The present paper provides some new stochastic inequalities for the characteristics of the M/GI/1/n and GI/M/1/n loss queueing systems. These stochastic inequalities are based on substantially deepen upand downcrossings analysis, and they are stronger than the known stochastic inequalities obtained earlier. Specifically, for a class of GI/M/1/n queueing system, twoside stochastic inequalities a...

The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality...

In this paper, we present a revision on some of the recent progresses made in characterising and understanding information inequalities, which are the fundamental physical laws in communications and compression. We will begin with the introduction of a geometric framework for information inequalities, followed by the first non-Shannon inequality proved by Zhang et al. in 1998 [1]. The discovery...

Many Bayesian clinical trial methods are based on random inequalities. For some distribution families, these inequalities can be computed in closed form. For example, [1] gives closed-form solutions to computing P(X > Y) when X and Y are either independent normal or independent gamma random variables. However the case of beta random variables is very important and no closed form solution for th...

In many network applications, one searches for a connected subset of vertices that exhibits other desirable properties. To this end, this paper studies the connected subgraph polytope of a graph, which is the convex hull of subsets of vertices that induce a connected subgraph. Much of our work is devoted to the study of two nontrivial classes of valid inequalities. The first are the a, b-separa...

Recently Cherchye et al. (2011) reformulated the Walrasian equilibrium inequalities, introduced by Brown and Matzkin (1996), as an integer programming problem and proved that solving the Walrasian equilibrium inequalities is NP-hard. Following Brown and Shannon (2000), we reformulate the Walrasian equilibrium inequalities as the dual Walrasian equilibrium inequalities. Brown and Shannon proved ...

The binary choice polytope appeared in the investigation of the binary choice problem formulated by Guilbaud (1953) and Block and Marschak (1960). It is nowadays known to be the same as the linear ordering polytope from operations research (Grötschel, Jünger and Reinelt, 1985). The central problem is to find facet-defining linear inequalities for the polytope. Fence inequalities constitute a pr...

Evidence now shows that the key drivers of poor health are social factors, such as education, employment, housing and urban environments. Variations in these social factors—or the conditions in which we live our lives—have lead to a growth in health inequalities within and between countries. One of the key challenges facing those concerned with health equity is how to effect change across the b...

In this study, delay-dependent robust stability problem is investigated for uncertain neutral systems with discrete and distributed delays. By constructing an augmented Lyapunov-Krasovskii functional involving triple integral terms and taking into account the relationships between the different delays, new less conservative stability and robust stability criteria are established first using the...

In the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. In this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. Two path inequalities for the node-only interdiction problem are represented. It has been proved that the integrality gap of relaxation of the maximum fl...