Evaluation of phosphate in fertilizers by means of the alkaline ammonium citrate extraction according to Petermann.

The phosphate extraction with alkaline ammonium citrate solution for the control of phosphate in fertilizers was subjected to a critical examination. The contribution of inferior phosphate forms such as tricalcium phosphates and apatites to the available P2O5 percentage can be excluded to a great extent by using a narrow sample solvent ratio. However, the dissolution rate of dicalcium phosphate in alkaline ammonium citrate solution limits the narrowing of the ratio. The dissolution rate of dicalcium phosphate can be increased, if instead of intermittent manual shaking, mechanical shaking is applied. Extraction of 1.0 g sample with 200 ml of alkaline ammonium citrate solution at 65 deg C under mechanical shaking for 1.5 hours is preferred to other methods for quality control of phosphate in fertilizers. The extraction method with neutral ammonium citrate solution is not reliable, because this method makes little or no distinction between high quality and low quality fertilizers. (Abstract retrieved from CAB Abstracts by CABI’s permission

A Tandem Fluid Network with L\'evy Input in Heavy Traffic

In this paper we study the stationary workload distribution of a fluid tandem queue in heavy traffic. We consider different types of L\'evy input, covering compound Poisson, $\alpha$-stable L\'evy motion (with $1<\alpha<2$), and Brownian motion. In our analysis we separately deal with L\'evy input processes with increments that have finite and infinite variance. A distinguishing feature of this paper is that we do not only consider the usual heavy-traffic regime, in which the load at one of the nodes goes to unity, but also a regime in which we simultaneously let the load of both servers tend to one, which, as it turns out, leads to entirely different heavy-traffic asymptotics. Numerical experiments indicate that under specific conditions the resulting simultaneous heavy-traffic approximation significantly outperforms the usual heavy-traffic approximation

Queues with delays in two-state strategies and Lévy input

We consider a reflected Lévy process without negative jumps, starting at the origin. When the reflected process first upcrosses level K, a timer is activated. After D time units, the timer expires and the Lévy exponent of the Lévy process is changed. As soon as the process hits zero again, the Lévy exponent reverses to the original function. If the process has reached the origin before the timer expires then the Lévy exponent does not change. Using martingale techniques, we analyze the steady-state distribution of the resulting process, reflected at the origin. We pay special attention to the cases of deterministic and exponential timers, and to the following three special Lévy processes: (i) a compound Poisson process plus negative drift (corresponding to an M/G/1 queue), (ii) Brownian motion, and (iii) a Lévy process that is a subordinator until the timer expires. © Applied Probability Trust 2008

Repair systems with exchangeable items and the longest queue mechanism

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according to which backorders are satisfied by repaired items is the longest queue rule: at the completion of a service (repair), the repaired item is delivered to the base that has the largest number of failed items. We point out a direct relation between our model and the classical longer queue model. We obtain simple expressions for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. Finally, we derive the sojourn time distributions

Analysis of a multi-server queueing model of ABR

In this paper we present a queueing model for the performance analysis of Available Bit Rate (ABR) traffic in Asynchronous Transfer Mode (ATM) networks. We consider a multi-channel service station with two types of customers, denoted by high priority and low priority customers. In principle, high priority customers have preemptive priority over low priority customers, except on a fixed number of channels that are reserved for low priority traffic. The arrivals occur according to two independent Poisson processes, and service times are assumed to be exponentially distributed. Each high priority customer requires a single server, whereas low priority customers are served in processor sharing fashion. We derive the joint distribution of the numbers of customers (of both types) in the system in steady state. Numerical results illustrate the effect of high priority traffic on the service performance of low priority traffic