Internet Engineering Task Force A.
Ford, Ed.Ford Internet-Draft Roke Manor Research Intended status: Informational C. Raiciu Expires: July 15,25, 2011 M. Handley University College London S. Barre Universite catholique de Louvain J. Iyengar Franklin and Marshall College January 11,21, 2011 Architectural Guidelines for Multipath TCP Development draft-ietf-mptcp-architecture-04draft-ietf-mptcp-architecture-05 Abstract Hosts are often connected by multiple paths, but TCP restricts communications to a single path per transport connection. Resource usage within the network would be more efficient were these multiple paths able to be used concurrently. This should enhance user experience through improved resilience to network failure and higher throughput. This document outlines architectural guidelines for the development of a Multipath Transport Protocol, with references to how these architectural components come together in the development of a Multipath TCP protocol. This document lists certain high level design decisions that provide foundations for the design of the MPTCP protocol, based upon these architectural requirements. Status of this Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." This Internet-Draft will expire on July 15,25, 2011. Copyright Notice Copyright (c) 2011 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) 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. Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1. Requirements Language . . . . . . . . . . . . . . . . . . 5 1.2. Terminology . . . . . . . . . . . . . . . . . . . . . . . 5 1.3. Reference Scenario . . . . . . . . . . . . . . . . . . . . 56 2. Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1. Functional Goals . . . . . . . . . . . . . . . . . . . . . 6 2.2. Compatibility Goals . . . . . . . . . . . . . . . . . . . 7 2.2.1. Application Compatibility . . . . . . . . . . . . . . 7 2.2.2. Network Compatibility . . . . . . . . . . . . . . . . 78 2.2.3. Compatibility with other network users . . . . . . . . 9 2.3. Security Goals . . . . . . . . . . . . . . . . . . . . . . 910 2.4. Related Protocols . . . . . . . . . . . . . . . . . . . . 910 3. An Architectural Basis For Multipath TCP . . . . . . . . . . . 10 4. A Functional Decomposition of MPTCP . . . . . . . . . . . . . 12 5. High-Level Design Decisions . . . . . . . . . . . . . . . . . 1314 5.1. Sequence Numbering . . . . . . . . . . . . . . . . . . . . 14 5.2. Reliability and Retransmissions . . . . . . . . . . . . . 15 5.3. Buffers . . . . . . . . . . . . . . . . . . . . . . . . . 1617 5.4. Signalling . . . . . . . . . . . . . . . . . . . . . . . . 1718 5.5. Path Management . . . . . . . . . . . . . . . . . . . . . 1819 5.6. Connection Identification . . . . . . . . . . . . . . . . 1920 5.7. Congestion Control . . . . . . . . . . . . . . . . . . . . 2021 5.8. Security . . . . . . . . . . . . . . . . . . . . . . . . . 2021 6. Software Interactions . . . . . . . . . . . . . . . . . . . . 22 6.1. Interactions with Applications . . . . . . . . . . . . . . 22 6.2. Interactions with Management Systems . . . . . . 21. . . . . 23 7. Interactions with Middleboxes . . . . . . . . . . . . . . . . 2223 8. Contributors . . . . . . . . . . . . . . . . . . . . . . . . . 2425 9. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 2425 10. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 2425 11. Security Considerations . . . . . . . . . . . . . . . . . . . 2425 12. References . . . . . . . . . . . . . . . . . . . . . . . . . . 2426 12.1. Normative References . . . . . . . . . . . . . . . . . . . 2426 12.2. Informative References . . . . . . . . . . . . . . . . . . 2526 Appendix A. Changelog . . . . . . . . . . . . . . . . . . . . . . 2628 A.1. Changes since draft-ietf-mptcp-architecture-03draft-ietf-mptcp-architecture-04 . . . . . . 2628 A.2. Changes since draft-ietf-mptcp-architecture-02draft-ietf-mptcp-architecture-03 . . . . . . 2628 A.3. Changes since draft-ietf-mptcp-architecture-01draft-ietf-mptcp-architecture-02 . . . . . . 2628 A.4. Changes since draft-ietf-mptcp-architecture-01 . . . . . . 28 A.5. Changes since draft-ietf-mptcp-architecture-00 . . . . . . 2728 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 2728 1. Introduction As the Internet evolves, demands on Internet resources are ever- increasing, but often these resources (in particular, bandwidth) cannot be fully utilised due to protocol constraints both on the end- systems and within the network. If these resources could insteadbe used concurrently, end user experience could be greatly improved. Such enhancements would also reduce the necessary expenditure on network infrastructure that would otherwise be needed to create an equivalent improvement in user experience. By the application of resource pooling , these available resources can be 'pooled' such that they appear as a single logical resource to the user. The purpose of a multipath transport, therefore, isMultipath transport aims to makerealize some of the goals of resource pooling by simultaneously making use of multiple available paths, through resource pooling, to bringdisjoint (or partially disjoint) paths across a network. The two key benefits:benefits of multipath transport are: o To increase the resilience of the connectivity by providing multiple paths, protecting end hosts from the failure of one. o To increase the efficiency of the resource usage, and thus increase the network capacity available to end hosts. Multipath TCP is a modified version of TCP  that implements a multipath transport and achieves these goals by pooling multiple paths within a transport connection, transparently to the application. Multipath TCP is primarily concerned with utilising multiple paths end-to-end, where one or both end host is multi-homed. It may also have applications where multiple paths exist within the network and can be manipulated by an end host, such as using different port numbers with ECMP . MPTCP, defined in ,, is a specific protocol that instantiates the Multipath TCP concept. This document looks both at general architectural principles for a Multipath TCP fulfilling the goals described in Section 2, as well as the key design decisions behind MPTCP, which are detailed in Section 5. Although multihoming and multipath functions are not new to transport protocols (SCTP  being a notable example), MPTCP aims to gain wide-scale deployment by recognising the importance of application and network compatibility goals. These goals, discussed in detail in Section 2, relate to the appearance of MPTCP to the network (so non- MPTCP-aware entities see it as TCP) and to the application (through providing an equivalentservice equivalent to TCP tofor non-MPTCP-aware applications). This document has three key purposes: (i) it describes goals for a multipath transport - goals that MPTCP is designed to meet; (ii) it lays out an architectural basis for MPTCP's design - a discussion that applies to other multipath transports as well; and (iii) it discusses and documents high-level design decisions made in MPTCP's development, and considers their implications. Companion documents to this architectural overview are those which provide details of the protocol extensions ,, congestion control algorithms ,, and application-level considerations .. Put together, these components specify a complete Multipath TCP design. We note that specific components are replaceable in accordance with the layer and functional decompositions discussed in this document. 