Internet Engineering Task Force (IETF)                         C. Raiciu
Request for Comments: 6356                Univ. Politehnica of Bucharest
Category: Experimental                                         M. Handly
ISSN: 2070-1721                                             D. Wischik
                                                    Univ. College London
                                                            October 2011
Internet Engineering Task Force (IETF)                         C. Raiciu
Request for Comments: 6356                Univ. Politehnica of Bucharest
Category: Experimental                                         M. Handly
ISSN: 2070-1721                                             D. Wischik
                                                    Univ. College London
                                                            October 2011

Coupled Congestion Control for Multipath Transport Protocols




Often endpoints are connected by multiple paths, but communications are usually restricted to a single path per connection. Resource usage within the network would be more efficient were it possible for these multiple paths to be used concurrently. Multipath TCP is a proposal to achieve multipath transport in TCP.


New congestion control algorithms are needed for multipath transport protocols such as Multipath TCP, as single path algorithms have a series of issues in the multipath context. One of the prominent problems is that running existing algorithms such as standard TCP independently on each path would give the multipath flow more than its fair share at a bottleneck link traversed by more than one of its subflows. Further, it is desirable that a source with multiple paths available will transfer more traffic using the least congested of the paths, achieving a property called "resource pooling" where a bundle of links effectively behaves like one shared link with bigger capacity. This would increase the overall efficiency of the network and also its robustness to failure.


This document presents a congestion control algorithm that couples the congestion control algorithms running on different subflows by linking their increase functions, and dynamically controls the overall aggressiveness of the multipath flow. The result is a practical algorithm that is fair to TCP at bottlenecks while moving traffic away from congested links.


Status of This Memo


This document is not an Internet Standards Track specification; it is published for examination, experimental implementation, and evaluation.


This document defines an Experimental Protocol for the Internet community. This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Not all documents approved by the IESG are a candidate for any level of Internet Standard; see Section 2 of RFC 5741.

本文档为互联网社区定义了一个实验协议。本文件是互联网工程任务组(IETF)的产品。它代表了IETF社区的共识。它已经接受了公众审查,并已被互联网工程指导小组(IESG)批准出版。并非IESG批准的所有文件都适用于任何级别的互联网标准;见RFC 5741第2节。

Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at


Copyright Notice


Copyright (c) 2011 IETF Trust and the persons identified as the document authors. All rights reserved.

版权所有(c)2011 IETF信托基金和确定为文件作者的人员。版权所有。

This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents ( in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.

本文件受BCP 78和IETF信托有关IETF文件的法律规定的约束(自本文件出版之日起生效。请仔细阅读这些文件,因为它们描述了您对本文件的权利和限制。从本文件中提取的代码组件必须包括信托法律条款第4.e节中所述的简化BSD许可证文本,并提供简化BSD许可证中所述的无担保。

Table of Contents


   1. Introduction ....................................................3
   2. Requirements Language ...........................................5
   3. Coupled Congestion Control Algorithm ............................5
   4. Implementation Considerations ...................................7
      4.1. Computing "alpha" in Practice ..............................7
      4.2. Implementation Considerations when CWND is
           Expressed in Packets .......................................8
   5. Discussion ......................................................9
   6. Security Considerations ........................................10
   7. Acknowledgements ...............................................11
   8. References .....................................................11
      8.1. Normative References ......................................11
      8.2. Informative References ....................................11
   1. Introduction ....................................................3
   2. Requirements Language ...........................................5
   3. Coupled Congestion Control Algorithm ............................5
   4. Implementation Considerations ...................................7
      4.1. Computing "alpha" in Practice ..............................7
      4.2. Implementation Considerations when CWND is
           Expressed in Packets .......................................8
   5. Discussion ......................................................9
   6. Security Considerations ........................................10
   7. Acknowledgements ...............................................11
   8. References .....................................................11
      8.1. Normative References ......................................11
      8.2. Informative References ....................................11
1. Introduction
1. 介绍

Multipath TCP (MPTCP, [MPTCP-MULTIADDRESSED]) is a set of extensions to regular TCP [RFC0793] that allows one TCP connection to be spread across multiple paths. MPTCP distributes load through the creation of separate "subflows" across potentially disjoint paths.


