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**11 - 14**of**14**### 1 Throughput Performance in Networks with Linear Capacity Contraints

"... Abstract — We consider a network whose resources are shared by a dynamic number of data flows according to balanced fairness. We give explicit bounds on the mean throughput that results from this stochastic resource sharing when the capacity constraints are linear. We illustrate the results on a few ..."

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Abstract — We consider a network whose resources are shared by a dynamic number of data flows according to balanced fairness. We give explicit bounds on the mean throughput that results from this stochastic resource sharing when the capacity constraints are linear. We illustrate the results on a few examples of wireline and wireless networks. Index Terms — Flow throughput, balanced fairness. I.

### Computational aspects of balanced fairness

"... Flow level behaviour of data networks depends on the allocation of link capacities between competing flows. It has been recently shown that there exist allocations with the property that the stationary distribution of the number of flows in progress on different routes depends only on the traffic lo ..."

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Flow level behaviour of data networks depends on the allocation of link capacities between competing flows. It has been recently shown that there exist allocations with the property that the stationary distribution of the number of flows in progress on different routes depends only on the traffic loads on these routes and is insensitive to any detailed traffic characteristics. Balanced fairness refers to the most efficient of such allocations. In this paper we develop a general recursive algorithm for efficiently calculating the corresponding performance metrics like flow throughput. Several examples are worked out using this algorithm including the practically interesting case of concentration tree networks. 1.

### A Processor-Sharing Heuristic for Multipath Congestion Control

"... Abstract — Protocols are currently being designed where a connection can simultaneously send traffic across multiple routes (or paths) of a communication network; for example, the IETF’s MP-TCP protocol. Traditional single-path congestion-control protocols, which increase and decrease transmission r ..."

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Abstract — Protocols are currently being designed where a connection can simultaneously send traffic across multiple routes (or paths) of a communication network; for example, the IETF’s MP-TCP protocol. Traditional single-path congestion-control protocols, which increase and decrease transmission rates depending on the level of congestion, can be argued to implicitly solve a network-wide utility optimization in a decentralized manner. It is well-known that this optimization implies desirable properties such as fairness. However, it is not really clear in the literature how to achieve such desirable optimization when a connection can use multiple paths. In this case, a connection aims at balancing traffic between the available routes striving a tradeoff between congested and uncongested routes. In this multipath framework, we propose a simple load-balancing heuristic for splitting traffic among multiple routes. Our load-balancer is inspired by the modus operandi of processor-sharing queues and, essentially, oper-ates as follows: every time a packet is acknowledged on a route, increase the congestion window of that route by one and decrease the congestion window of a route selected with probability proportional to the size of its congestion window. In our main result, we argue that this simple end-to-end policy achieves a desirable network-wide utility optimization for multipath routing, when the network is congested. Variants of our heuristic and its implications are discussed. I.

### FLOW-LEVEL CONVERGENCE AND INSENSITIVITY FOR MULTI-CLASS QUEUEING NETWORKS

"... We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochas-tic model as a model of document transfer in a communication net-work where the documents transferred have a general distribution. We prove the weak convergence of the mult ..."

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We consider a multi-class queueing network as a model of packet transfer in a communication network. We define a second stochas-tic model as a model of document transfer in a communication net-work where the documents transferred have a general distribution. We prove the weak convergence of the multi-class queueing process to the document transfer process. Our convergence result allows the comparison of general document size distributions, and consequently, we prove general insensitivity results for the limit queueing process. We discuss how this separation of time-scales method of proving in-sensitivity may be applied to other insensitive queueing systems. 1. Introduction. Introduced by Roberts and Massoulie ́ [14]