Throughput Estimation Research Articles

An algorithm for optimal buffer placement in reliable serial lines

The optima] allocation of buffer capacity in unbalanced production lines with reliable but variable workstations is a complex and little-researched topic. Analytic formulas for the throughput of these lines do not exist, so simulation is the only practical alternative for estimating throughput. Exhaustive search over all possible buffer allocations quickly becomes impractical beyond short lines and few buffers. Thus an algorithm is needed to efficiently find optimal or near-optimal allocations. We develop a simple search algorithm for determining the optimal allocation of a fixed amount of buffer capacity in an n-station serial line. The algorithm, which is an adaptation of the Spendley-Hext and Nelder-Mead simplex search algorithms, uses simulation to estimate throughput for every allocation considered. An important feature of the algorithm is that the simulation run length is adjusted during the running of the algorithm to save simulation run time when high precision in throughput estimates is not needed, and 10 ensure adequate precision when it is needed. We describe the algorithm and show that it can reliably find the known optimal allocation in balanced lines. Then we test the ability of the algorithm to find optimal allocations in unbalanced lines, first for cases in which the optimal allocation is known, and subsequently for cases in which the optimal allocation is not known. We focus particularly on lines with multiple imbalances in means and variances. In general, our algorithm proves highly efficient in finding a near-optimal allocation with short simulation run times. It also usually finds the true optimal allocation, but it is in the nature of this problem that many buffer allocations differ in throughput by small amounts that are difficult to resolve even with long simulation runs.

An algorithm for optimal buffer placement in reliable serial lines

The optimal allocation of buffer capacity in unbalanced production lines with reliable but variable workstations is a complex and little-researched topic. Analytic formulas for the throughput of these lines do not exist, so simulation is the only practical alternative for estimating throughput. Exhaustive search over all possible buffer allocations quickly becomes impractical beyond short lines and few buffers. Thus an algorithm is needed to efficiently find optimal or near-optimal allocations. We develop a simple search algorithm for determining the optimal allocation of a fixed amount of buffer capacity in an n-station serial line. The algorithm, which is an adaptation of the Spendley-Hext and Nelder-Mead simplex search algorithms, uses simulation to estimate throughput for every allocation considered. An important feature of the algorithm is that the simulation run length is adjusted during the running of the algorithm to save simulation run time when high precision in throughput estimates is not needed, and to ensure adequate precision when it is needed. We describe the algorithm and show that it can reliably find the known optimal allocation in balanced lines. Then we test the ability of the algorithm to find optimal allocations in unbalanced lines, first for cases in which the optimal allocation is known, and subsequently for cases in which the optimal allocation is not known. We focus particularly on lines with multiple imbalances in means and variances. In general, our algorithm proves highly efficient in finding a near-optimal allocation with short simulation run times. It also usually finds the true optimal allocation, but it is in the nature of this problem that many buffer allocations differ in throughput by small amounts that are difficult to resolve even with long simulation runs.

An approach to wide area WDM optical network design using genetic algorithm

This article presents a systemic method to generate and map an optimal virtual topology onto a certain physical wide area optical fiber network so as to maximize the scaleup which provides an estimate of the network throughput. The problem is to find the best possible virtual topology over a given wavelength-routed all-optical physical topology for wide area coverage. The physical topology consists of wavelength-routing nodes interconnected by fiber links in the network. The virtual topology consists of a set of lightpaths. For a given physical topology and traffic matrix, our objective is to maximize the throughput as well as to minimize the delay. We have also studied the scalability of various parameters, such as queuing delay, propagation delay and average-hop-distance, with increase in throughput. We present a heuristic algorithm for embedding a virtual topology to the given physical fiber network when the number of wavelength channels supported on each fiber is limited. A number of feasible virtual topologies are generated randomly using Prufer number method, and the optimum one is selected. The problem being computationally intractable, we use genetic algorithm (GA)for optimization. As GAs are expected to converge to globally optimal solutions, the proposed approach yields better solutions than previous ones. As a result of immense practical importance of the issues addressed in this work, the algorithms are expected to be significant for practitioners.

Setting WIP levels with statistical throughput control (STC) in CONWIP production lines

We develop a simple adaptive production control method for setting WIP levels to meet target production rates in a pull production operating under the CONWIP (Constant work in process) protocol. This method, termed Statistical Throughput Control (STC), uses real-time data to automatically adjust WIP levels (via kanban cards) in the face of noisy estimates of throughput. Because STC does not rely on a steady-state model, it is well-suited to systems subject to environmental changes such as those induced by continuous improvement efforts. Using simulation, we demonstrate the effectivness of STC under a variety of conditions, including single and multiple products, simple flow lines, routeings with shared resources and assembly systems.