1.1. Requirements Language 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 . 1.2. Terminology Regular/Single-Path TCP: The standard version of the TCP  protocol in use today, operating between a single pair of IP addresses. Multipath TCP: A modified version of the TCP protocol that supports the simultaneous use of multiple paths between hosts. Path: A sequence of links between a sender and a receiver, defined in this context by a source and destination address pair. Host: An end host either initiating or terminating a Multipath TCP connection. MPTCP: The proposed protocol extensions specified in  to provide a Multipath TCP implementation. Subflow: A flow of TCP segments operating over an individual path, which forms part of a larger Multipath TCP connection. (Multipath TCP) Connection: A set of one or more subflows combined to provide a single Multipath TCP service to an application at a host. 1.3. Reference Scenario The diagram shown in Figure 1 illustrates a typical usage scenario for Multipath TCP. Two hosts, A and B, are communicating with each other. These hosts are multi-homed and multi-addressed, providing two disjoint connections to the Internet. The addresses on each host are referred to as A1, A2, B1 and B2. There are therefore up to four different paths between the two hosts: A1-B1, A1-B2, A2-B1, A2-B2. +------+ __________ +------+ | |A1 ______ ( ) ______ B1| | | Host |--/ ( ) \--| Host | | | ( Internet ) | | | A |--\______( )______/--| B | | |A2 (__________) B2| | +------+ +------+ Figure 1: Simple Multipath TCP Usage Scenario The scenario could have any number of addresses (1 or more) on each host, soas long as the number of paths available between the two hosts is 2 or more (i.e. num_addr(A) * num_addr(B) > 1). The paths created by these address combinations through the Internet need not be entirely disjoint - potential fairness issues introduced by shared bottlenecks need to be handled by the Multipath TCP congestion controller. Furthermore, the paths through the Internet often do not provide a pure end-to-end service, and instead may be affected by middleboxes such as NATs and Firewalls. 2. Goals This section outlines primary goals that Multipath TCP aims to meet. These are broadly broken down into: functional goals, which steer services and features that Multipath TCP must provide; and compatibility goals, which determine how Multipath TCP should appear to entities that interact with it. 2.1. Functional Goals In supporting the use of multiple paths, Multipath TCP has the following two functional goals. o Improve Throughput: Multipath TCP MUST support the concurrent use of multiple paths. To meet the minimum performance incentives for deployment, a Multipath TCP connection over multiple paths SHOULD achieve no lesser throughput than a single TCP connection over the best constituent path. o Improve Resilience: Multipath TCP MUST support the use of multiple paths interchangeably for resilience purposes, by permitting segments to be sent and re-sent on any available path. It follows that, in the worst case, the protocol MUST be no less resilient than regular single-path TCP. As distribution of traffic among available paths and responses to congestion are done in accordance with resource pooling principles , a secondary effect of meeting these goals is that widespread use of Multipath TCP over the Internet should improve overall network utility by shifting load away from congested bottlenecks and by taking advantage of spare capacity wherever possible. Furthermore, Multipath TCP SHOULD feature automatic negotiation of its use. A host supporting Multipath TCP that requires the other host to do so too must be able to detect reliably whether this host does in fact support the required extensions, using them if so, and otherwise automatically falling back to single-path TCP. 2.2. Compatibility Goals In addition to the functional goals listed above, a Multipath TCP must meet a number of compatibility goals in order to support deployment in today's Internet. These goals fall into the following categories: 2.2.1. Application Compatibility Application compatibility refers to the appearance of Multipath TCP to the application both in terms of the API that can be used and the expected service model that is provided. Multipath TCP MUST follow the same service model as TCP : in- order, reliable, and byte-oriented delivery. Furthermore, a Multipath TCP connection SHOULD provide the application with no worse throughput or resilience than it would expect from running a single TCP connection over any one of its available paths. A Multipath TCP may not, however, be able to provide the same level of consistency of throughput and latency as a single TCP connection. These, and other, application considerations are discussed in detail in . A multipath-capable equivalent of TCP MUST retain some level of backward compatibility with existing TCP APIs, so that existing applications can use the newer transport merely by upgrading the operating systems of the end-hosts. This does not preclude the use of an advanced API to permit multipath-aware applications to specify preferences, nor for users to configure their systems in a different way from the default, for example switching on or off the automatic use of multipath extensions. 2.2.2. Network Compatibility In the traditional Internet architecture, network devices operate at the network layer and lower layers, with the layersIt is possible for regular TCP sessions today to survive brief breaks in connectivity by retaining state at end hosts before a timeout occurs. It would be desirable to support similar session continuity in MPTCP, however the circumstances could be different. Whilst in regular TCP the IP addresses will remain constant across the break in connectivity, in MPTCP a different interface may appear. It is desirable (but not mandated) to support this kind of "break-before- make" session continuity. This places constraints on security mechanisms, however, as discussed in Section 5.8. Timeouts for this function would be locally configured. 2.2.2. Network Compatibility In the traditional Internet architecture, network devices operate at the network layer and lower layers, with the layers above the network layer instantiated only at the end-hosts. While this architecture, shown in Figure 2, was initially largely adhered to, this layering no longer reflects the "ground truth" in the Internet with the proliferation of middleboxes .. Middleboxes routinely interpose on the transport layer; sometimes even completely terminating transport connections, thus leaving the application layer as the first real end-to-end layer, as shown in Figure 3. +-------------+ +-------------+ | Application |<------------ end-to-end ------------->| Application | +-------------+ +-------------+ | Transport |<------------ end-to-end ------------->| Transport | +-------------+ +-------------+ +-------------+ +-------------+ | Network |<->| Network |<->| Network |<->| Network | +-------------+ +-------------+ +-------------+ +-------------+ End Host Router Router End Host Figure 2: Traditional Internet Architecture +-------------+ +-------------+ | Application |<------------ end-to-end ------------->| Application | +-------------+ +-------------+ +-------------+ | Transport |<------------------->| Transport |<->| Transport | +-------------+ +-------------+ +-------------+ +-------------+ | Network |<->| Network |<->| Network |<->| Network | +-------------+ +-------------+ +-------------+ +-------------+ Firewall, End Host Router NAT, or Proxy End Host Figure 3: Internet Reality Middleboxes that interpose on the transport layer result in loss of "fate-sharing" ,, that is, they often hold "hard" state that, when lost or corrupted, results in loss or corruption of the end-to-end transport connection. The network compatibility goal requires that the multipath extension to TCP retains compatibility with the Internet as it exists today, including making reasonable efforts to be able to traverse predominant middleboxes such as firewalls, NATs, and performance enhancing proxies .. This requirement comes from recognizing middleboxes as a significant deployment bottleneck for any transport that is not TCP or UDP, and constrains Multipath TCP to appear as TCP does on the wire and to use established TCP extensions where necessary. To ensure end-to-endness of the transport, we further require Multipath TCP to preserve fate-sharing without making any assumptions about middlebox behavior. A detailed analysis of middlebox behaviour and the impact on the Multipath TCP architecture is presented in Section 7. In addition, network compatibility must be retained to the extent that Multipath TCP MUST fall back to regular TCP if there are insurmountable incompatibilities for the multipath extension on a path. Middleboxes may also cause some TCP features to be able to exist on one subflow but not another. Typically these will be at the subflow level (such as SACK )) and thus do not affect the connection-level behaviour. In the future, any proposed TCP connection-level extensions should consider how they can co-exist with MPTCP. The modifications to support Multipath TCP remain at the transport layer, although some knowledge of the underlying network layer is required. Multipath TCP SHOULD work with IPv4 and IPv6 interchangeably, i.e. one connection may operate over both IPv4 and IPv6 networks. 2.2.3. Compatibility with other network users As a corollary to both network and application compatibility, the architecture must enable new Multipath TCP flows to coexist gracefully with existing single-path TCP flows, competing for bandwidth neither unduly aggressively nor unduly timidly (unless low- precedence operation is specifically requested by the application, such as with LEDBAT). The use of multiple paths MUST NOT unduly harm users using single-path TCP at shared bottlenecks, beyond the impact that would occur from another single-path TCP flow. Multiple Multipath TCP flows on a shared bottleneck MUST share bandwidth between each other with similar fairness to that which occurs at a shared bottleneck with single-path TCP. 2.3. Security Goals The extension of TCP with multipath capabilities will bring with it a number of new threats, analysed in detail in .. The security goal for Multipath TCP is to provide a service no less secure than regular, single-path TCP. This will be achieved through a combination of existing TCP security mechanisms (potentially modified to align with the Multipath TCP extensions) and of protection against the new multipath threats identified. The design decisions derived from this goal are presented in Section 5.8. 2.4. Related Protocols There are several similarities between SCTP  and MPTCP, in that both can make use of multiple addresses at end hosts to give some multi-path capability. In SCTP, the primary use case is to support redundancy and mobility for multihomed hosts (i.e. a single path will change one of its end host addresses); the simultaneous use of multiple paths is not supported . Extensions are proposed to support simultaneous multipath transport ,, but these are yet to be standardised. By far the most widely used stream-based transport protocol is, however, TCP , and SCTP does not meet the network and application compatibility goals specified in Section 2.2. For network compatibility, there are issues with various middleboxes (especially NATs) that are unaware of SCTP and consequently end up blocking it. For application compatibility, applications need to actively choose to use SCTP, and with the deployment issues very few choose to do so. MPTCP's compatibility goals are in part based on these observations of SCTP's deployment issues. 3. An Architectural Basis For Multipath TCP We now present one possible transport architecture that we believe can effectively support the goals for Multipath TCP. The new Internet model described here is based on ideas proposed earlier in Tng ("Transport next-generation") .. While by no means the only possible architecture supporting multipath transport, Tng incorporates many lessons learned from previous transport research and development practice, and offers a strong starting point from which to consider the extant Internet architecture and its bearing on the design of any new Internet transports or transport extensions. +------------------+ | Application | +------------------+ ^ Application-oriented transport | | | functions (Semantic Layer) + - - Transport - -+ ---------------------------------- | | | Network-oriented transport +------------------+ v functions (Flow+Endpoint Layer) | Network | +------------------+ Existing Layers Tng Decomposition Figure 4: Decomposition of Transport Functions Tng loosely splits the transport layer into "application-oriented" and "network-oriented" layers, as shown in Figure 4. The application-oriented "Semantic" layer implements functions driven primarily by concerns of supporting and protecting the application's end-to-end communication, while the network-oriented "Flow+Endpoint" layer implements functions such as endpoint identification (using port numbers) and congestion control. These network-oriented functions, while traditionally located in the ostensibly "end-to-end" Transport layer, have proven in practice to be of great concern to network operators and the middleboxes they deploy in the network to enforce network usage policies   or optimize communication performance .. Figure 5 shows how middleboxes interact with different layers in this decomposed model of the transport layer: the application-oriented layer operates end-to-end, while the network- oriented layer operates "segment-by-segment" and can be interposed upon by middleboxes. +-------------+ +-------------+ | Application |<------------ end-to-end ------------->| Application | +-------------+ +-------------+ | Semantic |<------------ end-to-end ------------->| Semantic | +-------------+ +-------------+ +-------------+ +-------------+ |Flow+Endpoint|<->|Flow+Endpoint|<->|Flow+Endpoint|<->|Flow+Endpoint| +-------------+ +-------------+ +-------------+ +-------------+ | Network |<->| Network |<->| Network |<->| Network | +-------------+ +-------------+ +-------------+ +-------------+ Firewall Performance End Host or NAT Enhancing Proxy End Host Figure 5: Middleboxes in the new Internet model MPTCP's architectural design follows Tng's decomposition as shown in Figure 6. MPTCP, which provides application compatibility through the preservation of TCP-like semantics of global ordering of application data and reliability, is an instantiation of the "application-oriented" Semantic layer; whereas the subflow TCP component, which provides network compatibility by appearing and behaving as a TCP flow in the network, is an instantiation of the "network-oriented" Flow+Endpoint layer. +--------------------------+ +-------------------------------+ | Application | | Application | +--------------------------+ +-------------------------------+ | Semantic | | MPTCP | |------------+-------------| + - - - - - - - + - - - - - - - + | Flow+Endpt | Flow+Endpt | | Subflow (TCP) | Subflow (TCP) | +------------+-------------+ +---------------+---------------+ | Network | Network | | IP | IP | +------------+-------------+ +---------------+---------------+ Figure 6: Relationship between Tng (left) and MPTCP (right) As a protocol extension to TCP, MPTCP thus explicitly acknowledges middleboxes in its design, and specifies a protocol that operates at two scales: the MPTCP component operates end-to-end, while it allows the TCP component to operate segment-by-segment. 