How should congestion control be performed for multipath TCP? First, each subflow must have its own congestion control state (i.e., cwnd) so that capacity on that path is matched by offered load. The simplest way to achieve this goal is to simply run standard TCP congestion control on each subflow. However, this solution is unsatisfactory as it gives the multipath flow an unfair share when the paths taken by its different subflows share a common bottleneck.


Bottleneck fairness is just one requirement multipath congestion control should meet. The following three goals capture the desirable properties of a practical multipath congestion control algorithm:


o Goal 1 (Improve Throughput) A multipath flow should perform at least as well as a single path flow would on the best of the paths available to it.

o 目标1(提高吞吐量)多路径流的性能应至少与单路径流在其可用的最佳路径上的性能相同。

o Goal 2 (Do no harm) A multipath flow should not take up more capacity from any of the resources shared by its different paths than if it were a single flow using only one of these paths. This guarantees it will not unduly harm other flows.

o 目标2(无害)与仅使用其中一条路径的单个流相比,多路径流不应从其不同路径共享的任何资源中占用更多容量。这保证了它不会不适当地损害其他流量。

o Goal 3 (Balance congestion) A multipath flow should move as much traffic as possible off its most congested paths, subject to meeting the first two goals.

o 目标3(平衡拥塞)多径流应在满足前两个目标的前提下,将尽可能多的流量移出其最拥挤的路径。

Goals 1 and 2 together ensure fairness at the bottleneck. Goal 3 captures the concept of resource pooling [WISCHIK]: if each multipath flow sends more data through its least congested path, the traffic in the network will move away from congested areas. This improves robustness and overall throughput, among other things. The way to achieve resource pooling is to effectively "couple" the congestion control loops for the different subflows.


We propose an algorithm that couples the additive increase function of the subflows, and uses unmodified TCP behavior in case of a drop. The algorithm relies on the traditional TCP mechanisms to detect drops, to retransmit data, etc.


Detecting shared bottlenecks reliably is quite difficult, but is just one part of a bigger question. This bigger question is how much bandwidth a multipath user should use in total, even if there is no shared bottleneck.


The congestion controller aims to set the multipath flow's aggregate bandwidth to be the same as that of a regular TCP flow would get on the best path available to the multipath flow. To estimate the bandwidth of a regular TCP flow, the multipath flow estimates loss rates and round-trip times (RTTs) and computes the target rate. Then, it adjusts the overall aggressiveness (parameter alpha) to achieve the desired rate.


While the mechanism above applies always, its effect depends on whether the multipath TCP flow influences or does not influence the link loss rates (low versus high statistical multiplexing). If MPTCP does not influence link loss rates, MPTCP will get the same throughput as TCP on the best path. In cases with low statistical multiplexing, where the multipath flow influences the loss rates on the path, the multipath throughput will be strictly higher than that a single TCP would get on any of the paths. In particular, if using two idle paths, multipath throughput will be sum of the two paths' throughput.


This algorithm ensures bottleneck fairness and fairness in the broader, network sense. We acknowledge that current TCP fairness criteria are far from ideal, but a multipath TCP needs to be deployable in the current Internet. If needed, new fairness criteria can be implemented by the same algorithm we propose by appropriately scaling the overall aggressiveness.


It is intended that the algorithm presented here can be applied to other multipath transport protocols, such as alternative multipath extensions to TCP, or indeed any other congestion-aware transport protocols. However, for the purposes of example, this document will, where appropriate, refer to the MPTCP.


The design decisions and evaluation of the congestion control algorithm are published in [NSDI].


The algorithm presented here only extends standard TCP congestion control for multipath operation. It is foreseeable that other congestion controllers will be implemented for multipath transport to achieve the bandwidth-scaling properties of the newer congestion control algorithms for regular TCP (such as Compound TCP and Cubic).


2. Requirements Language
2. 需求语言

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119] .

本文件中的关键词“必须”、“不得”、“要求”、“应”、“不应”、“应”、“不应”、“建议”、“可”和“可选”应按照RFC 2119[RFC2119]中所述进行解释。

3. Coupled Congestion Control Algorithm
3. 耦合拥塞控制算法

The algorithm we present only applies to the increase phase of the congestion avoidance state specifying how the window inflates upon receiving an ACK. The slow start, fast retransmit, and fast recovery algorithms, as well as the multiplicative decrease of the congestion avoidance state are the same as in standard TCP [RFC5681].


