Network Utility Maximization for overcoming inefficiency in - - PowerPoint PPT Presentation

Network Utility Maximization for overcoming inefficiency in multirate wireless networks

Andr´ es Ferragut Jos´ e Garc´ ıa Fernando Paganini

Mate Research Group Universidad ORT Uruguay

RAWNET Workshop, 4th June 2010

Motivation

Wireless network are nowadays prevalent for Internet Access. The IEEE 802.11 protocol is the most used wireless access mechanism. We want to understand the resource sharing this protocol produces in the network.

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Motivation

Wireless network are nowadays prevalent for Internet Access. The IEEE 802.11 protocol is the most used wireless access mechanism. We want to understand the resource sharing this protocol produces in the network.

Some questions we want to answer:

Which is the throughput obtained by TCP connections in a 802.11 environment? Which is the resource allocation when multiple transmission rates are present? Can we do better?

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Our contributions

We characterize some of the inefficiencies of TCP over 802.11 in a downlink scenario:

Protocol overheads. The existence of concurrent multiple transmission rates.

We propose a new allocation based on Network Utility Maximization (NUM). We present an AQM policy that enables the new allocation. We discuss how to generalize these algorithms to more complex scenarios.

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Contents

1 The inefficiencies of TCP over 802.11. 2 TCP resource allocation in a multirate wireless environment 3 A more efficient resource allocation for a single cell 4 A word on more general topologies 5 Implementation and simulations 6 Conclusions

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Contents

1 The inefficiencies of TCP over 802.11. 2 TCP resource allocation in a multirate wireless environment 3 A more efficient resource allocation for a single cell 4 A word on more general topologies 5 Implementation and simulations 6 Conclusions

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Protocol overheads

IEEE 802.11 uses DCF as the main access mechanism to the shared medium.

This imposes some fixed and random times a station must comply with (DIFS, SIFS, Backoff slots, etc.)

Moreover, transmitting a packet of size L bits involves some amount

• f overhead due to MAC and PHY headers (i.e. PLCP).

In a downlink scenario these overheads predominate over the collisions. Therefore, the real transmission rate of packets is not “54Mbps” but

• less. How much?

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MAC level rates

The works pioneered by Bianchi [2] and followed by Kumar et. al. [5] established a formula for the MAC level rates. In the downlink case (where the station that predominantly accesses the medium is the AP) it takes the form: C0

i = L

Ti = L

CWmin 2

σ + T 0

i + L P HYi

L is the packet size, CWmin is the minimum contention window. σ is the slot time. T 0

i accounts for the fixed time overheads in transmission.

PHYi the modulation rate.

In the following, we assume L = 1500 bytes.

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Typical 802.11 parameters

Parameter Value Slot time σ 9µs SIFS 10µs DIFS 28µs PLCP Header H 24µs PHYi 6Mbps . . . 54Mbps CWmin 15 slots MAC ACK 24µs

Table: Typical IEEE 802.11g parameters

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Beware of TCP ACKs!

The previous model does not take into account the TCP ACKs that go in the uplink direction. TCP ACKs were designed to have low impact on the reverse path (40 bytes against 1500). However, due to the 802.11 overheads, their impact is greater: The effective rate becomes: Ci = L Ti + TCP ACKi TCP ACKi is the average time to transmit a TCP ACK packet (calculated in a similar fashion), with a typical length of Lack = 40 bytes.

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The real 802.11g data rates with TCP

PHY rates MAC rates (C0

i )

• Eff. data rate (Ci)

54 31.9 22.4 48 29.7 21.2 36 24.6 18.5 24 18.4 14.6 18 14.6 12.1 12 10.4 8.9 6 5.57 5.08

Table: MAC rates for the corresponding PHY rates of 802.11g in Mbps. L = 1500 bytes.

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The real 802.11g data rates with TCP

PHY rates MAC rates (C0

i )

• Eff. data rate (Ci)

54 31.9 22.4 48 29.7 21.2 36 24.6 18.5 24 18.4 14.6 18 14.6 12.1 12 10.4 8.9 6 5.57 5.08

Table: MAC rates for the corresponding PHY rates of 802.11g in Mbps. L = 1500 bytes.

