Workload distributions in ASIP queueing networks

Queueing Systems - The workload of a generalized n-site asymmetric simple inclusion process (ASIP) is investigated. Three models are analyzed. The first model is a serial network for which the...     

Convergence of the all-time supremum of a Lévy process in the heavy-traffic regime

In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let $\{Y^{(a)}_{n}:n\ge1\}In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let {Y^(a)_n:n 3 1}\{Y^{(a)}_{n}:n\ge1\} be a sequence of independent and identically distributed random variables and {X^(a)_t:t 3 0}\{X^{(a)}_{t}:t\ge0\} be a Lévy process such that X₁^(a)=^dY₁^(a)X_{1}^{(a)}\stackrel{d}{=}Y_{1}^{(a)}, \mathbbEX₁^(a) < 0\mathbb{E}X_{1}^{(a)}<0 and \mathbbEX₁^(a)-0\mathbb{E}X_{1}^{(a)}\uparrow0 as a↓0. Let S^(a)_n=?_k=1ⁿ Y^(a)_kS^{(a)}_{n}=\sum _{k=1}^{n} Y^{(a)}_{k}. Then, under some mild assumptions, , for some random variable and some function Δ(⋅). We utilize this result to present a number of limit theorems for suprema of Lévy processes in the heavy-traffic regime.     

Strobes: Pyrotechnic Compositions That Show a Curious Oscillatory Combustion

Strobes are pyrotechnic compositions which show an oscillatory combustion; a dark phase and a flash phase alternate periodically. The strobe effect has applications in various fields, most notably in the fireworks industry and in the military area. All strobe compositions mentioned in the literature were discovered by trial and error methods and the mechanisms involved remain unclear. Many oscillatory systems such as Belousov–Zhabotinsky reactions, cool flames, self‐propagating high‐temperature synthesis have been observed and theories developed to elucidate their unstable behavior based on chemical interactions or based on physical processes. These systems are compared to experimental observations made on strobe mixtures.     

Queues with random back-offs

We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation periods may be initiated after each service completion, and can be randomly terminated with certain probabilities that depend on the queue length. We first present exact queue-length and delay results for some specific cases and we derive stochastic bounds for a much richer set of scenarios. Using these, together with stochastic relations between systems with different vacation disciplines, we examine the scaled queue length and delay in a heavy-traffic regime, and demonstrate a sharp trichotomy, depending on how the activation rate and vacation probability behave as function of the queue length. In particular, the effect of the vacation periods may either (i) completely vanish in heavy-traffic conditions, (ii) contribute an additional term to the queue lengths and delays of similar magnitude, or even (iii) give rise to an order-of-magnitude increase. The heavy-traffic trichotomy provides valuable insight into the impact of the back-off algorithms on the delay performance in wireless random-access networks.     

Dissipativity of the delay semigroup

Under mild conditions a delay semigroup can be transformed into a (generalized) contraction semigroup by modifying the inner product on the (Hilbert) state space into an equivalent inner product. Applications to stability of differential equations with delay and stochastic differential equations with delay are given as examples.     

Milling of Organic Solids in a Jet Mill. Part 1: Determination of the Selection Function and Related Mechanical Material Properties

The particle size distribution of pharmaceutically active materials and other fine chemicals determines the performance of the final product to a large extent. Often milling of these particles is necessary. It is not possible to determine the milling conditions solely on the basis of the particle size distribution of the starting material, because the (mechanical) properties of the material also determine the desired milling conditions. It is often not possible to optimize milling conditions experimentally because the amount of material available is frequently highly limited. A theoretical approach towards predicting the best milling conditions is needed. The purpose of this study was to develop a method to predict the desired milling conditions given a specific (organic) solid material. The selection function and the breakage distribution function are usually the starting points in modeling the milling process. The selection function is the parameter that includes the material and mill properties. Dimensional analysis made it possible to correlate the selection function with material properties. A set of theories available in the literature enable prediction of the material properties. For different compounds (lactose, paracetamol, a steroidal compound, and two heterocyclic compounds) the selection functions were calculated. The calculations predict differences: lactose reduces slowly in size, while one of the heterocyclic compounds shows the most intense fracture.     

The Asymptotic Workload Behavior of Two Coupled Queues

We consider a system of two coupled queues Q ₁ and Q ₂. When both queues are backlogged, they are each served at unit rate. However, when one queue empties, the service rate at the other queue increases. Thus, the two queues are coupled through the mechanism for dynamically sharing surplus service capacity. We derive the asymptotic workload behavior at Q ₁ for various scenarios where at least one of the two queues has a heavy-tailed service time distribution. First of all, we consider a situation where the traffic load at Q ₁ is below the nominal unit service rate. We show that if the service time distribution at Q ₁ is heavy-tailed, then the workload behaves exactly as if Q ₁ is served in isolation at a constant rate, which only depends on the service time distribution at Q ₂ through its mean. In addition, we establish that if the service time distribution at Q ₁ is exponential, then the workload distribution is either exponential or semi-exponential, depending on whether the traffic load at Q ₂ exceeds the nominal service rate or not. Next, we focus on a regime where the traffic load at Q ₁ exceeds the nominal service rate, so that Q ₁ relies on the surplus capacity from Q ₂ to maintain stability. In that case, the workload distribution at Q ₁ is determined by the heaviest of the two service time distributions, so that Q ₁ may inherit potentially heavier-tailed characteristics from Q ₂.