Throughput estimation in cyclic queueing networks with blocking

The paper presents a new approach for estimating the throughput of a closed queueing network with exponential servers, finite buffer capacity and a blocking after service discipline. The problem is tackled by decomposing the network. The population constraint is enforced by requiring that the sum of the expected number of customers in the various subsystems is equal to the population size. Each subsystem is analyzed as an M/M/1/Ci+1 queue with state-dependent arrival and service rates. The rationale behind this last assumption is that the behavior of the system at a given time is affected by the history of blockings and starvations. The results obtained by applying the proposed algorithm to a set of test problems show a good agreement with those obtained with simulation, the difference on the maximum throughput of the network being of the order of 3%. The obtained results also compare favorably with those described in the literature.

Processing throughput estimation for radar intercept receivers

Analytical expressions for the computational requirements of broad classes of radar pulse deinterleaving algorithms are developed. The analysis applies to block collection systems and is principally intended for systems with insufficient monopulse resolution to uniquely sort emitters on monopulse parameters alone. The analysis begins with triplet sequence search approaches and is confirmed by simulation. It is also shown that this approach generalizes to more complex deinterleaving schemes, including M-tuple search and time of arrival (TOA) difference histogramming. All cases exhibit the same basic functional form of quadratic dependence on the number of emitters, linear dependence on the collection time, and complex dependence on the pulse deletion (or dropping) probability.

Dlpsim: a teaching harness for data link protocols

Protocol test harnesses have been in use for a number of years to assist implementers in checking conformance of their implementations with reference implementations. The system described here is designed for teaching the principles of data link protocols. Students write protocol implementations in a high-level language and exercise them on a simulator. The simulator checks that data is not duplicated or lost by the protocol. On suitable terminals, visualization of the transmitting window and of the frames traversing the link can provide useful feedback to students. Simple estimates of throughput are also calculated.

Progress on RTSS simulation-based analysis for real-time systems development at two laboratories

A new object-oriented Real Time System Simulator (RTSS) with the capability for simulation graphics and animation, has been developed and used for modeling the distributed data acquisition and processing systems at JET and ASIPP. Simulation allows estimates of response time, throughput and resource utilization for a variety of configurations to be investigated. Performance measurements, simulation and analysis are used together to calibrate and validate each other.

PVD equipment design: concepts for increased production throughput

It is now widely accepted that plasma-assisted PVD coatings have their strongest foothold in application sectors for which throughput is low and for which coated components have high added value, such as the aerospace industry. These sectors are typically supplied by batch-type coating facilities. This suggests that there is an important gap in the market, i.e. the low cost components found in high volume industries. This has prompted a design study of PVD coating equipment. Predictions are made for the number of selected components which a typical batch production system can process in a given time and the costs associated with that system. An estimation of throughput for a continuous system which has the same size of process chamber as the batch system is also given, and a comparison of the cost per component is made for each. A breakdown of the costs is given for the manufacturing and running of both batch and continuous systems. This is then used to highlight the areas where costs can be reduced in the design and manufacture of continuous coating plants.

Predicting intrawafer film thickness uniformity in an ultralow pressure chemical vapor deposition reactor

We present a reaction engineering analysis of a multiple wafer-in-tube ultrahigh vacuum chemical vapor deposition reactor which allows an estimate of wafer throughput for a reactor of fixed geometry and a given deposition chemistry with specified film thickness uniformity constraints. The model employs a description of ballistic transport and reaction based on the pseudosteady approximation to the Boltzmann equation in the limit of pure molecular flow. The model representation takes the form of an integral equation for the flux of each reactant or intermediate species to the wafer surfaces. Expressions for the reactive sticking coefficients (RSC) for each species must be incorporated in the term which represents reemission from a wafer surface. In our model we use a published expression for the RSC of silane as a function of flux and wafer temperature developed from molecular beam measurements. Numerical solution of the resulting integral equation using Gauss–Legendre quadrature yields quantitative estimates of intrawafer film thickness uniformities for epitaxial silicon deposition from silane for specified process conditions and wafer radius:wafer separation. For given reactor dimensions and specified uniformity, throughputs can then be estimated.

A design of a fast pipelined modular multiplier based on a diminished-radix algorithm

We present a new serial-parallel concurrent modular-multiplication algorithm and architecture suitable for standard RSA encryption. In the new scheme, multiplication is performed modulo a multiple of the RSA modulus n, which has a diminished-radix form 2 k -v, where k and v are positive integers and v < n. This design is the first concurrent modular multiplier to use a diminished-radix algorithm and to pipeline concurrent modular-reduction to optimize the clock rate. For a modular multiplier of order ranging from 1 to 10 (number of multiplier bits per clock cycle), a faster clock rate and throughput is possible than with other known designs including those of Brickell, Morita, Sedlak and Golze, and Miyaguchi. Throughput estimates for 512-bit RSA decryption range from 100 kbit/s in a serial mode to 650 kbit/s with a modular multiplier of order 10, at a clock rate of 20 MHz on 1.5 μm CMOS.

