TCP is the dominating transmission protocol in the Internet since decades. It proved its flexibility to adapt to unknown and changing network conditions. A distinguished TCP feature is the comparably fair resource sharing. Unfortunately, this abstract fairness is frequently misinterpreted as convergence towards equal sharing rates. In this paper we show in theory as well as in experiment that T...

For certain subordinators (Xt)t≥0 it is shown that the process (−t logXts)s>0 tends to an extremal process (η̂s)s>0 in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that (z ∧ (−t logXts))s≥0 converges weakly to (z ∧ η̂s)s≥0 in D[0,∞), the space of càdlàg functions equipped with Skorohod’s J1 metric.

This paper extends certain results of Iglehart and Whitt on multiple channel queues to the case where the inter-arrival times and service times are not necessarily identically distributed. It is shown that the weak convergence results in this case are exactly the same as those obtained by Iglehart and Whitt

In this paper, we first prove the weak convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Then we prove the weak convergence for the Moudafi’s iterative scheme of quasi-nonexpansive mapping and nonexpansive mapping. Finally, we prove the strong convergence for the Moudafi’s iterative scheme of two quasi-nonexpansive mappings. Our results generalize the recent res...

The stochastic heat equation driven by additive noise is discretized in the spatial variables by a standard finite element method. The weak convergence of the approximate solution is investigated and the rate of weak convergence is found to be twice that of strong convergence.

We deene an Euler type weak approximation for solutions of nonlinear diiusion processes. We nd the rate of convergence of this scheme in weak form. As in the diiusion case the weak rate of convergence is better than the strong one. The proof uses the integration by parts formula of Malliavin calculus.

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

We study classes of filters F on N such that weak and strong F -convergence of sequences in l1 coincide. We study also analogue of l1 weak sequential completeness theorem for filter convergence.