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(solution) A Case Study in Network Architecture Tradeoffs Nikolai Matni


I need help with Case Study Analysis supposed to be due yesterday at 11:59 P. M.  I really need your help with it. 

The topic is as follow and the document on the case study analysis based is attached. 

"A Case Study in Network Architecture Tradeoffs"


A Case Study in Network Architecture Tradeoffs?

 

Nikolai Matni Ao Tang John C. Doyle California Institute of

 

Technology

 

1200 E California Blvd

 

Pasadena, California Cornell University

 

337 Frank H. T. Rhodes Hall

 

Ithaca, NY California Institute of

 

Technology

 

1200 E California Blvd

 

Pasadena, California nmatni@caltech.edu atang@ece.cornell.edu doyle@caltech.edu ABSTRACT Categories and Subject Descriptors Software de?ned networking (SDN) establishes a separation

 

between the control plane and the data plane, allowing network intelligence and state to be centralized ? in this way the

 

underlying network infrastructure is hidden from the applications. This is in stark contrast to existing distributed networking architectures, in which the control and data planes

 

are vertically combined, and network intelligence and state,

 

as well as applications, are distributed throughout the network. It is also conceivable that some elements of network

 

functionality be implemented in a centralized manner via

 

SDN, and that other components be implemented in a distributed manner. Further, distributed implementations can

 

have varying levels of decentralization, ranging from myopic

 

(in which local algorithms use only local information) to

 

coordinated (in which local algorithms use both local and

 

shared information). In this way, myopic distributed architectures and fully centralized architectures lie at the two

 

extremes of a broader hybrid software de?ned networking

 

(HySDN) design space.

 

Using admission control as a case study, we leverage recent developments in distributed optimal control to provide

 

network designers with tools to quantitatively compare different architectures, allowing them to explore the relevant

 

HySDN design space in a principled manner. In particular, we assume that routing is done at a slower timescale,

 

and seek to stabilize the network around a desirable operating point despite physical communication delays imposed by

 

the network and rapidly varying tra?c demand. We show

 

that there exist scenarios for which one architecture allows

 

for fundamentally better performance than another, thus

 

highlighting the usefulness of the approach proposed in this

 

paper. C.2.1 [Network Architecture and Design]: Miscellaneous; C.4 [Performance of Systems]: Miscellaneous. ?N. Matni & J. C. Doyle were in part supported by the

 

AFOSR and the Institute for Collaborative Biotechnologies

 

through grant W911NF-09-0001 from the U.S. Army Research O?ce. A. Tang was in part supported by the ONR

 

under grant N00014-12-1- 1055.

 

Permission to make digital or hard copies of all or part of this work for

 

personal or classroom use is granted without fee provided that copies are not

 

made or distributed for pro?t or commercial advantage and that copies bear

 

this notice and the full citation on the ?rst page. Copyrights for components

 

of this work owned by others than ACM must be honored. Abstracting with

 

credit is permitted. To copy otherwise, or republish, to post on servers or to

 

redistribute to lists, requires prior speci?c permission and/or a fee. Request

 

permissions from Permissions@acm.org.

 

SOSR2015, June 17 - 18, 2015, Santa Clara, CA, USA

 

c 2015 ACM ISBN 978-1-4503-3451-8/15/06 ...$15.00

 

DOI: http://dx.doi.org/10.1145/2774993.2775011. General Terms

 

Design, Theory, Performance 1. INTRODUCTION A common challenge that arises in the design of networks

 

is that of achieving globally optimal behavior subject to the

 

latency, scalability and implementation requirements of the

 

system. Many system properties and protocols ? such as network throughput, resource allocation and congestion avoidance ? are inherently global in scope, and hence bene?t from

 

centralized solutions implemented through Software De?ned

 

Networking (SDN) (e.g., [3, 4, 9]). However, such centralized solutions are not always desirable due to latency and

 

scalability constraints ? in particular the delay inherent in

 

communicating the global state of the network, solving a

 

global optimization problem and redistributing the solution

 

to the network, can often negate the bene?ts achieved from

 

this holistic strategy. In these cases, distributed networking

 

solutions can be preferable (e.g., [1]).

 

Traditionally, there has been very little in the way of theoretical tools at the disposal of network designers to quantitatively compare di?erent architectures. Because of this,

 

the appropriateness of an architectural decision could only

 

be con?rmed once a suitable algorithm had been prototyped

 

and validated via experiment. This process is time consuming and expensive, and even worse, can be inconclusive. In

 

particular, if an algorithm performs poorly, it is not clear

 

if this poor performance is due to an inherent limitation of

 

the chosen architecture, or simply due to a poorly designed

 

algorithm, making it very di?cult to quantitatively compare

 

network architectures.