4. A Functional Decomposition of MPTCP The previous two sections have discussed the goals for a Multipath TCP design, and provided a basis for decomposing the functions of a transport protocol in order to better understand the form a solution should take. This section builds upon this analysis by presenting the functional components that are used within the MPTCP design. MPTCP makes use of (what appear to the network to be) standard TCP sessions, termed "subflows", to provide the underlying transport per path, and as such these retain the network compatibility desired. MPTCP-specific information is carried in a TCP-compatible manner, although this mechanism is separate from the actual information being transferred so could evolve in future revisions. Figure 7 illustrates the layered architecture. +-------------------------------+ | Application | +---------------+ +-------------------------------+ | Application | | MPTCP | +---------------+ + - - - - - - - + - - - - - - - + | TCP | | Subflow (TCP) | Subflow (TCP) | +---------------+ +-------------------------------+ | IP | | IP | IP | +---------------+ +-------------------------------+ Figure 7: Comparison of Standard TCP and MPTCP Protocol Stacks Situated below the application, the MPTCP extension in turn manages multiple TCP subflows below it. In order to do this, it must implement the following functions: o Path Management: This is the function to detect and use multiple paths between two hosts. MPTCP uses the presence of multiple IP addresses at one or both of the hosts as an indicator of this. The path management features of the MPTCP protocol are the mechanisms to signal alternative addresses to hosts, and mechanisms to set up new subflows joined to an existing MPTCP connection. o Packet Scheduling: This function breaks the bytestream received from the application into segments to be transmitted on one of the available subflows. The MPTCP design makes use of a data sequence mapping, associating segments sent on different subflows to a connection-level sequence numbering, thus allowing segments sent on different subflows to be correctly re-ordered at the receiver. The packet scheduler is dependent upon information about the availability of paths exposed by the path management component, and then makes use of the subflows to transmit queued segments. This function is also responsible for connection-level re-ordering on receipt of packets from the TCP subflows, according to the attached data sequence mappings. o Subflow (single-path TCP) Interface: A subflow component takes segments from the packet-scheduling component and transmits them over the specified path, ensuring detectable delivery to the host. MPTCP uses TCP underneath for network compatibility; TCP ensures in-order, reliable delivery. TCP adds its own sequence numbers to the segments; these are used to detect and retransmit lost packets at the subflow layer. On receipt, the subflow passes its reassembled data to the packet scheduling component for connection-level reassembly; the data sequence mapping from the sender's packet scheduling component allows re-ordering of the entire bytestream. o Congestion Control: This function coordinates congestion control across the subflows. As specified, this congestion control algorithm MUST ensure that a MPTCP connection does not unfairly take more bandwidth than a single path TCP flow would take at a shared bottleneck. An algorithm to support this is specified in .. These functions fit together as follows. The Path Management looks after the discovery (and if necessary, initialisation) of multiple paths between two hosts. The Packet Scheduler then receives a stream of data from the application destined for the network, and undertakes the necessary operations on it (such as segmenting the data into connection-level segments, and adding a connection-level sequence number) before sending it on to a subflow. The subflow then adds its own sequence number, ACKs, and passes them to network. The receiving subflow re-orders data (if necessary) and passes it to the packet scheduling component, which performs connection level re-ordering, and sends the data stream to the application. Finally, the congestion control component exists as part of the packet scheduling, in order to schedule which segments should be sent at what rate on which subflow. 5. High-Level Design Decisions There is seemingly a wide range of choices when designing a multipath extension to TCP. However, the goals as discussed earlier in this document constrain the possible solutions, leaving relative little choice in many areas. Here, we outline high-level design choices that draw from the architectural basis discussed earlier in Section 3, which the design of MPTCP  takes into account. 5.1. Sequence Numbering MPTCP uses two levels of sequence spaces: a connection level sequence number, and another sequence number for each subflow. This permits connection-level segmentation and reassembly, and retransmission of the same part of connection-level sequence space on different subflow-level sequence space. The alternative approach would be to use a single connection level sequence number, which gets sent on multiple subflows. This has two problems: first, the individual subflows will appear to the network as TCP sessions with gaps in the sequence space; this in turn may upset certain middleboxes such as intrusion detection systems, or certain transparent proxies, and would thus go against the network compatibility goal. Second, the sender would not be able to attribute packet losses or receptions to the correct path when the same segment is sent on multiple paths (i.e. in the case of retransmissions). The sender must be able to tell the receiver how to reassemble the data, for delivery to the application. In order to achieve this, the receiver must determine how subflow-level data (carrying subflow sequence numbers) maps at the connection level. We refer to this as the Data Sequence Mapping. This mapping takes the form (data seq, subflow seq, length), i.e. for a given number of bytes (the length), the subflow sequence space beginning at the given sequence number maps to the connection-level sequence space (beginning at the given data seq number). This information could conceivably have various sources. One option to signal the Data Sequence Mapping would be to use existing fields in the TCP segment (such as subflow seqno, length) and only add the data sequence number to