Math 484/884 Data Networks

MATH 884 Project Report Optimal Decentralized Control of Random Access Multipacket Channels

MATH 484 Report: A Minimum Delay Routing Algorithm Using Distributed Computation

One of the most basic problems in data networks is that of assigning routing paths. In the context of this paper, the problem can be divided into two parts. First, understanding the solutions which minimize the expected delay, and second, finding a way to effectively find these solutions (i.e. computationally tractable). In the paper ”A Minimum Delay ”routing Algorithm Using Distirbuted Computa...

Large normal ideals concentrating on a fixed small cardinality

The property on the filter in Definition 1, a kind of large cardinal property, suffices for the proof in Liu Shelah [484] and is proved consistent as required there (see conclusion 6). A natural property which looks better, not only is not obtained here, but is shown to be false (in Claim 7). On earlier related theorems see Gitik Shelah [GiSh310]. * * * 1. Definition (1) Let κ be a cardinal and...

Flow Synchronization for Network Coding

Network Coding (NC) is a means to improve network performance in various ways. Most evaluations so far were done with simplified assumptions about the application scenario, namely equal data rates and packet sizes for traffic to be encoded. Traffic in real networks, however, does not have this property. Hence, as deterministic and random NC require these properties, flows have to be synchronize...

On a Certain Subordination Result and Its Generalizations

This paper presents a result relating to subordination of analytic function in the unit disk and provides an improved version of a result published recently in [Math. Slovaca 60 (4) (2010), 471-484]. Besides stating and proving here a corrected form of this result, we also consider its generalization. The concluding remarks indicate briefly other possibilities of extensions to some of the resul...