Variable-Volume Flushing (V-VF) device for water conservation in toilets

Thirty five percent of residential indoor water used is flushed down the toilet. Five out of six flushes are for liquid waste only, which requires only a fraction of the water needed for solid waste. Designers of current low-flush toilets (3.5-gal. flush) and ultra-low-flush toilets (1.5-gal. flush) did not consider the vastly reduced amount of water needed to flush liquid waste versus solid waste. Consequently, these toilets are less practical than desired and can be improved upon for water conservation. This paper describes a variable-volume flushing (V-VF) device that is more reliable than the currently used flushing devices (it will not leak), is simple, more economical, and more water conserving (allowing one to choose the amount of water to use for flushing solid and liquid waste)

The Invariant Measure of Random Walks in the Quarter-plane: Representation in Geometric Terms

We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a finite linear combination of geometric terms and present conditions on the structure of these linear combinations such that the resulting measure may yield an invariant measure of a random walk. We demonstrate that each geometric term must individually satisfy the balance equations in the interior of the state space and further show that the geometric terms in an invariant measure must have a pairwise-coupled structure. Finally, we show that at least one of the coefficients in the linear combination must be negative

The invariant measure of homogeneous Markov processes in the quarter-plane: Representation in geometric terms

We consider the invariant measure of a homogeneous continuous-time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geometric distribution. Second, we show that a countable linear combination of geometric terms can be an invariant measure only if it consists of pairwise-coupled terms. As a consequence, we obtain a complete characterization of all countable linear combinations of geometric distributions that may yield an invariant measure for a homogeneous continuous-time Markov process in the quarter-plane

Energy consumption in coded queues for wireless information exchange

We show the close relation between network coding and queuing networks with negative and positive customers. Moreover, we develop Markov reward error bounding techniques for networks with negative and positive customers. We obtain bounds on the energy consumption in a wireless information exchange setting using network coding

A Linear Programming Approach to Error Bounds for Random Walks in the Quarter-plane

We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities along the boundaries of the state space. A Markov reward approach is used to bound the approximation error. The main contribution of the work is the formulation of a linear program that provides the approximation error

Linear programming error bounds for random walks in the quarter-plane

We consider approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities along the boundaries of the state space. A Markov reward approach is used to bound the approximation error. The main contribution of the work is the formulation of a linear program that provides the approximation error

Energy-delay tradeoff in wireless network coding

A queueing model for wireless communication network in which network coding is employed is introduced. It is shown that networks with coding are closely related to queueing networks with positive and negative customers. Analytical upper and lower bounds on the energy consumption and the delay are obtained using a Markov reward approach. The tradeoff between minimizing energy consumption and minimizing delay is investigated. Exact expressions are given for the minimum energy consumption and the minimum delay attainable in a network