 

In this paper, we argue that due to both the increased

 

?exibility a?orded to network designers by SDN and to recent advances in distributed optimal control, the gap between theory and practice has closed signi?cantly. Although

 

the gap has not yet completely closed, we show that in the

 

context of certain network applications, existing theory can

 

indeed be used to quantitatively compare the fundamental performance limits of di?erent network architectures. In

 

particular, we leverage the fact that new theory can now

 

explicitly take into account the e?ect of communication delays inherent to coordinating control actions in a networked

 

setting. Towards this end, we de?ne the broader Hybrid Software

 

De?ned Networking (HySDN) design space (§2) of network

 

architectures, and argue that an important metric in determining the appropriateness of an architecture is the optimal

 

performance achievable by any algorithm implemented on

 

that architecture. This additional metric can then be used

 

by a network designer to quantify the performance tradeo?s

 

associated with using a simpler or more complex architecture, allowing for more informed decisions about architecture early in the design process.

 

We further explain how recent advances in distributed

 

optimal control theory allow us to apply this approach to

 

a class of network control problems in which the objective is to regulate network state around a pre-speci?ed desired set-point. In §3, we illustrate the usefulness of this

 

approach with an admission control case study. Perhaps

 

surprisingly, we show that for two nearly identical routing

 

topologies, there can be signi?cant di?erences in the performance achievable by centralized and distributed network

 

architectures.

 

We emphasize that we are not arguing that a speci?c implementation, algorithm or architecture is best suited for a

 

given application ? rather, we are illustrating the usefulness

 

of a methodology that allows network designers to make

 

quantitative decisions about architectural choices early in

 

the design process. We are also not proposing that this

 

method replace the important steps of simulation, prototyping and experiments, but rather as a complement to it.

 

Indeed, in order to achieve theoretical tractability, simplifying assumptions such as linearized ?ow models, constant

 

delays, reliable control packet communication and negligible

 

computation time are made ? the validity of these assumptions can only be con?rmed through experiments. We do

 

however believe that the proposed tools can help network designers streamline the prototyping process by allowing them

 

to narrow down the range of potential architectures that

 

need to be explored. 2. ARCHITECTURAL TRADEOFFS Completely distributed network architectures, in

 

which local algorithms take local actions using only locally

 

available information, and centralized network architectures,

 

in which a centralized algorithm takes global action using

 

global information, can be viewed as lying at the extremes

 

of a much richer design space. It is possible to build a network architecture in which certain network logic elements

 

are implemented in a centralized fashion via SDN, and in

 

which other network logic elements are implemented in a

 

distributed fashion. Further, distributed architectures can

 

have varying levels of decentralization, ranging from completely distributed (as described above), or myopic, architectures to coordinated distributed architectures, in which

 

local algorithms take local actions using both locally available information and shared subsets of global state information. We call this broad space of architectures the Hybrid

 

Software De?ned Networking (HySDN) design space (illustrated in Figure 1), as its constituent architectures are naturally viewed as hybrids of distributed and software de?ned

 

networks.

 

The question then becomes how to explore this even larger

 

design space in a systematic way. As we have already alluded to, there are inherent tradeo?s associated with any architecture: algorithms running on centralized architectures typically achieve better steady state performance, but often

 

react with higher latency than those implemented on a distributed architecture ? conversely distributed algorithms are

 

often simpler to implement but can lead to less predictable

 

steady state performance.

 

We pause here to recognize that network architectures and

 

algorithms are judged by many di?erent metrics, including

 

but not limited to performance, scalability, ease of deployment and troubleshooting, and ?exibility. We argue that

 

as much as possible, each of these di?erent metrics should

 

be traded o? against each other in a quantitative way ? for

 

example, it is important for a network designer to be able

 

to quantify the performance degradation su?ered by using a

 

network architecture or algorithm that is simpler to deploy

 

and troubleshoot. Our approach to exploring these tradeo?s

 

is simple: we compare network architectures by comparing

 

the optimal performance achievable by any algorithm implemented using them. This approach allows for a network

 

designer to compare fundamental limits of achievable performance across di?erent architectures. The approach also

 

allows for the comparison of the performance of more scalable, ?exible, or easier to deploy algorithms implemented

 

using a given network architecture to that network architecture?s best possible performance, allowing for a quanti?able

 

tradeo? between these metrics of interest.

