Extraction studies of antimony bromide into benzene

Antimony(III) can be extracted rapidly and quantitatively into benzene from a 10 M H₂SO₄–0.03 M HBr system. The extracted antimony bromide has an antimony to bromine ratio of 1:3. Under the above optimum conditions for extraction of antimony, the behaviour of 35 other elements was studied; As³⁺, Ge⁴⁺, Se⁴⁺, and Sn²⁺ were extracted almost quantitatively, and the percentage extraction of Hg²⁺, Bi³⁺, and Te⁴⁺ was 74.1%, 10% and 5.5% respectively. The extraction of the elements into benzene from a 5 M H₂SO₄–0.01 M KI system was also investigated, A comparison of the two systems is given.     

A unified set of proposals for control and design of high speed data networks

In this paper we articulate our philosophy and approach to the design and control of high speed data networks. The object is to put into perspective and to explain the coordination of various isolated pieces of detailed technical analyses that have been reported in several recent papers. In the process we summarize what we have learnt in our recent work and, also, we give indications of the direction of our future work. Our scheme integrates feedback and open loop control. The feedback control is exercised by sliding windows; access controllers regulate bursty sources. All our design proposals are rooted in asymptotic analyses; the justification for asymptotics comes from the largeness of the parameters, such as propagation delay, speed, window size, buffer size, and the number of virtual circuits. This analysis makes a strong case for operating in a specific moderate usage regime, and adaptive dynamic windowing algorithms are given that make this happen; moreover, when in this regime, buffers may be sized aggressively small without jeopardizing performance and the simplicity of the retransmission protocol. The topics in the paper are: model of communication, results on the steady-state behavior of the basic model, access control, small buffers and retransmission protocols, dynamic adaptive windows, bursty sources, and contrast with previous work.I. Mitrani's work was done while AT&T Bell Laboratories.     

A semidefinite programming approach to the optimal control of a single server queueing system with imposed second moment constraints

Classical analyses of the dynamic control of multi-class queueing systems frequently yield simple priority policies as optimal. However, such policies can often result in excessive queue lengths for the low priority jobs/customers. We propose a stochastic optimisation problem in the context of a two class M/M/1 system which seeks to mitigate this through the imposition of constraints on the second moments of queue lengths. We analyse the performance of two families of parametrised heuristic policies for this problem. To evaluate these policies we develop lower bounds on the optimum cost through the achievable region approach. A numerical study points to the strength of performance of threshold policies and to directions for future research.     

Analysis of job transfer policies in systems with unreliable servers

We consider a system where incoming jobs may be executed at different servers, each of which goes through alternating periods of being available and unavailable. Neither the states of the servers nor the relevant queue sizes are known at moments of arrival. Hence, a load balancing mechanism that relies on random time-out intervals and job transfers from one queue to another is adopted. The object is to minimize a cost function which may include holding costs and transfer costs. A model of a single queue with an unreliable server and timeouts is analyzed first. The results are then used to obtain an approximate solution for arbitrary number of queues. Several transfer policies are evaluated and compared.     

Multiprocessor systems with reserves and preferences

Two models involving multiprocessor systems with two different groups of processors are examined. In the first model, the processors which are in use break down from time to time; one of the two groups is used only when the other one is entirely inoperative. In the second model, the breakdowns are replaced by a Poisson stream of jobs. Again, one group of processors is used in preference to the other one. In both cases, the analysis is based on finding a polynomial in two variables which satisfies a partial differential-functional equation. Exact solutions are obtained.     

Efficient window flow control for high speed data networks with small buffers

As the transmission speeds of emerging data networks scale up, the effects of propagation delays, which do not scale, become quite consequential for the design of sliding windows which are needed for congestion control. It was previously shown that optimal window lengths grow linearly with transmission speed , thus making the cost of memory for buffers a major factor. However, it was also shown that the moments of the number of packets in the buffers are onlyO( ), the remaining packets are in the course of being propagated. This fact underlies the proposal made here which requires smallO( ) buffers and yet guarantees that the ratio of the realized throughput to the ideal throughput approaches unity with increasing . That is, buffers when properly sized overflow so rarely that even with a rudimentary (conversely, easily implemented) protocol like go-back-n, the loss in throughput due to retransmissions is negligible. This result is arrived at by obtaining an explicit characterization for large of thetail of the distribution of buffer occupancy in the closed network with window sized buffers; in the case of a single-hop virtual circuit the characterization is by a Gaussian conditioned to be nonnegative. Numerical and simulation results are presented to corroborate the performance predictions of the theory for the case of 45 Mbits/sec transmission speed.Work done while visiting AT&T Bell Laboratories.     

Limiting results for multiprocessor systems with breakdowns and repairs

An M/M/N queue, where each of the processors is subject to independent random breakdowns and repairs, is analyzed in the steady state under two limiting regimes. The first is the usual heavy traffic limit where the offered load approaches the available processing capacity. The (suitably normalized) queue size is shown to be asymptotically exponentially distributed and independent of the number of operative processors. The second limiting regime involves increasing the average lengths of the operative and inoperative periods, while keeping their ratio constant. Again the asymptotic distribution of an appropriately normalized queue size is determined. This time it turns out to have a rational Laplace transform with simple poles. In both cases, the relevant parameters are easily computable.     

Static and dynamic server allocation in systems with on/off sources

A system consisting of a number of servers, where demands of different types arrive in bursts (modelled by interrupted Poisson processes), is examined in the steady state. The problem is to decide how many servers to allocate to each job type, so as to minimize a cost function expressed in terms of average queue sizes. First, an exact analysis is provided for an isolated IPP/M/n queue. The results are used to compute the optimal static server allocation policy. The latter is then compared to four heuristic policies which employ dynamic switching of servers from one queue to another (such switches take time and hence incur costs). This work was carried out in the framework of the collaborative project DOPCHE (Dynamic Operative Policies for Commercial Hosting Environments), funded by the UK Engineering and Physical Sciences Research Council under its E-Science programme. The support of the Network of Excellence EuroNGI, funded by the EU, is also acknowledged.     

Large Scale and Heavy Traffic Asymptotics for Systems with Unreliable Servers

The asymptotic behaviour of the M/M/n queue, with servers subject to independent breakdowns and repairs, is examined in the limit where the number of servers tends to infinity and the repair rate tends to 0, such that their product remains finite. It is shown that the limiting two-dimensional Markov process corresponds to a queue where the number of servers has the same stationary distribution as the number of jobs in an M/M/ queue. Hence, the limiting model is referred to as the M/M/[M/M/] queue. Its numerical solution is discussed.Next, the behaviour of the M/M/[M/M/] queue is analysed in heavy traffic when the traffic intensity approaches 1. The convergence of the (suitably normalized) process of the number of jobs to a diffusion is proved.     

Qubits versus bits for measuring an integral of a classical field

Methods for measuring an integral of a classical field via local interaction of classical bits or local interaction of qubits passing through the field one at a time are analyzed. A quantum method, which has an exponentially better precision than any classical method we could see, is described.