each segment, for instance as a TCP option. This would be vulnerable, however, to middleboxes that resegment or assemble data, since there is no specified behaviour for coalescing TCP options. If one signalled (data seqno, length), this would still be vulnerable to middleboxes that coalesce segments and do not understand MPTCP signalling so do not correctly rewrite the options. Because of these potential issues, the design decision taken in the MPTCP protocol is that whenever a mapping for subflow data needs to be conveyed to the other host, all three pieces of data (data seq, subflow seq, length) must be sent. To reduce the overhead, it would be permissible for the mapping to be sent periodically and cover more than a single segment. Further experimentation is required to determine what tradeoffs exist regarding the frequency at which mappings should be sent. It could also be excluded entirely in the case of a connection before more than one subflow is used, where the data-level and subflow-level sequence space is the same. 5.2. Reliability and Retransmissions MPTCP features acknowledgements at connection-level as well as subflow-level acknowledgements, in order to provide a robust service to the application. Under normal behaviour, MPTCP can use the data sequence mapping and subflow ACKs to decide when a connection-level segment was received. The transmission of TCP ACKs for a subflow are handled entirely at the subflow level, in order to maintain TCP semantics and trigger subflow-level retransmissions. This has certain implications on end- to-end semantics. It means that once a segment is ACKed at the subflow level it cannot be discarded in the re-order buffer at the connection level. Secondly, unlike in standard TCP, a receiver cannot simply drop out-of-order segments if needed (for instance, due to memory pressure). Under certain circumstances, therefore, it may be desirable to drop segments after acknowledgement on the subflow but before delivery to the application, and this can be facilitated by a connection-level acknowledgement. Furthermore, it is possible to conceive of some cases where connection-level acknowledgements could improve robustness. Consider a subflow traversing a transparent proxy: if the proxy ACKs a segment and then crashes, the sender will not retransmit the lost segment on another subflow, as it thinks the segment has been received. The connection grinds to a halt despite having other working subflows, and the sender would be unable to determine the cause of the problem. An example situation where this may occur would be mobility between wireless access points, each of which operates a transport-level proxy. Finally, as an optimisation, it may be feasible for a connection-level acknowledgement to be transmitted over the shortest Round-Trip Time (RTT) path, potentially reducing send buffer requirements (see Section 5.3). Therefore, to provide a fully robust multipath TCP solution given the above constraints, MPTCP for use on the public Internet MUST feature explicit connection-level acknowledgements, in addition to subflow- level acknowledgements. A connection-level acknowledgement would only be required in order to signal when the receive window moves forward; the heuristics for using such a signal are discussed in more detail in the protocol specification .. Regarding retransmissions, it MUST be possible for a segments to be retransmitted on a different subflow to that on which it was originally sent. This is one of MPTCP's core goals, in order to maintain integrity during temporary or permanent subflow failure, and this is enabled by the dual sequence number space. The scheduling of retransmissions will have significant impact on MPTCP user experience. The current MPTCP specification suggests that data outstanding on subflows that have timed out should be rescheduled for transmission on different subflows. This behaviour aims to minimize disruption when a path breaks, and uses the first timeout as indicators. More conservative versions would be to use second or third timeouts for the same segment. Typically, fast retransmit on an individual subflow will not trigger retransmission on another subflow, although this may still be desirable in certain cases, for instance to reduce the receive buffer requirements. However, in all cases with retransmissions on different subflows, the lost segments SHOULD still be sent on the path that lost them. This is currently believed to be necessary to maintain subflow integrity, as per the network compatibility goal. By doing this, some efficiency is lost, and it is unclear at this point what the optimal retransmit strategy is. Large-scale experiments are therefore required in order to determine the most appropriate retransmission strategy, and recommendations will be refined once more information is available. 5.3. Buffers To ensure in-order delivery, MPTCP must use a connection level receive buffer, where segments are placed until they are in order and can be read by the application. In regular, single-path TCP, it is usually recommended to set the receive buffer to 2*BDP (Bandwidth-Delay Product, i.e. BDP = BW*RTT, where BW = Bandwidth and RTT = Round-Trip Time). One BDP allows supporting reordering of segments by the network. The other BDP allows the connection to continue during fast retransmit: when a segment is fast retransmitted, the receiver must be able to store incoming data during one more RTT. For MPTCP, the story is a bit more complicated. The ultimate goal is that a subflow packet loss or subflow failure should not affect the throughput of other working subflows; the receiver should have enough buffering to store all data until the missing segment is re- transmitted and reaches the destination. The worst case scenario would be when the subflow with the highest RTT/RTO (Round-Trip Time or Retransmission TimeOut) experiences a timeout; in that case the receiver has to buffer data from all subflows for the duration of the RTO. Thus, the smallest connection- level receive buffer that would be needed to avoid stalling with subflow failures is sum(BW_i)*RTO_max, where BW_i = Bandwidth for each subflow and RTO_max is the largest RTO across all subflows. This is an order of magnitude more than the receive buffer required for a single connection, and is probably too expensive for practical purposes. A more sensible requirement is to avoid stalls in the absence of timeouts. Therefore, the RECOMMENDED receive buffer is 2*sum(BW_i)*RTT_max, where RTT_max is the largest RTT across all subflows. This buffer sizing ensures subflows do not stall when fast retransmit is triggered on any subflow. The resulting buffer size should be small enough for practical use. However, there may be extreme cases where fast, high throughput paths (e.g. 100Mb/s, 10ms RTT) are used in conjunction with slow paths (e.g. 1Mb/s, 1000ms RTT). In that case the required receive buffer would be 12.5MB, which is likely too big. In extreme cases such as this example, it may be prudent to only use some of the fastest available paths for the MPTCP connection, potentially using the slow path(s) for backup only. Send Buffer: The RECOMMENDED send buffer is the same size as the recommended receive buffer i.e., 2*sum(BW_i)*RTT_max. This is because the sender must store locally the segments sent but unacknowledged by the connection level ACK. The send buffer size matters particularly for hosts that maintain a large number of ongoing connections. If the required send buffer is too large, a host can choose to only send data on the fast subflows, using the slow subflows only in cases of failure. 