Logic simulation of RSFQ circuits

It is shown how to modify a conventional logic editor-simulator to make it suitable for design of rapid single flux quantum (RSFQ) circuits containing thousands of Josephson junctions. The key new component of the simulator is a library of RSFQ cells. This library has been developed based on an original representation of timing constraints in RSFQ of these constraints. The extended tool supports detection and location of logic design errors in an RSFQ circuit, estimation of circuit speed and throughput, and optimization of the general architecture of the circuit and its synchronization scheme. It is shown how the RSFQ editor-simulator has been employed for designing a decimation filter, a component of a digital signal processing chip currently under development at the University of Rochester. >

Sharp approximate models of deflection routing in mesh networks

Deflection routing is a simple, decentralized, and adaptive method for routing data packets in communication networks. The focus of this work is on deflection routing in the Manhattan street network (a two-dimensional directed mesh), although the analytic approach should apply to any regular network. Two approximate performance models that give sharp estimates of the steady-state throughput and the average packet delay for packets admitted to the network are presented. The results of extensive simulation experiments are reported, which corroborate the models' predictions. The results show that deflection routing is very effective. Two measures of the merit of a network for deflection routing are its diameter and its deflection index. Networks are presented whose diameter and deflection index are near the optimal values.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Experimental and statistical determination of the static position repeatability and a recommended specification for a SCARA robot

This paper describes an experiment and the statistical analysis performed to evaluate the repeatability of a SCARA robot and proposes an alternative form of specification for repeatability. Repeatability has been chosen because the precision obtained from teach-and-play-back programming for pick-and-place tasks, which is still widely used, depends primarily upon this performance value. The measuring method uses two theodolites, which though laborious in set-up is nevertheless simple, economical and sufficiently accurate for the purpose intended. The results are used for comparison with the given specification and for studying the influence of factors such as load, speed and spatial location in the working envelope using analysis of variance; the estimate of the repeatability value is calculated using the standard deviations of the measured coordinates of representative points modified by a factor from Student's t curves. From the analysis, it can be inferred that the repeatability value is dependent upon operating speed, load and plane location. The experimental study also points to a possible form of specification. For example, for the specification to be useful in the study of arrangement of feeders of parts to be assembled by the robot and the estimation of throughput given part weight, it could be given in a table form showing the range of the repeatability value for the designed combinations of speed, payload and position in the envelope.

A controlled multiaccess protocol for packet satellite communication

This protocol is fully distributed and no onboard processing is required for the satellite. A control parameter f is used to adaptively control the packet transmission rate such that maximum system capacity can be attained and the average delay is always minimized for a given throughput. The controlled protocol is found to give a smaller average delay than slotted ALOHA even when the throughput is as low as 0.05. On the other hand, under heavy traffic conditions, it can provide a throughput close to unity and an average delay not much more than one round-trip propagation delay. The system performance is also robust, in the sense that a 15% error in throughput estimation results in no more than a 3% increase of the overall average packet delay. >

An exact discrete-event model and control policies for production lines with buffers

The authors present a hybrid simulation/analytic model for the analysis and design of unreliable production lines with buffers and discrete workparts. The model is exact and much faster than conventional piece-by-piece simulators. It can analyze, efficiently and accurately, lines of any size during either transient or steady-state periods by taking into account effectively all transients associated with the function of the line. It is demonstrated that the model is superior to both brute-force and event-driven models and is an efficient practical tool in the analysis and design of production lines. By incorporating the perturbation analysis technique into the proposed algorithm. the gradient estimation of the system's throughput can be performed during a single simulation run for various design parameters. A number of experimental results are reported for the repair allocation problem, and the optimality of various control policies is investigated. >

Emulating concurrency in a circuit card assembly system

Typical component-placement systems for populating surface mount technology printed circuit boards now exhibit a high degree of concurrency in their functional operations. This concurrency ideally yields high “burst-rate” estimates of throughput. However, if the concurrency is not properly understood and exploited, the burst rate is severely degraded, as exhibited by process rates observed in the actual production environment. This discernment requires an experimental characterization of the system's functional operation, which must also reflect the peculiarities of the controller. Such an experimental analysis is an essential precursor to performance-optimization procedures of numerically controlled flexible manufacturing systems. This article describes our analysis of an extremely complex workcell with a high degree of concurrency. Due to its enveloping complexity, the methodological framework for the analysis should be applicable to a broad class of concurrent systems. Empirically verifying the characterization required the development of an emulator that quantitatively defines the system to be modeled. As such, it is a numerical, off-line design and analysis tool. It has been utilized to obtain the process rate for particular products, preevaluate proposed engineering changes, interactively construct setups and sequences, and obtain parameters required for line-balancing procedures.

