Generalised halfspace depth function is proposed. Basic properties of this depth function including the strong consistency are studied. We show, on several examples that our depth function may be considered to be more appropriate for nonsymetric distributions or for mixtures of distributions.

In recent years, various non-linear phenomena of the Internet have been discovered. For instance, it is reported that congestion of a router propagates to neighboring routers like a wave. Several researches on congestion propagation among routers have been performed. However, in these researches, cause of congestion propagation and condition that congestion propagation occurs have not been suff...

Many researchers use abstract models to simulate network congestion, finding patterns that might foreshadow onset of congestion collapse. We investigate whether such abstract models yield congestion behaviors sufficiently similar to more realistic models. Beginning with an abstract model, we add elements of realism in various combinations, culminating with a high-fidelity simulation. By compari...

For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...

In ATM network environments congestion control plays an important role to support dif ferent quality of service guarantees for a large variety of tra c types While for real time communications like CBR and VBR services a preventive open loop congestion control mechanism is applied a reactive closed loop mechanism has been suggested for the ABR service class which was introduced mainly for data ...

The paper deals with the best unbiased estimators of the blocked compound symmetric covariance structure for m−variate observations over u sites under the assumption of multivariate normality. The free-coordinate approach is used to prove that the quadratic estimation of covariance parameters is equivalent to linear estimation with a properly defined inner product in the space of symmetric matr...

A k-hypertournament is a complete k-hypergraph with each k-edge endowed with an orientation, that is, a linear arrangement of the vertices contained in the edge. In a k-hypertournament, the score si (losing score ri) of a vertex vi is the number of arcs containing vi in which vi is not the last element (in which vi is the last element). The total score of vi is defined as ti = si − ri. In this ...

Congestion has been considered as one of the basic important issue in packet switched network [1][9]. Congestion control refers to the mechanisms and techniques to control the congestion and keep the load below the capacity. This paper provides an overview of category provided by congestion control .It also includes how TCP uses congestion control to avoid congestion or alleviate congestion in ...

Current congestion control mechanisms in today’s Internet rely on end-to-end TCP congestion avoidance algorithms that back off sources when congestion occurs, detected by packet loss or explicit congestion notification signals. But one of the major setbacks of such mechanisms is making sure that all sources respond correctly in applying congestion avoidance measures during periods of high conge...