5.4. Signalling Since MPTCP uses TCP as its subflow transport mechanism, a MPTCP connection will also begin as a single TCP connection. Nevertheless, it must signal to the peer that it supports MPTCP and wishes to use it on this connection. As such, a TCP Option will be used to transmit this information, since this is the established mechanism for indicating additional functionality on a TCP session. In addition, further signalling is required during the operation of a MPTCP session, such as that for reassembly for multiple subflows, and for informing the other host about potential other available addresses. The MPTCP protocol design will, however, use TCP Options for this additional signalling. This has been chosen as the mechanism most fitting in with the goals as specified in Section 2. With this mechanism, the signalling requires to operate MPTCP is transported separately from the data, allowing it to be created and processed separately from the data stream, and retaining architectural compatibility with network entities. This decision is the consensus of the Working Group (following detailed discussions at IETF78), and the main reasons for this are as follows: o TCP options are the traditional signalling method for TCP; o A TCP option on a SYN is the most compatible way for an end host to signal it is MPTCP-capable; o If connection-level ACKs are signalled in the payload then they may suffer from packet loss and may be congestion-controlled, which may affect the data throughput in the forward direction and could lead to head-of-line blocking; o Middleboxes, such as NAT traversal helpers, can easily parse TCP options, e. g., to rewrite addresses. On the other hand, the main drawbacks of TCP options compared to TLV encoding in the payload are: o There is limited space for signalling messages; o A middlebox may, potentially, drop a packet with an unknown option; o The transport of control information in options is not necessarily reliable. The detailed design of MPTCP alleviates these issues as far as possible by carefully considering the size of MPTCP options, and seamlessly falling back to regular TCP on the loss of control data. Both option and payload encoding may interfere with offloading of TCP processing to high speed network interface cards, such as segmentation, checksumming, and reassembly. For network cards supporting MPTCP, signalling in TCP options should simplify offloading due to the separate handling of MPTCP signalling and data. 5.5. Path Management Currently, the network does not expose path diversity between pairs of IP addresses. In order to achieve path diversity from today's IP networks, in the typical case MPTCP uses multiple addresses at one or both hosts to infer different paths across the network. It is expected that these paths, whilst not necessarily entirely non- overlapping, will be sufficiently disjoint to allow multipath to achieve improved throughput and robustness. The use of multiple IP addresses is a simple mechanism that requires no additional features in the network. Multiple different (source, destination) address pairs will thus be used as path selectors in most cases. Each path will be identified by a standard five-tuple (i.e. source address, destination address, source port, destination port, protocol), however, which can allow the extension of MPTCP to use ports as well as addresses as path selectors. This will allow hosts to use port-based load balancing with MPTCP, for example if the network routes different ports over different paths (which may be the case with technologies such as Equal Cost MultiPath (ECMP) routing ).). It should be noted, however, that ISPs often undertake traffic engineering in order to optimise resource utilisation within their networks, and care should be taken (by both ISPs and developers) that MPTCP using broadly similar paths does not adversely interfere with this. For increased chance of successfully setting up additional subflows (such as when one end is behind a firewall, NAT, or other restrictive middlebox), either host SHOULD be able to add new subflows to a MPTCP connection. MPTCP MUST be able to handle paths that appear and disappear during the lifetime of a connection (for example, through the activation of an additional network interface). The path management is a separate function from the packet scheduling, subflow interface, and congestion control functions of MPTCP, as documented in Section 4. As such it would be feasible to replace this IP-address-based design with an alternative path selection mechanism in the future, with no significant changes to the other functional components. 5.6. Connection Identification Since a MPTCP connection may not be bound to a traditional 5-tuple (source address and port, destination address and port, protocol number) for the entirety of its existence, it is desirable to provide a new mechanism for connection identification. This will be useful for MPTCP-aware applications, and for the MPTCP implementation (and MPTCP-aware middleboxes) to have a unique identifier with which to associate the multiple subflows. Therefore, each MPTCP connection requires a connection identifier at each host, which is locally unique within that host. In many ways, this is analogous to aan ephemeral port number in regular TCP. The manifestation and purpose of such an identifier is out of the scope of this architecture document. Legacy applications will not, however, have access to this identifier and in such cases a MPTCP connection will be identified by the 5-tuple of the first TCP subflow. It is out of the scope of this document, however, to define the behaviour of the MPTCP implementation if the first TCP subflow later fails. If there are MPTCP-unaware applications that make assumptions about continued existence of the initial address pair, their behaviour could be disrupted by carrying on regardless. It is expected that this is a very small, possibly negligible, set of applications, however. In the case ofMPTCP MUST NOT be used for applications that have used an existing API callrequest to bind to a specific address or interface, the MPTCP extension MUST NOT be used,since thesuch applications are indicatingmaking a cleardeliberate choice of path to use and thus will have expectations of behaviour that must be maintained,in order to adhere to the application compatibility goals.use. Since the requirements of applications are not clear at this stage, however, it is as yet unconfirmed whatwhether carrying on in the bestevent of the loss of the initial address pair would be a damaging assumption to make. This behaviour is. Itwill be an implementation-specific solution, however,and as such the behaviourit is expected to be chosen by implementors once more research has been undertaken to determine its impact. 5.7. Congestion Control As discussed in network-layer compatibility requirements Section 2.2.3, there are three goals for the congestion control algorithms used by a MPTCP implementation: improve throughput (at least as well as a single-path TCP connection would perform); do no harm to other network users (do not take up more capacity on any one path than if it was a single path flow using only that route - this is particularly relevant for shared bottlenecks); and balance congestion by moving traffic away from the most congested paths. To achieve these goals, the congestion control algorithms on each subflow must be coupled in some way. A proposal for a suitable congestion control algorithm is given in .. 