 

In order to make the discussion concrete, we focus on algorithms that can be viewed as controllers that aim to keep the

 

state of the network as close to a nominal operating point as

 

possible, while exchanging and collecting information subject to the communication delays imposed by the network.

 

For example, in §3, we consider admission control algorithms

 

that aim to keep the link ?ow rates at a user-speci?ed setpoint while minimizing the admission bu?er size, despite

 

physically imposed communication delays and rapidly varying source rates. In particular, we are not addressing the

 

problem of determining what nominal operating point the

 

controllers should attempt to bring the network state to ?

 

we aim to extend our analysis to such problems in future

 

work. We recognize that this measure of performance is not

 

standard in the networking community, but note that it is a

 

natural one to consider when explicitly taking into account

 

rapidly varying and unpredictable source rates.

 

By restricting ourselves to problems of this nature, we

 

can leverage recent results in distributed optimal control

 

theory to classify those architectures for which the optimal algorithm and achievable performance can be computed

 

e?ciently.1 It is well known that the optimal centralized

 

controller, delayed or not, can be computed e?ciently via

 

convex optimization [13]. Further, it is known that myopic

 

distributed optimal controllers are in general NP-hard to

 

compute [12, 8]. Up until recently however, it was unclear if

 

and when coordinated distributed optimal controllers could

 

be speci?ed as the solution to a convex optimization problem.

 

The challenge inherent in optimizing distributed control

 

algorithms is that control actions (e.g., local admission control decisions) can potentially serve two purposes: actions

 

taken by local controllers can be used to both control the

 

state of the system in a manner consistent with performance

 

1

 

Throughout this discussion, we assume that the dynamics

 

of the network are linear around a neighborhood of the nominal operating point. This assumption holds true for many

 

commonly used network ?ow models [5, 2]. Centralized'Applica1on'Plane'

 

Centralized'

 

Centralized'

 

Applica1on'

 

Applica1on' Centralized'

 

Applica1on' Centralized'

 

Applica1on' Applica1on'Controller'Plane'Interface''

 

Control'Plane' Applica/on'Plane'

 

Centralized'

 

Centralized'

 

Applica/on'

 

Applica/on' Network'Opera1ng'System' Centralized'

 

Applica/on' Centralized'

 

Applica/on' Applica/on'Controller'Plane'Interface''

 

Control'Plane' Applica3ons$ Applica3ons$

 

OS$

 

Data$

 

Forwarding$$ OS$

 

Data$

 

Forwarding$$ Applica3ons$ Data'Controller'Plane'Interface'' Network'Opera/ng'System' Data'Plane' Applica3ons$

 

OS$

 

Data$

 

Forwarding$$ OS$

 

Data$

 

Forwarding$$ (a) Distributed Networking Dist.'App'

 

Local'OS'

 

Data' Dist.'App'

 

Local'OS'

 

Data'

 

Dist.'App'

 

Local'OS'

 

Data' Data'Controller'Plane'Interface''

 

Dist.'App'

 

Local'OS'

 

Data' Data'Plane' Data'

 

Forwarding'' Data'

 

Forwarding'' Data'

 

Forwarding''

 

Data'

 

Forwarding'' (b) Hybrid Software De?ned Networking (c) Centralized Software De?ned Networking Figure 1: The Hybrid Software De?ned Networking Design space, ranging from distributed (Fig 1a) to centralized (Fig 1c)

 

network protocols. objectives, and to signal to other local controllers, allowing

 

for implicit communication and coordination. Intuitively, it

 

is this attempt to both control the system and to implicitly communicate that makes the problem di?cult to solve

 

computationally. However, if local controllers are able to

 

coordinate their actions via explicit communication, rather

 

than by implicit signaling through the system, then the optimal controller synthesis problem becomes computationally

 

tractable [11, 10]. Further it is not di?cult to argue that

 

distributed controllers using explicit communication to coordinate will outperform those relying on implicit signaling through the system. Removing the incentive to signal

 

through the system can be done in a network control setting

 

by giving control dedicated packets, i.e., packets containing

 

the information exchanged between local algorithms, priority in the network.2

 

These theoretical developments thus provide the necessary tools to explore a much larger section of the HySDN

 

design space in a principled manner. We propose leveraging these results to compare the performance achievable by

 

algorithms implemented on four di?erent classes of architectures, described below:

 

1. The GOD architecture: in order to quantify the

 

fundamental limits on achievable performance, we propose computing the optimal controller implemented

 

using the Globally Optimal Delay-free (GOD) architecture. This architecture assumes instantaneous communication to and from a central decision maker ?