The TCP ACKs may waste 25% of the bandwidth at high rates!

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The issue of multiple rates

From now on we consider only the effective rates Ci as given. We will focus on the resource allocation provided by TCP in the presence of these multiple rates. Why are multiple rates an issue? An example...

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The issue of multiple rates

Internet Access

Point of Presence

802.11 AP

Coverage Area

Class 2 Class 1 Class 3

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The issue of multiple rates

Internet Access

Point of Presence

802.11 AP

Coverage Area

Class 2 Class 1 Class 3

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The issue of multiple rates

Internet Access

Point of Presence

802.11 AP

Coverage Area

Class 2 Class 1 Class 3

Andr´ es Ferragut (Universidad ORT (Uruguay)) NUM in multirate wireless networks RAWNET 2010 12 / 48

The issue of multiple rates

Internet Access

Point of Presence

802.11 AP

Coverage Area

Class 2 Class 1 Class 3

Andr´ es Ferragut (Universidad ORT (Uruguay)) NUM in multirate wireless networks RAWNET 2010 12 / 48

Contents

1 The inefficiencies of TCP over 802.11. 2 TCP resource allocation in a multirate wireless environment 3 A more efficient resource allocation for a single cell 4 A word on more general topologies 5 Implementation and simulations 6 Conclusions

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Modelling TCP over 802.11

Assume: N stations are downloading data from a single Access Point (AP). Each station i has an effective data rate Ci. Data is queued at the AP. The input rate for connection i is xi and the output rate yi. Assuming a fluid model for the queue we have yi = xi

• j xj/Cj

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Modelling TCP over 802.11

TCP can be modelled as adapting rate according to some congestion signal (c.f. Srikant, 2004 [9]). ˙ xi = k(xi)(U ′

i(xi) − pi)

where U(x) is an increasing and concave utility function, pi is the congestion signal and k(xi) > 0 a scale factor. For TCP/Reno like algorithms we can take pi the loss probability. The utility function represents the protocol desire for bandwidth and is typically chosen as U ′(x) = Kx−α with α > 0 a parameter. Example: TCP/Reno takes α = 2.

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Modelling TCP over 802.11

To complete the loop, we model the loss probability as the proportion

• f excess rate. The loss probability for station i becomes:

pi = xi − yi xi + =

• 1 −

1

• j xj/Cj

+ = p where as usual (·)+ = max(·, 0).

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TCP over 802.11: the downlink model

Putting the previous equations together we have: ˙ xi = k(xi)(U ′

i(xi) − p),

p =

• 1 −

1

• j xj/Cj

+ . which is a Kelly [4, 9] type model of TCP behavior, adapted to the multiple rates scenario of wireless networks.

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TCP over 802.11: the downlink model

Putting the previous equations together we have: ˙ xi = k(xi)(U ′

i(xi) − p),

p =

• 1 −

1

• j xj/Cj

+ . which is a Kelly [4, 9] type model of TCP behavior, adapted to the multiple rates scenario of wireless networks. Which is the equilibrium of these dynamics? Is this equilibrium globally asymptotically stable?

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Characterizing the equilibrium

Consider the following convex optimization problem:

Problem 1

max

x

• i

1 Ci Ui(xi) − Φ(x) where: Φ(x) =

• i

xi Ci − 1 − log

• i

xi Ci

• ,

whenever

i xi Ci > 1 and 0 otherwise.

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Characterizing the equilibrium

Consider the following convex optimization problem:

Problem 1

max

x

• i

1 Ci Ui(xi) − Φ(x) where: Φ(x) =

• i

xi Ci − 1 − log

• i

xi Ci

• ,

whenever

i xi Ci > 1 and 0 otherwise.

We have the following:

Theorem

The equilibrium of the TCP dynamics is the unique optimum of Problem

• 1. This equilibrium is globally asymptotically stable.