Let cwnd_i be the congestion window on the subflow i. Let cwnd_total be the sum of the congestion windows of all subflows in the connection. Let p_i, rtt_i, and MSS_i be the loss rate, round-trip time (i.e., smoothed round-trip time estimate used by TCP), and maximum segment size on subflow i.


We assume throughout this document that the congestion window is maintained in bytes, unless otherwise specified. We briefly describe the algorithm for packet-based implementations of cwnd in section Section 4.2.


Our proposed "Linked Increases" algorithm MUST:


o For each ACK received on subflow i, increase cwnd_i by

o 对于在子流i上接收到的每个ACK,将cwnd_i增加

                alpha * bytes_acked * MSS_i   bytes_acked * MSS_i
          min ( --------------------------- , ------------------- )  (1)
                         cwnd_total                   cwnd_i
                alpha * bytes_acked * MSS_i   bytes_acked * MSS_i
          min ( --------------------------- , ------------------- )  (1)
                         cwnd_total                   cwnd_i

The increase formula (1) takes the minimum between the computed increase for the multipath subflow (first argument to min), and the increase TCP would get in the same scenario (the second argument). In this way, we ensure that any multipath subflow cannot be more aggressive than a TCP flow in the same circumstances, hence achieving Goal 2 (do no harm).


"alpha" is a parameter of the algorithm that describes the aggressiveness of the multipath flow. To meet Goal 1 (improve throughput), the value of alpha is chosen such that the aggregate throughput of the multipath flow is equal to the throughput a TCP flow would get if it ran on the best path.


To get an idea of what the algorithm is trying to do, let's take the case where all the subflows have the same round-trip time and Maximum Segment Size (MSS). In this case, the algorithm will grow the total window by approximately alpha*MSS per RTT. This increase is distributed to the individual flows according to their instantaneous window size. Subflow i will increase by alpha*cwnd_i/cwnd_total segments per RTT.


Note that, as in standard TCP, when cwnd_total is large the increase may be 0. In this case, the increase MUST be set to 1. We discuss how to implement this formula in practice in the next section.


We assume implementations use an approach similar to appropriate byte counting (ABC, [RFC3465]), where the bytes_acked variable records the number of bytes newly acknowledged. If this is not the case, bytes_acked SHOULD be set to MSS_i.


To compute cwnd_total, it is an easy mistake to sum up cwnd_i across all subflows: when a flow is in fast retransmit, its cwnd is typically inflated and no longer represents the real congestion window. The correct behavior is to use the ssthresh (slow start threshold) value for flows in fast retransmit when computing cwnd_total. To cater to connections that are app limited, the computation should consider the minimum between flight_size_i and cwnd_i, and flight_size_i and ssthresh_i, where appropriate.

要计算cwnd_total,将所有子流中的cwnd_i相加很容易出错:当流处于快速重传时,其cwnd通常会膨胀,不再代表真正的拥塞窗口。正确的行为是在计算cwnd_total时,对快速重传中的流使用ssthresh(慢启动阈值)值。为了迎合APP有限的连接,计算应考虑FelthySsiZi I和CWNDWI I之间的最小值,以及FLASTYSIZEZI I和SSVeldHythi,在适当的情况下。

The total throughput of a multipath flow depends on the value of alpha and the loss rates, maximum segment sizes, and round-trip times of its paths. Since we require that the total throughput is no worse than the throughput a single TCP would get on the best path, it is impossible to choose, a priori, a single value of alpha that achieves the desired throughput in every occasion. Hence, alpha must be computed based on the observed properties of the paths.


The formula to compute alpha is:


                        MAX (cwnd_i/rtt_i^2)
   alpha = cwnd_total * -------------------------           (2)
                        (SUM (cwnd_i/rtt_i))^2
                        MAX (cwnd_i/rtt_i^2)
   alpha = cwnd_total * -------------------------           (2)
                        (SUM (cwnd_i/rtt_i))^2



MAX (x_i) means the maximum value for any possible value of i.


SUM (x_i) means the summation for all possible values of i.