 

although not possible to implement, the performance

 

achieved by this architecture cannot be beaten, and

 

as such represents the standard against which other

 

architectures should be compared.

 

2. The centralized architecture: this architecture corresponds to the SDN approach, in which a centralized

 

decision maker collects global information, computes

 

2 Speci?cally, if local controllers can communicate with each

 

other as quickly as the e?ect of their actions propagate

 

through the network, then the resulting optimal control

 

problem is convex. By giving such communication packets

 

priority in the network and ensuring that they are routed

 

along suitably de?ned shortest paths, this property is guaranteed to be satis?ed [10]. a global control action to be taken, and broadcasts it

 

to the network. Although global in scope, the latency

 

of algorithms implemented using this architecture is

 

determined by the communication delays inherent in

 

collecting the global network state and broadcasting

 

global actions.

 

3. The coordinated architecture: this architecture is

 

distributed, but allows for su?cient coordination between local controllers so that the optimal control law

 

can be computed e?ciently [11, 10]. This architecture

 

takes both rapid action based on timely local information, and slower scale action based on global but

 

delayed shared information, and can thus be viewed as

 

an intermediate between centralized and myopic architectures.

 

4. The myopic architecture: this architecture is one

 

in which local controllers take action based on local

 

information. Although the optimal controller cannot

 

be computed, the performance achieved by any myopic controller can be compared with the performance

 

achieved by an optimal coordinated controller, thus

 

providing a bound on the performance di?erence between the two architectures.

 

It should be noted that the coordinated architecture will

 

always perform at least as well as the myopic and centralized

 

architectures, as any algorithm implemented on the latter

 

architectures can also be implemented on the former. It is

 

clear why this holds for myopic algorithms, but it is worth

 

emphasizing why this holds for centralized algorithms. This

 

is true because the delays faced by a coordinated distributed

 

algorithm in collecting and sharing state information are also

 

faced by a centralized algorithm. Whereas a centralized algorithm waits until the global state has been collected and

 

processed to react to make changes to the system, a coordinated distributed algorithm takes both local timely actions

 

based on local information and delayed actions based on

 

shared information.

 

What we seek to understand is how large of a gap in performance exists between these di?erent architectures. By

 

computing the performance of each of these architectures,

 

the network designer can then quantify tradeo?s in implementation complexity and performance in a computationally e?cient and inexpensive manner. We demonstrate the usefulness of this approach on an admission control case study

 

in the next section. 3. Noisy source

 

xs (t) = x? (t) + s (t)

 

s ADMISSION CONTROL DESIGN In this section we pose an admission control problem, de?ne the relevant HySDN design space and show that it can

 

be explored in a principled and quantitative manner using

 

tools from distributed optimal control theory. We discuss

 

the problem at a conceptual level in this section, and refer

 

the interested reader to [7] for the technical details. 3.1 Figure 3: Diagram of an edge admission controller. Ingoing ?ows

 

f 1 (t)

 

f 2 (t)

 

f 3 (t) Problem We consider the following admission control task: given

 

a set of source-destination pairs (s, d), a set of desired ?ow

 

rates f ,(s,d) on each link for said source-destination pairs,

 

and a ?xed routing strategy that achieves these ?ow rates,

 

design an admission control policy that maintains the link

 

?ow rates f ,(s,d) (t) as close as possible to f ,(s,d) while minimizing the amount of data stored in each of the admission

 

control bu?ers, despite ?uctuations in the source rates xs (t).

 

The architectural decision that the network designer is

 

faced with is whether to implement the admission control

 

policy in a myopic, coordinated, or centralized manner ?

 

representative examples of these possible architectures are

 

illustrated in Figure 2 for the case of three sources. In the

 

myopic distributed architecture, local admission controllers

 

AC1, AC2 and AC3 have policies that depend solely on their

 

local information ? in what follows, we de?ne the local information available to a local algorithm for the speci?c case

 

studies that we consider. In the coordinated distributed architecture, the local admission controllers take action based

 

on both locally available information and on information

 

shared amongst themselves ? this shared information is delayed, as it must be communicated across the network and is

 

therefore subject to propagation delays. Finally, in the centralized architecture, a central decision maker collects the

 

admission control bu?er and link ?ow rate states subject to

 

appropriate delays, determines a global admission control

 

strategy to be implemented and broadcasts it to the local

 

AC controllers ? this strategy also su?ers from delay due to

 

the need to collect global state information and to broadcast

 

the global policy to each AC controller.

