Asymptotic expansions of moments of the waiting time in closed and open processor-sharing systems with multiple job classes

1983 ◽  
Vol 15 (4) ◽  
pp. 813-839 ◽  
Author(s):  
Debasis Mitra ◽  
J. A. Morrison
Keyword(s):  
Waiting Time ◽  
Open System ◽  
Closed System ◽  
Asymptotic Expansions ◽  
Queueing Networks ◽  
Open Systems ◽  
Asymptotic Series ◽  
Processor Sharing ◽  
Single Class ◽  
Closed Systems

We present new results based on novel techniques for the problem of characterizing the waiting-time distribution in a class of queueing networks. We give effective methods for computing, for each of possibly several job-classes, the second moment of the equilibrium waiting time for closed systems as well as for open systems. Both open and closed systems have a CPU operating under the processor-sharing (‘time-slicing') discipline in which service-time requirements may depend on job-class. The closed system also includes a bank of terminals grouped according to job-classes, with the class structure allowing distinctions in the user's behavior in the terminal. In the contrasting open system, the job streams submitted to the CPU are Poisson with rate parameters dependent on job-classes.Our results are exact for the open system and, for the closed system, in the form of an asymptotic series in inverse powers of a parameter N. In fact, the result for open networks is simply the first term in the asymptotic series. For larger closed systems, the parameter N is larger and thus fewer terms of the series need be computed to achieve a desired degree of accuracy. The complexity of the calculations for the asymptotic expansions is polynomial in number of classes and, importantly, independent of the class populations. Only the results on the single-class systems, closed and open, were previously known.

Asymptotic expansions of moments of the waiting time in closed and open processor-sharing systems with multiple job classes

1983 ◽  
Vol 15 (04) ◽  
pp. 813-839 ◽  
Author(s):  
Debasis Mitra ◽  
J. A. Morrison
Keyword(s):  
Waiting Time ◽  
Open System ◽  
Closed System ◽  
Asymptotic Expansions ◽  
Queueing Networks ◽  
Open Systems ◽  
Asymptotic Series ◽  
Processor Sharing ◽  
Single Class ◽  
Closed Systems

We present new results based on novel techniques for the problem of characterizing the waiting-time distribution in a class of queueing networks. We give effective methods for computing, for each of possibly several job-classes, the second moment of the equilibrium waiting time for closed systems as well as for open systems. Both open and closed systems have a CPU operating under the processor-sharing (‘time-slicing') discipline in which service-time requirements may depend on job-class. The closed system also includes a bank of terminals grouped according to job-classes, with the class structure allowing distinctions in the user's behavior in the terminal. In the contrasting open system, the job streams submitted to the CPU are Poisson with rate parameters dependent on job-classes. Our results are exact for the open system and, for the closed system, in the form of an asymptotic series in inverse powers of a parameter N. In fact, the result for open networks is simply the first term in the asymptotic series. For larger closed systems, the parameter N is larger and thus fewer terms of the series need be computed to achieve a desired degree of accuracy. The complexity of the calculations for the asymptotic expansions is polynomial in number of classes and, importantly, independent of the class populations. Only the results on the single-class systems, closed and open, were previously known.

E-Cigarettes: Policy Options and Legal Issues Amidst Uncertainty

2015 ◽  
Vol 43 (S1) ◽  
pp. 23-26 ◽  
Author(s):  
Nancy Kaufman ◽  
Margaret Mahoney
Keyword(s):  
Smoking Cessation ◽  
Propylene Glycol ◽  
Open System ◽  
Closed System ◽  
Open Systems ◽  
Delivery Systems ◽  
Legal Issues ◽  
Policy Options ◽  
Electronic Nicotine Delivery Systems ◽  
Closed Systems

E-cigarettes, sometimes referred to as ENDS (Electronic Nicotine Delivery Systems), include a broad range of products that deliver nicotine via heating and aerosolization of the drug. ENDS come in a variety of forms, but regardless of form generally consist of a solution containing humectant (e.g., propylene glycol or glycerol), flavorings, and usually nicotine (some solutions do not contain nicotine); a battery-powered coil that heats the solution into an aerosol (usually referred to as vapor) in an atomizing chamber; and a mouthpiece through which the user draws the vapor into the mouth and lungs. The devices may be closed systems containing prefilled cartridges, or open systems, where the user manually refills a 1-2 ml. tank with solution. What started as closed-system cigarette-shaped devices marketed as an adjunct for smoking cessation, has transitioned rapidly to literally thousands of hip and funky-designed open-system hookah pens, vape pens, and modifiable devices. For younger people, these forms are the “in” thing, while traditional cigarette-shaped devices are “out.”