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The modified Network problem

Problem 1 can be interpreted as a barrier function approximation of:

Modified Network Problem

max

x

• i

1 Ci Ui(xi) subject to the constraint:

• i

xi Ci 1

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The modified Network problem

Problem 1 can be interpreted as a barrier function approximation of:

Modified Network Problem

max

x

• i

1 Ci Ui(xi) subject to the constraint:

• i

xi Ci 1 This problem is related the Network problem of [4] to the wireless scenario, with two variants:

The constraint is rewritten in terms of xi/Ci, the “time proportion” the shared medium is used by connection i. The scaling factor Ci. This implies a negative bias to users with higher rates, since they would have less weight in the net utility.

Which is the effect of this bias?

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Slow users slow the whole network

Remark

In the case where all users share a common utility function (e.g. equal RTT TCP/Reno connections), the solution of the MNP reduces to x∗

i =

1

• j 1/Cj

, which is the harmonic mean of the data rates. This is in accordance with [5] where this rate is obtained as an upper bound on the realistic rate permanent connections experiment, and collisions are considered. As compared with [5], in our result the behavior of TCP is fully taken into account. Note that x∗

i minj Cj.

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Contents

1 The inefficiencies of TCP over 802.11. 2 TCP resource allocation in a multirate wireless environment 3 A more efficient resource allocation for a single cell 4 A word on more general topologies 5 Implementation and simulations 6 Conclusions

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Issues with the current allocation

The current implementation of TCP over wireless induces inefficiency. The MAC layer actually determines the allocation (as in previous example). Can we change things in order to get more throughput for the cell?

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Solving the right problem

The natural problem to solve would be:

Wireless Network Problem

max

x

• i

Ui(xi) subject to the constraint:

• i

xi Ci 1, This is similar to the problems in the scheduling literature (Lin et. al. [6]). Our purpose is to analyze how to achieve this optimum without resorting to a complicated scheduling mechanism in the AP.

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Achieving the WNP optimum

By considering the Lagrangian of WNP, we obtain a simple primal-dual gradient algorithm to solve this optimization: ˙ xi = k(xi)

• U ′

i(xi) − p

Ci

• ,

˙ p =

• i

xi Ci − 1 +

p

, It is well known [1, 3] that the trajectories of these dynamics converge globally to the optimum of WNP. Questions: what is p?, how to implement this?

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Price is queueing delay!

In congestion control literature, the dual variable has been interpreted as queueing delay [7, 8]. This is also the case here (proof in the paper).

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Price is queueing delay!

In congestion control literature, the dual variable has been interpreted as queueing delay [7, 8]. This is also the case here (proof in the paper). But this price must be scaled... Connections must react to a price scaled by Ci. ˙ xi = k(xi)

• U ′

i(xi) − p

Ci

• Moreover, typical TCPs react to losses instead of delay.

Can we overcome this issue?

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Price is queueing delay!

In congestion control literature, the dual variable has been interpreted as queueing delay [7, 8]. This is also the case here (proof in the paper). But this price must be scaled... Connections must react to a price scaled by Ci. ˙ xi = k(xi)

• U ′

i(xi) − p

Ci

• Moreover, typical TCPs react to losses instead of delay.

Can we overcome this issue? Answer: apply a Multirate RED algorithm in the queue.

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The Multirate RED algorithm (MRED)

MRED: is a simple Active Queue Management policy that emulates the previous primal-dual algorithm. Idea: use buffer content b as a proxy for queueing delay. The AP discards packets randomly with probability pi proportional to

b Ci for connection i.

Remark: we discard more packets when the buffer is full, and when the data rate is low. Moreover, this mechanism can be implemented in the AP resorting

• nly to local information (dst. address, current rate).

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Contents

1 The inefficiencies of TCP over 802.11. 2 TCP resource allocation in a multirate wireless environment 3 A more efficient resource allocation for a single cell 4 A word on more general topologies 5 Implementation and simulations 6 Conclusions

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Extending the model to general topologies

We would like to extend the previous analysis to general topologies, in particular:

mixed wired-wireless networks. multi-hop wireless.

Which constraints we have? 3 classes:

Classical wired:

i xi c.