5.8. Security A detailed threat analysis for Multipath TCP is presented in a separate document .. This focuses on flooding attacks and hijacking attacks that can be launched against a Multipath TCP connection. The basic security goal of Multipath TCP, as introduced in Section 2.3, can be stated as: "provide a solution that is no worse than standard TCP". From the threat analysis, and with this goal in mind, three key security requirements can be identified. A multi-addressed Multipath TCP SHOULD be able to: o Provide a mechanism to confirm that the parties in a subflow handshake are the same as in the original connection setup (e.g. require use of a key exchanged in the initial handshake in the subflow handshake, to limit the scope for hijacking attacks). o Provide verification that the peer can receive traffic at a new address before adding it (i.e. verify that the address belongs to the other host, to prevent flooding attacks). o Provide replay protection, i.e. ensure that a request to add/ remove a subflow is 'fresh'. Additional mechanisms have been deployed as part of standard TCP stacks to provide resistance to Denial-of-Service attacks. For example, there are various mechanisms to protect against TCP reset attacks , and Multipath TCP should continue to support similar protection. In addition, TCP SYN Cookies  were developed to allow a TCP server to defer the creation of session state in the SYN_RCVD state, and remain stateless until the ESTABLISHED state had been reached. Multipath TCP should, ideally, continue to provide such functionality and, at a minimum, avoid significant computational burden prior to reaching the ESTABLISHED state (of the Multipath TCP connection as a whole). It should be noted that aspects of the Multipath TCP design space place constraints on the security solution: o The use of TCP options significantly limits the amount of information that can be carried in the handshake. o The need to work through middleboxes results in the need to handle mutability of packets. o The desire to support a 'break-before-make' (as well as a 'make- before-break') approach to adding subflows (within a limited time period) implies that a host cannot rely on using a pre-existing subflow to support the addition of a new one. The MPTCP protocol will be designed with these security requirements in mind, and the protocol specification  will document how these are met. 6. Software Interactions with Applications6.1. Interactions with Applications In the case of applications are presented in  - including, but not limited to, performances changes that may be expected, semantic changes, and new featuresthat may be requested throughhave used an enhanced API. TCPexisting API call to bind to a specific address or interface, the MPTCP extension MUST NOT be used. This is because the applications are indicating a clear choice of path to use and thus will have expectations of behaviour that must be maintained, in order to adhere to the application compatibility goals. Interactions with applications are presented in  - including, but not limited to, performances changes that may be expected, semantic changes, and new features that may be requested through an enhanced API. TCP features the ability to send out-of-band ("Urgent") data. Although"Urgent" data, the delivery of which to the application may or may not be out-of-band. The use of Urgent datathis feature is not recommended (see ),due to security implications and implementation differences . MPTCP SHOULD stillrequires contiguous data to support this feature if requested byits Data Sequence Mapping over multiple segments, and therefore the Urgent pointer cannot interrupt an application.existing mapping. An MPTCP implementation MAY choose to support sending Urgent data, and if it does, it SHOULD send the Urgent data on onethe soonest available unassigned subflow ofsequence space. Incoming Urgent data SHOULD be mapped to connection-level sequence space and delivered to the application analogous to Urgent data in regular TCP. 6.2. Interactions with Management Systems To enable interactions between TCP and network management systems, the TCP  and TCP Extended Statistics (ESTATS)  MIBs have been defined. MPTCP connection; it MAY choose thisshould share the these MIBs for aspects that are designed to be transparent to the best performing subflow.application. It is anticipated that a MPTCP MIB will be defined in the future, once experience of experimental MPTCP deployments is gathered. This MIB would provide access to MPTCP-specific properties such as whether MPTCP is enabled, and the number and properties of the individual paths in use. 7. Interactions with Middleboxes As discussed in Section 2.2, it is a goal of MPTCP to be deployable today and thus compatible with the majority of middleboxes. This section summarises the issues that may arise with NATs, firewalls, proxies, intrusion detection systems, and other middleboxes that, if not considered in the protocol design, may hinder its deployment. This section is intended primarily as a description of options and considerations only. Protocol-specific solutions to these issues will be given in the companion documents. Multipath TCP will be deployed in a network that no longer provides just basic datagram delivery. A myriad of middleboxes are deployed to optimize various perceived problems with the Internet protocols: NATs primarily address IP address space shortage ,, Performance Enhancing Proxies (PEPs) optimize TCP for different link characteristics ,, firewalls  and intrusion detection systems try to block malicious content from reaching a host, and traffic normalizers  ensure a consistent view of the traffic stream to Intrusion Detection Systems (IDS) and hosts. All these middleboxes optimize current applications at the expense of future applications. In effect, future applications will often need to behave in a similar fashion to existing ones, in order to increase the chances of successful deployment. Further, the precise behaviour of all these middleboxes is not clearly specified, and implementation errors make matters worse, raising the bar for the deployment of new technologies. The following list of middlebox classes documents behaviour that could impact the use of MPTCP. This list is used in  to describe the features of the MPTCP protocol that are used to mitigate the impact of these middlebox behaviours. o NATs: Network Address Translators decouple the host's local IP address (and, in the case of NAPTs, port) with that which is seen in the wider Internet when the packets are transmitted through a NAT. This adds complexity, and reduces the chances of success, when signalling IP addresses. o PEPs: Performance Enhancing Proxies, which aim to improve the performance of protocols over low-performance (e.g. high latency or high error rate) links. As such, they may "split" a TCP connection and behaviour such as proactive ACKing may occur, and therefore it is no longer guaranteed that one host is communicating directly with another. PEPs, firewalls or other middleboxes may