Heavy-usage asymptotic expansions for the waiting time in closed processor-sharing systems with multiple classes

1985 ◽  
Vol 17 (1) ◽  
pp. 163-185 ◽  
Author(s):  
J. A. Morrison ◽  
D. Mitra
Keyword(s):  
Waiting Time ◽  
Asymptotic Expansions ◽  
Queueing Networks ◽  
Parabolic Cylinder ◽  
Processor Sharing ◽  
Closed Queueing Networks ◽  
Second Moments ◽  
Large Numbers ◽  
Sharing Time ◽  
Leading Term

We present new results based on novel techniques for the problem of characterizing the waiting-time distribution in a class of closed queueing networks in heavy usage, which in practical terms means that the processor is utilized more than about 80 per cent. This paper extends recent work by Mitra and Morrison [10] on the same system in normal usage. The closed system has a CPU operating under the processor-sharing (‘time-slicing’) discipline and a bank of terminals. The presence of multiple job-classes allows distinctions in the user’s behavior in the terminal and in the service requirements. This work is primarily applicable to the case of large numbers of terminals. We give an effective method for calculating, for the equilibrium waiting time, the first and second moments and the leading term in the asymptotic approximation to the distribution. Our results are in the form of asymptotic expansions in inverse powers of , where N is a large parameter. The expansion coefficients depend on the classical parabolic cylinder functions.

Heavy-usage asymptotic expansions for the waiting time in closed processor-sharing systems with multiple classes

1985 ◽  
Vol 17 (01) ◽  
pp. 163-185
Author(s):  
J. A. Morrison ◽  
D. Mitra
Keyword(s):  
Waiting Time ◽  
Asymptotic Expansions ◽  
Queueing Networks ◽  
Parabolic Cylinder ◽  
Processor Sharing ◽  
Closed Queueing Networks ◽  
Second Moments ◽  
Large Numbers ◽  
Sharing Time ◽  
Leading Term

We present new results based on novel techniques for the problem of characterizing the waiting-time distribution in a class of closed queueing networks in heavy usage, which in practical terms means that the processor is utilized more than about 80 per cent. This paper extends recent work by Mitra and Morrison [10] on the same system in normal usage. The closed system has a CPU operating under the processor-sharing (‘time-slicing’) discipline and a bank of terminals. The presence of multiple job-classes allows distinctions in the user’s behavior in the terminal and in the service requirements. This work is primarily applicable to the case of large numbers of terminals. We give an effective method for calculating, for the equilibrium waiting time, the first and second moments and the leading term in the asymptotic approximation to the distribution. Our results are in the form of asymptotic expansions in inverse powers of , where N is a large parameter. The expansion coefficients depend on the classical parabolic cylinder functions.

Amplifying the Significance of Systems Theory

2017 ◽  
pp. 301-308
Author(s):  
Mambo Mupepi
Keyword(s):  
System Theory ◽  
Open System ◽  
Closed System ◽  
Open Systems ◽  
System Behavior ◽  
Internal Dynamics ◽  
Key Stakeholders ◽  
Stable Performance ◽  
Regulate System ◽  
Increase Productivity

In system theory organizations are viewed as closed or open systems. An open system interacts with the environment for its sustainability. The closed system does not interact with its setting consequently its behavior depends largely on internal dynamics of its parts. The centricity of an open organizational structure is one created and empowered to learn and change very fast to successfully achieve desired goals. However open systems need to embrace change as follows: transform inputs of energy and information to produce the products demanded by the customers, transact with key stakeholders to access resources, regulate system behavior to achieve stable performance, and adapt to continuously changing high velocity competition to increase productivity.