Wireless multirate:

i xi ci 1.

Contention between cells constraints:

j αj 1, where αj is the

proportion of time each contending node is using the shared medium.

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The general NUM problem

It turns out that the general NUM problem in this case can be written as:

Wired-Wireless Network Problem

max

x

• i

Ui(xi) subject to: Hx 1. where H is a matrix that transforms input rate into link time proportions (summarizes the topology and contention).

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Example: wireless distribution scenario

An interesting example that can be modelled by the previous framework is:

AP1 AP2 Backhaul Access (C)

cAP1 cAP2 c1 c2 c3 c4

Figure: Mixed wired-wireless distribution system with 4 end-users.

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Solving the general NUM problem

By taking the Lagrangian of the general NUM problem and applying a primal-dual algorithm, we find that the correct price is again queueing delay at each contention graph. But it also must be scaled by link capacity. If there is a queue associated, then the price can be generated via MRED. However, decentralization is not always possible (details in the paper). Decentralization is indeed possible in tree topologies (like the previous example).

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Contents

1 The inefficiencies of TCP over 802.11. 2 TCP resource allocation in a multirate wireless environment 3 A more efficient resource allocation for a single cell 4 A word on more general topologies 5 Implementation and simulations 6 Conclusions

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Implementing MRED in ns-2

We implemented the proposed algorithms in ns-2 Two main issues were solved:

We adapted the dei80211mr library to implement destination based PHY rate to reflect the real behavior of APs. We programmed the MRED algorithm in a new Queue object that talks to the MAC layer.

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Implementing MRED in ns-2

We implemented the proposed algorithms in ns-2 Two main issues were solved:

We adapted the dei80211mr library to implement destination based PHY rate to reflect the real behavior of APs. We programmed the MRED algorithm in a new Queue object that talks to the MAC layer.

The algorithm: whenever a packet for next-hop j is received, it is discarded with probability pj = κb/Cj

κ acts as a scaling parameter. b is the current queue length. Cj is the corresponding effective rate for the current modulation rate the AP maintains with destination i. for wired links, Cj = C, the link capacity.

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Scenario 1: Single-cell

We simulated the following topology:

802.11 AP

Coverage Area

Bad link

Figure: Topology of a single-cell scenario.

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Scenario 1: Single-cell

3 users are connected with a modulation rate PHYi = 54Mbps... ...some time later a fourth user appears with PHY4 = 6Mbps. The effective data rates are: Ci ≈ 22.4Mbps, i = 1, 2, 3 and C4 ≈ 5.1Mbps

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Scenario 1: Single-cell without MRED

50 100 150 200 2 4 6 8 10 Time (s) Throughput (Mbps)

The throughputs converge approximately to the harmonic mean x∗

i = 3.0Mbps as predicted.

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Scenario 1: Single-cell WITH MRED

50 100 150 200 1 2 3 4 5 6 7 8 9 Time (s) Throughput (Mbps)

Now the throughputs converge approximately to the solution of the WNP, x∗

i = 4.2Mbps, i = 1, 2, 3 and x∗ 4 = 2.1Mbps!

Net throughput is increased by ≈ 20%.

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Scenario 2: wired-wireless network

We simulate the following topology:

AP

TCP1 TCP2

to check the model when utilities are not the same (different RTTs). PHY1 = 54Mbps and PHY2 = 6Mbps.

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Scenario 2: wired-wireless network. Results

10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 Time (s) Throughput (Mbps) TCP1 TCP2 10 20 30 40 50 60 70 80 90 1 2 3 4 5 6 7 Time (s) Throughput (Mbps) TCP1 TCP2

Figure: Wired-wireless topology simulation. Left: original allocation. Right: MRED algorithm.

The model predicts accurately both equilibriums. Applying MRED we

• btain again almost 20% throughput increase.

