on understanding the
advantages and limitations of designing network algorithms based on convex
optimization theory. Lin, Shroff and Srikant are collaborating on
understanding the impact of static architectural design on dynamic
networks. Lin, Shroff, Srikant, Shakkottai and students are collaborating
on understanding the tradeoffs between complexity and performance in
distributed algorithms. Chiang, Lin and students are collaborating on
understanding the impact of suboptimal protocol components on the overall
network architecture. Chiang and Shroff, along with Chiang’s student Tian
Lan (who spent the Spring Quarter with Shroff) are investigating the use of
optimization tools in developing new architectures for overlay network
security. Chiang and Rexford are jointly supervising students that are
investigating new routing architectures and providing the architectural
foundation for adaptive network virtualization.
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1.
L. Bui, R.
Srikant and A. L. Stolyar. Optimal
Resource Allocation for Multicast Flows in
Multihop Wireless Networks. Philosophical Transactions of the Royal
Society, Series A, 2008.
2.
L. Ying, B.
Tan and R. Srikant. On the
Delay Optimality of Proportional Fairness.. Proc. ITA
Workshop, UCSD, Jan-Feb. 2008.
3.
A. Reddy,
S. Shakkottai and Lei Ying. Distributed
Power Control in Wireless Ad Hoc Networks Using Message Passing: Throughput
Optimality and Network Utility Maximization . In
Proceedings of CISS 2008, Princeton, NJ.
4.
L. Ying and
S. Shakkottai. On
Throughput-Optimal Scheduling with Delayed Channel State
Feedback. In Proc. Information Theory and Applications Workshop, San
Diego, CA, February
2008.
5.
T. Lan, X.
Lin, M. Chiang and R. Lee. How
Bad Is Suboptimal Rate Allocation? In Proceedings
of IEEE INFOCOM, Phoenix, AZ, 2008.
6.
V. J.
Venkataramanan and X. Lin. On Characterizing the Delay Performance of
Wireless
Scheduling Algorithms. To be submitted shortly.
7.
X. Lin and
N. B. Shroff and R. Srikant. “On the
Connection-Level Stability of Congestion-
Controlled Communication Networks.” to appear in the IEEE Trans. on
Information Theory,
2008.
8.
G. Gupta
and N. B. Shroff, “Scheduling
With Queue Length Guarantees For Shared Resource
Systems,” ACM Sigmetrics Poster, June 2008.
9.
C. Joo, X.
Lin, and N. B. Shroff, “Understanding
the Capacity Region of the Greedy Maximal Scheduling Algorithm in Multi-hop
Wireless Networks,” IEEE INFOCOM 2008, Phoenix, AZ,
April 2008 (Best
Paper Award, 2008).
10.
C. Joo, X.
Lin, and N. B. Shroff, “Performance
Limits of Greedy Maximal Matching in Multi-hop
Wireless Networks,” IEEE Conference on Decision and Control (CDC), New
Orleans, Louisiana,
USA, Dec. 2007.
11.
C. Joo, X.
Lin, and N. B. Shroff, “Understanding
the Capacity Region of the Greedy Maximal
Scheduling Algorithm in Multi-hop Wireless Networks,” submitted to
IEEE/ACM Trans. on
Networking, 2008.
12.
D. Xu, M.
Chiang, and J. Rexford, 'DEFT: Distributed
exponentially-weighted flow splitting', Proc. IEEE INFOCOM, Anchorage,
Alaska, May 2007.
13.
J. He, M. Bresler,
M. Chiang, and J. Rexford, 'Towards
robust multi-layer traffic engineering', IEEE Journal of Selected Areas
in Communications, vol. 25, no. 5, pp. 868-880, June 2007.
14.
J. W. Lee,
A. Tang, J. Huang, M. Chiang, and A. R. Calderbank, 'Reverse
engineering MAC: A game-theoretic model', IEEE Journal of Selected
Areas in Communication, vol. 25, no. 6, pp. 1135-1147, August 2007.
15.
J. He, J.
Rexford, and M. Chiang 'Don't optimize existing protocols, design optimizable
protocols', ACM Sigcomm Computer Communications Review, vol. 37, no. 3,
pp. 53-58, August 2007.
16.
J. Zhang,
D. Zheng, and M. Chiang, 'The
impact of stochastic noisy feedback on distributed network utility
maximization', IEEE Transactions on Information Theory, vol. 54, no. 2,
pp. 645-665, February 2008.
17.
M. Yu, Y.
Yi, J. Rexford, and M. Chiang, 'Rethinking
virtual network embedding: Support of path splitting and migration', ACM
Computer Communication Review, April 2008.
18.
Y. Yi and
M. Chiang, 'Stochastic network utility maximization: A tribute to
Kelly's paper published in this journal a decade ago', European Transactions
on Telecommunications, June 2008.
19.
D. Xu, Y.
Li, M. Chiang, and A. R. Calderbank, 'Elastic
service availability: Utility framework and optimal provisioning', To
appear in IEEE Journal of Selected Areas in Communications, 2008.
20.
J. He, J.
Rexford, and M. Chiang, 'Design
for Optimizability: Traffic Management for a Future Internet', To appear
in Algorithms for Next Generation Networks, Ed. M. Thottan and G. Cormode,
Springer, 2009.
21.
D. Xu, Y.
Li, M. Chiang, and A. R. Calderbank, 'Optimal
provision of elastic service availability', Proc. IEEE INFOCOM,
Anchorage, Alaska, May 2007.
22.
Y. Li, M.
Chiang, and A. R. Calderbank, 'Optimal delay-rate-reliability tradeoff in
networks with composite links', Proc. IEEE INFOCOM, Anchorage, Alaska, May
2007.
23.
J. Liu, A.
Proutiere, Y. Yi, M. Chiang, and H. V. Poor, 'Flow-level stability of
utility maximization under nonconvex and time-varying rate regions', Proc.
ACM Sigmetrics, June 2007.
24.
J. He, M.
Suchara, M. Bresler, M. Chiang, and J. Rexford, 'Rethinking
Internet traffic management: from multiple decompositions to a practical
protocol',Proc. ACM CoNEXT, December 2007.
25.
Y. Li, Z.
Li, M. Chiang, and A. R. Calderbank, 'Content aware distortion fair video
streaming in networks', Proc. IEEE GLOBECOM, New Orleans, LA, Nov. 2008.
26.
V. J.
Venkataramanan and and Xiaojun Lin. On Characterizing the Delay Performance
of Wireless Scheduling Algorithms. Submitted.
27.
A.
Lakshmikantha, R. Srikant and C. Beck, Impact of
file arrivals and departures on buffer sizing in core routers,
Proceedings of IEEE Infocom, 2008.
28.
S. Liu, R.
Zhang-Shen, W. Jiang, J. Rexford, and M. Chiang, 'Performance bounds for
peer-assisted live streaming', Proc. ACM Sigmetrics, Annapolis, MD,
June 2008.
29.
W. Jiang,
R. Zhang-Shen, J. Rexford, and M. Chiang, 'Traffic engineering and server
selection: ISP-CDN interactions', Proc. ACM Sigcomm NetEcon Workshop,
August 2008.
30.
J. He, R.
Zhang-Shen, Y. Li, C.-Y. Lee, J. Rexford, and M. Chiang, "DaVinci: Dynamically
Adaptive Virtual Networks for a Customized Internet," in
submission, July 2008.
31.
Dahai Xu,
Mung Chiang, and Jennifer Rexford, "Link-state
routing with hop-by-hop forwarding can achieve optimal traffic engineering,"
in Proc. IEEE INFOCOM, April 2008.
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