# A Mathematical Model for Efficient and Fair Resource Assignment in Multipath Transport
## 1 Introduction  
The aim of transport-layer protocols is the reliable end-to-end transport of data. For best performance and resulting user satisfaction, Internet providers expect that transport protocols utilize links in an optimum way and avoid congestion in the network. Furthermore, protocols have to consider that links are in most cases shared by multiple users. Therefore, the available capacity on a shared link should be assigned to the users in a fair way so that no user has to starve. Fairness means that a transport protocol should respond to congestion notifications such as packet loss or increase of delay by reducing the traffic load injected into the network. The most commonly used transport protocol in today's Internet is the Transmission Control Protocol (TCP) [1]. It is not only used by \"classical\" applications which rely on reliable transmissions--such as web, e-mail or file transfer--but also by some soft-real-time applications where delay is less critical, such as video streaming. In the context of TCP coexisting with other transport protocols on shared links, the term \"TCP friendliness\" means that a flow should not use a larger portion of the link capacity than a legacy TCP flow [2]. An extension for legacy TCP developed in recent years is Multipath TCP (MPTCP) [3] which makes use of multiple interfaces in the sender or receiver in contrast to legacy TCP, which is only able to use a single interface for a given data flow. Each interface connects the sender or receiver node to a different network so that packets are sent to the opposite station along different paths. Over each of the paths, a subset of the overall amount of packets is transported; this subset is called MPTCP subflow. The protocol stack hides details about the transport from the application, it behaves in a transparent way and appears to the application as a legacy connection. An alternative transport-layer protocol developed in recent years which from the beginning has been designed for multihoming operation is the Stream Control Transmission Protocol (SCTP)[4]. However, although multihoming means that alternative interfaces on a node and the resulting additional data paths are identified, they are only used for redundancy, so that an extension named Concurrent Multipath Transfer SCTP (CMT-SCTP) has been investigated [5] and is currently proposed as an Internet Engineering Task Force (IETF) draft [6]. It was pointed out that any transport-layer protocol, irrespective of whether it supports multipath, should coexist in a fair way with legacy TCP, so fairness has to be ensured when sharing resources with normal TCP flows. A resource can either be a link which is part of an end-to-end connection, or it can be the entire network. Moreover, when discussing fairness, different participants can be specified. On the one hand, there are data flows which transport the entire data of a stream or file. On the other hand, such a flow can be divided into subflows where each of them transports a subset of the data. The TCP-friendliness policy may require that an entire data flow may behave equivalently to a TCP connection, or each of the subflows should do so. This option of different resources and participants means that there is not \"the\" fairness as such, but there are different ways regarding how to interpret fairness. Another aspect of multipath transport is that it can not only consider the entire _network_ as a resource which should be fairly shared as described in Section 3.2.3 of this article, but also focus on individual links as the shared resource as shown in Sections 3.2.1 and 3.2.2, respectively. This paper discusses the theoretical analysis of resource assignment and fairness in the domain of multipath _transport_. In the multipath transport case, at least one of the end nodes of a connection has multiple interfaces, usually connected to different access networks, so that a data flow can be split at the transport layer.