The formula (2) is derived by equalizing the rate of the multipath flow with the rate of a TCP running on the best path, and solving for alpha.


4. Implementation Considerations
4. 实施考虑

Equation (2) implies that alpha is a floating point value. This would require performing costly floating point operations whenever an ACK is received. Further, in many kernels, floating point operations are disabled. There is an easy way to approximate the above calculations using integer arithmetic.


4.1. Computing "alpha" in Practice
4.1. 在实践中计算“alpha”

Let alpha_scale be an integer. When computing alpha, use alpha_scale * cwnd_total instead of cwnd_total and do all the operations in integer arithmetic.


Then, scale down the increase per ACK by alpha_scale. The resulting algorithm is a simple change from Equation (1):


o For each ACK received on subflow i, increase cwnd_i by:

o 对于在子流i上接收到的每个ACK,将cwnd_i增加:

                alpha * bytes_acked * MSS_i   bytes_acked * MSS_i
          min ( --------------------------- , ------------------- )  (3)
                 alpha_scale * cwnd_total              cwnd_i
                alpha * bytes_acked * MSS_i   bytes_acked * MSS_i
          min ( --------------------------- , ------------------- )  (3)
                 alpha_scale * cwnd_total              cwnd_i

The alpha_scale parameter denotes the precision we want for computing alpha. Observe that the errors in computing the numerator or the denominator in the formula for alpha are quite small, as the cwnd in bytes is typically much larger than the RTT (measured in ms).


With these changes, all the operations can be done using integer arithmetic. We propose alpha_scale be a small power of two, to allow using faster shift operations instead of multiplication and division. Our experiments show that using alpha_scale=512 works well in a wide range of scenarios. Increasing alpha_scale increases precision, but also increases the risk of overflow when computing alpha. Using 64- bit operations would solve this issue. Another option is to dynamically adjust alpha_scale when computing alpha; in this way, we avoid overflow and obtain maximum precision.


It is possible to implement the algorithm by calculating cwnd_total on each ack; however, this would be costly especially when the number of subflows is large. To avoid this overhead, the implementation MAY choose to maintain a new per-connection state variable called "cwnd_total". If it does so, the implementation will update the cwnd_total value whenever the individual subflow's windows are


updated. Updating only requires one more addition or subtraction operation compared to the regular, per-subflow congestion control code, so its performance impact should be minimal.


Computing alpha per ACK is also costly. We propose alpha be a per-connection variable, computed whenever there is a drop and once per RTT otherwise. More specifically, let cwnd_new be the new value of the congestion window after it is inflated or after a drop. Update alpha only if the quotient of cwnd_i/MSS_i differs from the quotient of cwnd_new_i/MSS_i.


In certain cases with small RTTs, computing alpha can still be expensive. We observe that if RTTs were constant, it is sufficient to compute alpha once per drop, as alpha does not change between drops (the insight here is that cwnd_i/cwnd_j = constant as long as both windows increase). Experimental results show that even if round-trip times are not constant, using average round-trip time per sawtooth instead of instantaneous round-trip time (i.e., TCP's smoothed RTT estimator) gives good precision for computing alpha. Hence, it is possible to compute alpha only once per drop using a modified version of equation (2) where rtt_i is replaced with rtt_avg_i.


If using average round-trip time, rtt_avg_i will be computed by sampling the rtt_i whenever the window can accommodate one more packet, i.e., when cwnd / MSS < (cwnd+increase)/MSS. The samples are averaged once per sawtooth into rtt_avg_i. This sampling ensures that there is no sampling bias for larger windows.


Given cwnd_total and alpha, the congestion control algorithm is run for each subflow independently, with similar complexity to the standard TCP increase code [RFC5681].


4.2. Implementation Considerations when CWND is Expressed in Packets
4.2. 以数据包表示CWND时的实现注意事项

When the congestion control algorithm maintains cwnd in packets rather than bytes, the algorithms above must change to take into account path MSS.


To compute the increase when an ACK is received, the implementation for multipath congestion control is a simple extension of the standard TCP code. In standard, TCP cwnd_cnt is an additional state variable that tracks the number of segments acked since the last cwnd increment; cwnd is incremented only when cwnd_cnt > cwnd; then, cwnd_cnt is set to 0.