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Scenario 3: tree topology

We simulate the topology:

AP1 APn Internet

Access (Caccess) Distribution (Cdist) Distribution (Cdist)

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Scenario 3: tree topology. Results

Simulation parameters: caccess = 20Mbps representing a typical access capacity. cdist = 100Mbps (overprovisioned) Identical non-interfering wireless cells, PHY1 = PHY3 = 54Mbps and PHY2 = PHY4 = 6Mbps. Each user has a single TCP connection and all connections have equal RTTs. Plugging these values in the general NUM problem gives: x∗

1 = x∗ 3 = 6.5Mbps

x∗

2 = x∗ 4 = 3.5Mbps

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Scenario 3: tree topology. Results

10 20 30 40 50 60 70 80 1 2 3 4 5 6 7 8 9 10 Time (s) Throughput (Mbps) TCP1 TCP2 TCP3 TCP4

Figure: Throughputs of TCP connections for a wireless access scenario with 4

• users. MRED is in use.

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Contents

1 The inefficiencies of TCP over 802.11. 2 TCP resource allocation in a multirate wireless environment 3 A more efficient resource allocation for a single cell 4 A word on more general topologies 5 Implementation and simulations 6 Conclusions

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Conclusions

We applied the NUM framework to characterize the cross-layer interaction between the TCP and MAC layers where multiple modulation rates coexist. We analyzed the impact of overheads in the throughput of TCP connections. We described the resource allocation imposed by current wireless networks in this framework, characterizing its equilibrium through a suitable NUM problem. We proposed an alternative resource allocation that generalized the fairness and efficiency notions of wired networks. We also showed a simple mechanism to impose these more efficient equilibria in single cell scenarios and also showed possible generalizations of this procedure to more complex topologies. Simulations support the theoretical results.

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Future work

Determine the topologies where Multirate RED can be applied (when decentralization is possible?) Generalize these models to the case of IEEE 802.11n networks where:

Higher PHY rates are possible, so the overheads become a problem. Packet aggregation is used, so dropping packets must be done carefully.

Propose new message passing mechanisms (using the RTS/CTS?) to drive the network to the proposed allocation when MRED is not sufficient. Tie this analysis with connection level models.

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Thank you!

Andr´ es Ferragut (Universidad ORT (Uruguay)) NUM in multirate wireless networks RAWNET 2010 46 / 48

Questions?

Andr´ es Ferragut (Universidad ORT (Uruguay)) NUM in multirate wireless networks RAWNET 2010 46 / 48

Questions?

Mail: ferragut@ort.edu.uy

Andr´ es Ferragut (Universidad ORT (Uruguay)) NUM in multirate wireless networks RAWNET 2010 46 / 48

References I

• K. Arrow, L. Urwicz, and H. Uzawa.

Studies in Linear and Nonlinear Programming. Stanford University Press, Stanford, CA, 1958.

• G. Bianchi.

Performance analysis of the IEEE 802.11 distributed coordination function. IEEE Journal on Selected Areas in Communications, 18(3):535–547, Mar. 2000.

• D. Feijer and F. Paganini.

Krasovskii’s method in the stability of network control. In Proceedings of the American Control Conference, June 2009.

• F. Kelly, A. Maulloo, and D. Tan.

Rate control in communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research Society, 39:237–252, 1998.

Andr´ es Ferragut (Universidad ORT (Uruguay)) NUM in multirate wireless networks RAWNET 2010 47 / 48

References II

• A. Kumar, E. Altman, D. Miorandi, and M. Goyal.

New insights from a fixed-point analysis of single cell IEEE 802.11 WLANs. IEEE/ACM Transactions on Networking, 15(3):588–601, June 2007.

• X. Lin, N. B. Shroff, and R. Srikant.

A tutorial on cross-layer optimization in wireless networks. IEEE Journal on Selected Areas in Communication, pages 1452–1463, Aug. 2006.

• S. H. Low and D. Lapsley.

Optimization flow control, I: basic algorithm and convergence. IEEE/ACM Transactions on Networking, 7(6):861–874, 1999.

• S. H. Low, F. Paganini, and J. C. Doyle.

Internet congestion control. IEEE Control Systems Magazine, 22(1):28–43, Feb. 2002.

• R. Srikant.

The Mathematics of Internet Congestion Control. Birkh¨ auser, Boston, MA, 2004.

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