 

As mentioned in the previous section, we know a priori

 

that the coordinated distributed optimal control architecture will perform no worse than either the myopic or centralized architecture. Conversely, the myopic and centralized schemes are signi?cantly easier to deploy, and the centralized scheme is signi?cantly easier to troubleshoot. Thus,

 

in quantifying the gaps in performance between the centralized, myopic and distributed architectures, the network

 

designer is able to make an informed decision as to whether

 

the added complexity of the coordinated distributed scheme

 

is warranted.

 

As described in §2, our approach to exploring the HySDN

 

design space is to compute optimal admission controllers implemented on each of these di?erent architectures. In particular we compute admission controllers that minimize a

 

performance metric of the form

 

N f

 

t=1 ,(s,d) ,(s,d) (t) ?f 2

 

,(s,d) + ? A(t) 2 ,

 

2 (1) Admission

 

Control

 

Bu?er

 

Admitted ?ow

 

as (t)

 

As (t) Admission

 

Control

 

Bu?er Admitted

 

a1 (t) ?ows

 

a2 (t)

 

As (t)

 

a3 (t) Figure 4: Diagram of an internal admission controller. where A(t) is a vector containing the size of the admission

 

control bu?ers and N is the optimization horizon. Thus the

 

controllers aim to minimize a weighted sum of ?ow rate deviations and admission queue lengths over time, where ? > 0

 

determines the relative weighting assigned to each of these

 

two terms in the ?nal cost. By solving the corresponding

 

optimal control problems, we obtain two parameters: an

 

optimal cost and an admission control policy that achieves

 

it. These optimal costs thus serve as a quantitative measure

 

of the performance of a given architecture, as by de?nition,

 

they correspond to the best performance achievable by any

 

admission control policy implemented on that architecture. 3.2 Case Study We consider a simple routing topology overlaid onto the

 

abilene network, and two di?erent admission control scenarios: one in which only edge admission control is allowed (cf.

 

Figure 3) and one in which edge and internal admission control is allowed (cf. Figure 4). We model the dynamics of the

 

system using a ?ow based model and solve the optimal control problem with the cost (1) taken to be the in?nite horizon

 

LQG cost using the methods described in [13] and [6] ? we

 

refer the reader to [7] for the technical details. Intuitively,

 

this cost measures the amount of ?energy? transferred from

 

the source rate deviations to the ?ow rate deviations and

 

bu?er sizes. We assume that the nominal source rates xs (t)

 

and the nominal ?ow rates f ,(s,d) are all equal to 1 (this

 

is without loss of generality through appropriate normalization of units), and empirically choose ? = 50 based on the

 

observed responses of the synthesized controllers.

 

We compute three optimal controllers for each of the scenarios considered: a coordinated distributed optimal controller in which local admission controllers are able to exchange information via the network in order to coordinate

 

their actions, as illustrated in the middle pane of Figure

 

2, a centralized optimal controller subject to the delays induced by collecting global state information and broadcasting a global control action, and the GOD controller. We also

 

compare the performance of these controllers with the performance achieved by the best myopic distributed controller

 

we are able to compute via non-linear optimization (recall

 

that optimal myopic controllers are in general computationally intractable to compute). Noisy&

 

Src&1& AC1& AC2& AC3& AC1& AC2& AC3&

 

Flow&3&

 

Flow&2& Flow&1& Flow&3& Flow&2& Flow&1& Flow&3& Flow&2& Flow&1& Network& Network& Network& Myopic&Distributed& Coordinated&Distributed& Info&3& AC3& Info&2& AC2& Noisy&

 

Src&3& Admission&Controller& Info&1& AC1& Info&3& Noisy&

 

Src&3& Info&2& Noisy&

 

Src&2& Info&1& Noisy&

 

Src&1& Info&3& Noisy&

 

Src&3& Info&2& Noisy&

 

Src&2& Info&1& Noisy&

 

Src&1& Noisy&

 

Src&2& Centralized& Figure 2: The HySDN design space for an admission control problem with three sources. Blue arrows denote the ?ow of tra?c,

 

whereas dashed black lines denote the ?ow of admission control related information. Note that the dotted lines correspond to

 

virtual connections, and can be implemented using either control dedicated communication links, or using control dedicated

 

t...

 


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