also change the declared receive window size. o Traffic Normalizers: These aim to eliminate ambiguities and potential attacks at the network level, and amongst other things are unlikely to permit holes in TCP-level sequence space (which has impact on MPTCP's retransmission and subflow sequence numbering design choices). o Firewalls: on top of preventing incoming connections, firewalls may also attempt additional protection such as sequence number randomization (so a sender cannot reliably know what TCP sequence number the receiver will see). o Intrusion Detection Systems: IDSs may look for traffic patterns to protect a network, and may have false positives with MPTCP and drop the connections during normal operation. Future MPTCP-aware middleboxes will require the ability to correlate the various paths in use. o Content-aware Firewalls: Some middleboxes may actively change data in packets, such as re-writing URIs in HTTP traffic. In addition, all classes of middleboxes may affect TCP traffic in the following ways: o TCP Options: some middleboxes may drop packets with unknown TCP options, or strip those options from the packets. o Segmentation and Coalescing: middleboxes (or even something as close to the end host as TCP Segmentation Offloading (TSO) on a Network Interface Card (NIC)) may change the packet boundaries from those which the sender intended. It may do this by splitting packets, or coalescing them together. This leads to two major impacts: we cannot guarantee where a packet boundary will be, and we cannot say for sure what a middlebox will do with TCP options in these cases (they may be repeated, dropped, or sent only once). 8. Contributors The authors would like to acknowledge the contributions of Andrew McDonald and Bryan Ford to this document. The authors would also like to thank the following people for detailed reviews: Olivier Bonaventure, Gorry Fairhurst, Iljitsch van Beijnum, Philip Eardley, Michael Scharf, Lars Eggert, andCullen Jennings.Jennings, Joel Halpern, Juergen Quittek, Alexey Melnikov, David Harrington, Jari Arkko and Stewart Bryant. 9. Acknowledgements Alan Ford, Costin Raiciu, Mark Handley, and Sebastien Barre are supported by Trilogy (http://www.trilogy-project.org), 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. 10. IANA Considerations None. 11. Security Considerations This informational document provides an architectural overview for Multipath TCP and so does not, in itself, raise any security issues. A separate threat analysis  lists threats that can exist with a Multipath TCP. However, a protocol based on the architecture in this document will have a number of security requirements. The high level goals for such a protocol are identified in Section 2.3, whilst Section 5.8 provides more detailed discussion of security requirements and design decisions which are applied in the MPTCP protocol design .. 12. References 12.1. Normative References  Postel, J., "Transmission Control Protocol", STD 7, RFC 793, September 1981.  Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. 12.2. Informative References  Wischik, D., Handley, M., and M. Bagnulo Braun, "The Resource Pooling Principle", ACM SIGCOMM CCR vol. 38 num. 5, pp. 47-52, October 2008, <http://ccr.sigcomm.org/online/files/p47-handleyA4.pdf>.  Hopps, C., "Analysis of an Equal-Cost Multi-Path Algorithm", RFC 2992, November 2000.  Ford, A., Raiciu, C., and M. Handley, "TCP Extensions for Multipath Operation with Multiple Addresses", draft-ietf-mptcp-multiaddressed-02 (work in progress), October 2010.  Stewart, R., "Stream Control Transmission Protocol", RFC 4960, September 2007.  Raiciu, C., Handley, M., and D. Wischik, "Coupled Congestion Control for Multipath Transport Protocols", draft-ietf-mptcp-congestion-01 (work in progress), January 2011.  Scharf, M. and A. Ford, "MPTCP Application Interface Considerations", draft-ietf-mptcp-api-00 (work in progress), November 2010.  Carpenter, B. and S. Brim, "Middleboxes: Taxonomy and Issues", RFC 3234, February 2002.  Carpenter, B., "Internet Transparency", RFC 2775, February 2000.  Mathis, M., Mahdavi, J., Floyd, S., and A. Romanow, "TCP Selective Acknowledgment Options", RFC 2018, October 1996.  Bagnulo, M., "Threat Analysis for Multi-addressed/Multi-path TCP", draft-ietf-mptcp-threat-06TCP Extensions for Multi-path Operation with Multiple Addresses", draft-ietf-mptcp-threat-07 (work in progress), December 2010. January 2011.  Becke, M., Dreibholz, T., Iyengar, J., Natarajan, P., and M. Tuexen, "Load Sharing for the Stream Control Transmission Protocol (SCTP)", draft-tuexen-tsvwg-sctp-multipath-01 (work in progress), December 2010.  Ford, B. and J. Iyengar, "Breaking Up the Transport Logjam", ACM HotNets, October 2008.  Srisuresh, P. and K. Egevang, "Traditional IP Network Address Translator (Traditional NAT)", RFC 3022, January 2001.  Freed, N., "Behavior of and Requirements for Internet Firewalls", RFC 2979, October 2000.  Border, J., Kojo, M., Griner, J., Montenegro, G., and Z. Shelby, "Performance Enhancing Proxies Intended to Mitigate Link-Related Degradations", RFC 3135, June 2001.  Hopps, C., "Analysis of an Equal-Cost Multi-Path Algorithm", RFC 2992, November 2000. Ramaiah, A., Stewart, R., and M. Dalal, "Improving TCP's Robustness to Blind In-Window Attacks", RFC 5961, August 2010.  Eddy, W., "TCP SYN Flooding Attacks and Common Mitigations", RFC 4987, August 2007.  Gont, F. and A. Yourtchenko, "On the Implementation of the TCP Urgent Mechanism", RFC 6093, January 2011.  Raghunarayan, R., "Management Information Base for the Transmission Control Protocol (TCP)", RFC 4022, March 2005.  Mathis, M., Heffner, J., and R. Raghunarayan, "TCP Extended Statistics MIB", RFC 4898, May 2007.  Handley, M., Paxson, V., and C. Kreibich, "Network Intrusion Detection: Evasion, Traffic Normalization, and End-to-End Protocol Semantics", Usenix Security 2001, 2001, <http:// www.usenix.org/events/sec01/full_papers/handley/handley.pdf>. Appendix A. Changelog (For removal by the RFC Editor) A.1. Changes since draft-ietf-mptcp-architecture-04 o Responded to IETF Last Call and IESG review comments. A.2. Changes since draft-ietf-mptcp-architecture-03 o Responded to AD review comments. A.2.A.3. Changes since draft-ietf-mptcp-architecture-02 o Responded to WG last call review comments. Included editorial fixes, adding Section 2.4, and improving Section 5.4 and Section 7. A.3.A.4. Changes since draft-ietf-mptcp-architecture-01 o Responded to review comments. o Added security sections. A.4.A.5. Changes since draft-ietf-mptcp-architecture-00 o Added middlebox compatibility discussion (Section 7). o Clarified path identification (TCP 4-tuple) in Section 5.5. o Added brief scenario and diagram to Section 1.3. Authors' Addresses Alan Ford (editor)Roke Manor Research Old Salisbury Lane Romsey, Hampshire SO51 0ZN UK Phone: +44 1794 833 465 Email: email@example.com Costin Raiciu University College London Gower Street London WC1E 6BT UK Email: firstname.lastname@example.org Mark Handley University College London Gower Street London WC1E 6BT UK Email: email@example.com Sebastien Barre Universite catholique de Louvain Pl. Ste Barbe, 2 Louvain-la-Neuve 1348 Belgium Phone: +32 10 47 91 03 Email: firstname.lastname@example.org Janardhan Iyengar Franklin and Marshall College Mathematics and Computer Science PO Box 3003 Lancaster, PA 17604-3003 USA Phone: 717-358-4774 Email: email@example.com