A new serial cost sharing rule, called mixed serial cost sharing, is defined on the class of cost functions which equal a sum of an increasing convex and increasing concave function. This rule is based on a particular decomposition principle known as complementary-slackness decomposition and it coincides with the original serial rule of Moulin and Shenker (1992) [Moulin, H., Shenker, S., 1992. ...

This paper concerns the forward kinematics and tension distribution of sinking winches mechanism, which is a type of four-cable-driven partly constrained parallel robot. Conventional studies on forward kinematics of cable-driven parallel robot assumed that all cables are taut. Actually, given the lengths of four cables, some cables may be slack when the platform is in static equilibrium. Theref...

First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlle...

Solving fastest distributed consensus averaging problem (i.e., finding weights on the edges to minimize the second-largest eigenvalue modulus of the weight matrix) over networks with different topologies is one of the primary areas of research in the field of sensor networks and one of the well known networks in this issue is tree network. Here in this work we present analytical solution for th...

The primal-dual method (or primal-dual schema) is another means of solving linear programs. The basic idea of this method is to start from a feasible solution y to the dual program, then attempt to find a feasible solution x to the primal program that satisfies the complementary slackness conditions. If such an x cannot be found, it turns out that we can find a better y in terms of its objectiv...

A method is given to nd an analytical description of models of computer systems, whose evolution in time may be considered as a homogeneous Markov process. It is shown that existence of symmetry in the model allows one to consider the equivalence classes under symmetry transformations and the probabilities of transitions between them. Utilisation of symmetry reduces the order of the linear equa...

The central curve of a linear program is an algebraic curve specified by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizing or maximizing the cost function over any region in the associated hyperplane arrangement. We determine the degree, arithmetic genus and defining prime ideal of the central curve, thereby answer...

We generalize the -relaxation method of [BPT97a] for the single commodity, linear or separable convex cost network flow problem to network flow problems with positive gains. The method maintains -complementary slackness at all iterations and adjusts the arc flows and the node prices so as to satisfy flow conservation upon termination. Each iteration of the method involves either a price change ...

First we give a short description of the Extended Linear Complementarity Problem (ELCP), which is a mathematical programming problem. We briefly discuss how this problem can be used in the analysis of discrete event systems and continuous variable systems. Next we show that the ELCP can also be used to model and to analyze hybrid systems. More specifically, we consider a traffic-light-controlle...

Cellular networks are now rapidly evolving to the renewable heterogeneous network (HetNet) architectures, where a mixture of macro base stations (BSs) and small cell BSs coexist. Particularly, these BSs are partly-powered or self-powered by renewable energy sources (RES). In this context, joint user association and resource allocation is challenging. In addition, wireless backhaul is rapidly be...