Soft-electron background in x-ray telescopes using Wolter I grazing-incidence optics in near-Earth orbits

The background in x-ray telescopes in near-Earth orbits from low-energyelectrons (<100 keV) haslong been a sourceofconcern. Recent data on low-energy electron populations and improvements in the modeling of the propagation of low-energy electrons through Wolter I grazing- incidence optical systems now allow better quantitative estimates of the electron throughput of such systems. The modeling that has recently been done with respect to the U.K. soft x-ray telescope (Wide Field Camera) on ROSAT is described. The results from the modeling are then applied to several other missions using grazing-incidence optics, and the implications are discussed.

Iterative algorithms for estimating the capacity of automated production lines with finite buffers

SUMMARY The paper describes two fast iterative algorithms for estimating the capacity of automated production lines with finite buffers. These algorithms are based on the linear programming formulation of the problem developed earlier by the author, and provide a range of values in which the throughput of the line is expected to lie. The throughput estimates of the two algorithms, compared with an estimate based on a simple workload analysis, indicate the amount of blocking/starvation as well as the probable causes of this unproductive time. The paper illustrates how inferences can be drawn from the two algorithms and used to improve the loading sequence and lot sizes. Managers can decide if the potential for improvement, which would be to get rid of all blocking/starvation, justifies the time to be spent on such an effort. New alternatives can be developed based on the insights provided by the algorithms and tested quickly.

Application of the x-Plot Technique to the Study of Water Influx in the Sidi El-Itayem Reservoir, Tunisia (includes associated paper 17548 )

Summary. The x-plot technique is extended and a relationship is developedbetween water throughput and water cut by use of field performance data. This relationship allows the estimation of water that has invaded thedrainage area of a well, a group of wells, or a field under water injectionor natural water influx. Applications to a simulated waterflood, an actualwaterflood in Long Beach, CA, and the water influx in the Sidi El-Itayemreservoir in Tunisia are discussed. Introduction The x-plot technique introduced by Ershaghi and Omoregie and Ershaghi and Abdassah is a convenientmethod for representing oilfield performance historyunder water injection or natural water drive. The procedureis a linearization of water cut vs. recovery plot, allowingextrapolation to higher cuts. From the relationship one (1) may also derive a field composite relative-permeability-ratiocurve. Flood pot test data are often used to derive a relationshipbetween water throughput and water cut. This approachrequires the availability of core material representativeof reservoir properties. Additionally, such core-derived correlations, which are based on laboratory relative-permeabilitycurves, may not be extrapolated to actual field conditionsbecause of layering and permeability variations that affectthe field composite relative permeabilities. Our experimentation with Eq. 1 in which both a reservoirsimulation approach and actual field performance datawere used shows that one may obtain a fair estimate ofthe cumulative water throughput at any high water cut from the slope of the x-plot. This paper describes the proposed technique and itsapplication to the Sidi El-Itayem reservoir in Tunisia, which is under a strong water drive. Method Description The x-plot procedure requires plotting × ln(1/fw − 1) − 1/fw vs. fractional recovery. In the absence of layeringeffects and remedial profile corrections, a linear plot isobtained for cut values above 50%. The formation of astraight line indicates that the performance is beingcontrolled by the relative-permeability-ratio characteristicsof the reservoir. If the oil recovery is expressed in terms of the fractionof oil in place(Eq. 1), then rn and n may be used to obtaina field relative-permeability-ratio curve. The amount of water throughput at any fw from thefrontal advance equation may be expressed as (2) In practice, Eq. 2 requires a fieldwide relative-permeability-ratio curve. With a simple transformation of Eq. 1 and the derivationshown in Ref. 1 for dfw/dSw, we have developed a procedure toobtain estimates of water through-put from the slope of the x-plot. If we express oil recovery in terms of actual volumes produced, Eq. 1 can be written as x--m'N +n', where m'=1/(Nm) and n'= -n/m. From Ref. 1, (3) and b=1/[m(1 − Swi)]. Therefore, with the definitionfor m', = = Now the water throughput in terms of actual volume canbe estimated from (4) where m' is in 1/vol. Application to Waterflood Application of Eq. 4 to both a simulated and an actualwaterflood is demonstrated here. JPT P. 1127^