Versatile Markovian models for networks with asymmetric TCP sources

In this paper we use Stochastic Petri Nets (SPNs) to study the interaction of multiple TCP sources that share one or two buffers, thereby considerably extending earlier work. We first consider two sources sharing a buffer and investigate the consequences of two popular assumptions for the loss process in terms of fairness and link utilization. The results obtained by our model are in agreement with existing analytic models or are closer to results obtained by ns-2 simulations. We then study a network consisting of three sources and two buffers and provide evidence that link sharing is approximately minimum-potential-delay-fair in case of equal round-trip times. \u

Analysis of Multiple Flows using Different High Speed TCP protocols on a General Network

We develop analytical tools for performance analysis of multiple TCP flows (which could be using TCP CUBIC, TCP Compound, TCP New Reno) passing through a multi-hop network. We first compute average window size for a single TCP connection (using CUBIC or Compound TCP) under random losses. We then consider two techniques to compute steady state throughput for different TCP flows in a multi-hop network. In the first technique, we approximate the queues as M/G/1 queues. In the second technique, we use an optimization program whose solution approximates the steady state throughput of the different flows. Our results match well with ns2 simulations.Comment: Submitted to Performance Evaluatio

Interacting multi-class transmissions in large stochastic networks

The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes of the route. Since several classes of connections going through the nodes of the network are considered, an original mean-field result in a multi-class context is established. It is shown that, as the number of connections goes to infinity, the behavior of the different classes of connections can be represented by the solution of an unusual nonlinear stochastic differential equation depending not only on the sample paths of the process, but also on its distribution. Existence and uniqueness results for the solutions of these equations are derived. Properties of their invariant distributions are investigated and it is shown that, under some natural assumptions, they are determined by the solutions of a fixed-point equation in a finite-dimensional space.Comment: Published in at http://dx.doi.org/10.1214/09-AAP614 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic Approximations for TCP Compound

In this paper, we derive an approximation for throughput of TCP Compound connections under random losses. Throughput expressions for TCP Compound under a deterministic loss model exist in the literature. These are obtained assuming the window sizes are continuous, i.e., a fluid behaviour is assumed. We validate this model theoretically. We show that under the deterministic loss model, the TCP window evolution for TCP Compound is periodic and is independent of the initial window size. We then consider the case when packets are lost randomly and independently of each other. We discuss Markov chain models to analyze performance of TCP in this scenario. We use insights from the deterministic loss model to get an appropriate scaling for the window size process and show that these scaled processes, indexed by p, the packet error rate, converge to a limit Markov chain process as p goes to 0. We show the existence and uniqueness of the stationary distribution for this limit process. Using the stationary distribution for the limit process, we obtain approximations for throughput, under random losses, for TCP Compound when packet error rates are small. We compare our results with ns2 simulations which show a good match.Comment: Longer version for NCC 201

Phase transitions with infinitely many absorbing states in complex networks

We instigate the properties of the threshold contact process (TCP), a process showing an absorbing-state phase transition with infinitely many absorbing states, on random complex networks. The finite size scaling exponents characterizing the transition are obtained in a heterogeneous mean field (HMF) approximation and compared with extensive simulations, particularly in the case of heterogeneous scale-free networks. We observe that the TCP exhibits the same critical properties as the contact process (CP), which undergoes an absorbing-state phase transition to a single absorbing state. The accordance among the critical exponents of different models and networks leads to conjecture that the critical behavior of the contact process in a HMF theory is a universal feature of absorbing state phase transitions in complex networks, depending only on the locality of the interactions and independent of the number of absorbing states. The conditions for the applicability of the conjecture are discussed considering a parallel with the susceptible-infected-susceptible epidemic spreading model, which in fact belongs to a different universality class in complex networks.Comment: 9 pages, 6 figures to appear in Phys Rev