为了计算接收到ACK时的增量,多径拥塞控制的实现是标准TCP代码的简单扩展。在标准中,TCP cwnd_cnt是一个额外的状态变量,用于跟踪自上次cwnd增量以来确认的段数;仅当cwnd_cnt>cwnd时,cwnd才递增;然后,将cwnd_cnt设置为0。

In the multipath case, cwnd_cnt_i is maintained for each subflow as above, and cwnd_i is increased by 1 when cwnd_cnt_i > max(alpha_scale * cwnd_total / alpha, cwnd_i).


When computing alpha for packet-based stacks, the errors in computing the terms in the denominator are larger (this is because cwnd is much smaller and rtt may be comparatively large). Let max be the index of the subflow used in the numerator. To reduce errors, it is easiest to move rtt_max (once calculated) from the numerator to the denominator, changing equation (2) to obtain the equivalent formula below.




 alpha = alpha_scale * cwnd_total * ------------------------------------
                                    (SUM ((rtt_max * cwnd_i) / rtt_i))^2
 alpha = alpha_scale * cwnd_total * ------------------------------------
                                    (SUM ((rtt_max * cwnd_i) / rtt_i))^2

Note that the calculation of alpha does not take into account path MSS and is the same for stacks that keep cwnd in bytes or packets. With this formula, the algorithm for computing alpha will match the rate of TCP on the best path in B/s for byte-oriented stacks, and in packets/s in packet-based stacks. In practice, MSS rarely changes between paths so this shouldn't be a problem.


However, it is simple to derive formulae allowing packet-based stacks to achieve byte rate fairness (and vice versa) if needed. In particular, for packet-based stacks wanting byte-rate fairness, equation (4) above changes as follows: cwnd_max is replaced by cwnd_max * MSS_max * MSS_max, while cwnd_i is replaced with cwnd_i * MSS_i.


5. Discussion
5. 讨论

The algorithm we've presented fully achieves Goals 1 and 2, but does not achieve full resource pooling (Goal 3). Resource pooling requires that no traffic should be transferred on links with higher loss rates. To achieve perfect resource pooling, one must couple both increase and decrease of congestion windows across subflows, as in [KELLY].


There are a few problems with such a fully coupled controller. First, it will insufficiently probe paths with high loss rates and will fail to detect free capacity when it becomes available. Second, such controllers tend to exhibit "flappiness": when the paths have similar levels of congestion, the congestion controller will tend to allocate all the window to one random subflow and allocate zero


window to the other subflows. The controller will perform random flips between these stable points. This doesn't seem desirable in general, and is particularly bad when the achieved rates depend on the RTT (as in the current Internet): in such a case, the resulting rate with fluctuate unpredictably depending on which state the controller is in, hence violating Goal 1.


By only coupling increases our proposal probes high loss paths, detecting free capacity quicker. Our proposal does not suffer from flappiness but also achieves less resource pooling. The algorithm will allocate window to the subflows such that p_i * cwnd_i = constant, for all i. Thus, when the loss rates of the subflows are equal, each subflow will get an equal window, removing flappiness. When the loss rates differ, progressively more windows will be allocated to the flow with the lower loss rate. In contrast, perfect resource pooling requires that all the window should be allocated on the path with the lowest loss rate. Further details can be found in [NSDI].


6. Security Considerations
6. 安全考虑

One security concern relates to what we call the traffic-shifting attack: on-path attackers can drop packets belonging to a multipath subflow, which, in turn, makes the path seem congested and will force the sender's congestion controller to avoid that path and push more data over alternate subflows.


The attacker's goal is to create congestion on the corresponding alternative paths. This behavior is entirely feasible but will only have minor effects: by design, the coupled congestion controller is less (or similarly) aggressive on any of its paths than a single TCP flow. Thus, the biggest effect this attack can have is to make a multipath subflow be as aggressive as a single TCP flow.


Another effect of the traffic-shifting attack is that the new path can monitor all the traffic, whereas before it could only see a subset of traffic. We believe that if privacy is needed, splitting traffic across multiple paths with MPTCP is not the right solution in the first place; end-to-end encryption should be used instead.


Besides the traffic-shifting attack mentioned above, the coupled congestion control algorithm defined in this document adds no other security considerations to those found in [MPTCP-MULTIADDRESSED] and [RFC6181]. Detailed security analysis for the Multipath TCP protocol itself is included in [MPTCP-MULTIADDRESSED] and [RFC6181].


7. Acknowledgements
7. 致谢

We thank Christoph Paasch for his suggestions for computing alpha in packet-based stacks. The authors are supported by Trilogy (, a research project (ICT-216372) partially funded by the European Community under its Seventh Framework Program. The views expressed here are those of the author(s) only. The European Commission is not liable for any use that may be made of the information in this document.

我们感谢Christoph Paasch提出的在基于包的堆栈中计算alpha的建议。作者得到了三部曲的支持(,一个研究项目(ICT-216372),部分由欧洲共同体根据其第七个框架计划资助。此处表达的观点仅为作者的观点。欧盟委员会对可能使用本文件中的信息不承担任何责任。

8. References
8. 工具书类
8.1. Normative References
8.1. 规范性引用文件

[RFC0793] Postel, J., "Transmission Control Protocol", STD 7, RFC 793, September 1981.

[RFC0793]Postel,J.,“传输控制协议”,标准7,RFC 793,1981年9月。

[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997.

[RFC2119]Bradner,S.,“RFC中用于表示需求水平的关键词”,BCP 14,RFC 2119,1997年3月。

[RFC5681] Allman, M., Paxson, V., and E. Blanton, "TCP Congestion Control", RFC 5681, September 2009.

[RFC5681]Allman,M.,Paxson,V.和E.Blanton,“TCP拥塞控制”,RFC 56812009年9月。

8.2. Informative References
8.2. 资料性引用

[KELLY] Kelly, F. and T. Voice, "Stability of end-to-end algorithms for joint routing and rate control", ACM SIGCOMM CCR vol. 35 num. 2, pp. 5-12, 2005, <>.

[KELLY]KELLY,F.和T.Voice,“用于联合路由和速率控制的端到端算法的稳定性”,ACM SIGCOMM CCR第35卷第2期,第5-12页,2005年<>.

[MPTCP-MULTIADDRESSED] Ford, A., Raiciu, C., Handley, M., and O. Bonaventure, "TCP Extensions for Multipath Operation with Multiple Addresses", Work in Progress, July 2011.


[NSDI] Wischik, D., Raiciu, C., Greenhalgh, A., and M. Handley, "Design, Implementation and Evaluation of Congestion Control for Multipath TCP", Usenix NSDI , March 2011, <htt p://>.

[NSDI]Wischik,D.,Raiciu,C.,Greenhalgh,A.,和M.Handley,“多路径TCP拥塞控制的设计、实施和评估”,Usenix NSDI,2011年3月,<htt p:// NSDI.pdf>。

[RFC3465] Allman, M., "TCP Congestion Control with Appropriate Byte Counting (ABC)", RFC 3465, February 2003.

[RFC3465]Allman,M.,“具有适当字节计数的TCP拥塞控制(ABC)”,RFC 3465,2003年2月。

[RFC6181] Bagnulo, M., "Threat Analysis for TCP Extensions for Multipath Operation with Multiple Addresses", RFC 6181, March 2011.

[RFC6181]Bagnulo,M.,“具有多个地址的多路径操作的TCP扩展的威胁分析”,RFC 61812011年3月。

[WISCHIK] Wischik, D., Handley, M., and M. Bagnulo Braun, "The Resource Pooling Principle", ACM SIGCOMM CCR vol. 38 num. 5, pp. 47-52, October 2008, <>.

[WISCHIK]WISCHIK,D.,Handley,M.和M.Bagnulo Braun,“资源池原则”,ACM SIGCOMM CCR第38卷第5期,第47-52页,2008年10月<>.

Authors' Addresses


Costin Raiciu University Politehnica of Bucharest Splaiul Independentei 313 Bucharest Romania



Mark Handley University College London Gower Street London WC1E 6BT UK

马克·汉德利大学学院伦敦高尔街伦敦WC1E 6BT英国


Damon Wischik University College London Gower Street London WC1E 6BT UK

Damon Wischik大学学院伦敦高尔街伦敦WC1E 6BT英国