The Structure of the Nervous System in Velella

1960 ◽  
Vol s3-101 (54) ◽  
pp. 119-131
Author(s):  
G. O. MACKIE
Keyword(s):  
Nervous System ◽  
Open System ◽  
Closed System ◽  
Silver Staining ◽  
Sensory Cells ◽  
Nerve Fibres ◽  
Nerve Net ◽  
Two Systems ◽  
Staining Methods ◽  
Closed Systems

Silver staining methods have been applied to the nervous system of Velella. Two histologically distinct plexuses are described under the headings ‘open’ and ‘closed’ systems. The open system consists of neurones with fine processes which run for distances of up to 2 mm, retaining their independence ins pite of frequent contacts with other fibres. The fibres of the closed system are large and run together, forming a nerve-net in which neurofibrillar material from different neurones intermingles; it is provisionally to be regarded as a syncytium. A certain type of ‘fibre’ in this system is believed to arise secondarily by the drawing out of adhesion connexions into long strands. Free nerve-endings resembling growing-points occur in both systems. The two systems occur throughout the ectoderm, but in the invaginated ectoderm the open system is poorly developed. The functions of the two systems are not known, but the closed system is probably specialized for through-conduction. Neuro-sensory cells occur in the external ectoderm, making contact with fibres of both open and closed systems. No specialized endings have been found in a muscular region examined. No nerve-rings or centres have been found. Nerves are sparsely distributed in the endoderm, but they lie independently of one another and of ectodermal nerve-fibres crossing the mesogloea between the invaginated and external ectoderm layers.

Denitrification kinetics in an activated sludge system

1995 ◽  
Vol 32 (9-10) ◽  
pp. 323-330
Author(s):  
M. Roš
Keyword(s):  
Activated Sludge ◽  
Closed System ◽  
Open Systems ◽  
Aeration Tank ◽  
Activated Sludge System ◽  
Denitrification Kinetics ◽  
Closed Systems ◽  
Nitrate And Nitrite ◽  
Sludge Concentration

For all water bodies especially for sea, lakes, and ground waters it is very important that nutrient pollution is the least possible (minimal). From municipal and industrial waste waters where considerable amount of nutrients is expected it is possible to remove nutrients with biological treatment. The first step is usually aerobic activated sludge treatment and the second step is combined anaerobic-anoxic-aerobic step in different combinations. A very effective process for nitrogen removal is anoxic activated sludge system. It is very important that in the first aerobic step complete nitrification is achieved. In our laboratory denitrification kinetics was studied. The objective of this study was determination of denitrification velocity and attendance of different parallel phenomena such as nitrite, disappearance of nitrate and nitrite, sulphide formation, etc. Denitrification process was studied in two systems, in closed system (such as in closed reactors for denitrification) and in open systems (such as in open denitrification tanks). We found out that denitrification rate in closed systems was from about 8 to 52 mg/l.h and was dependent on activated sludge type, sludge concentration, and temperature of the system. In open system (such as in an anoxic aeration tank) the rate of denitrification was lower than in closed system; it was from 4 to 15 mg/l.h dependent on activated sludge type, sludge concentration, and temperature of the system. Experiments were carried out in the range of temperature from 20° to 30°C.

scholarly journals Comparative Study on Mechanical Properties of Compacted Clay under Freeze-Thaw Cycles with Closed and Open Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Shaohua Xian ◽  
Zheng Lu ◽  
Hailin Yao ◽  
Ran Fang ◽  
Jianbo She
Keyword(s):  
Mechanical Properties ◽  
Moisture Content ◽  
Open System ◽  
Closed System ◽  
Open Systems ◽  
Engineering Properties ◽  
Compacted Clay ◽  
Freeze Thaw ◽  
Attenuation Rate ◽  
Deterioration Effect

The frost heave and thaw settlement caused by freeze-thaw cycles will seriously affect the engineering properties of soil. This paper attempts to comparatively investigate the deterioration effect of freeze-thaw cycles on the mechanical properties of compacted clay in closed and open systems. The specimens were frozen and thawed from the top to bottom in two systems. The moisture contents and deformations after freeze-thaw cycles were measured. Mechanical parameters of soil were examined through triaxial compression tests. Results show that the moisture content and deformation of soil change evidently with the increase of freeze-thaw cycles in the open system, while these parameters in the closed system change little. In the open system, the attenuation rate of failure strength, elastic modulus, and angle of internal friction of soil subjected to 7 freeze-thaw cycles are all about 2 times as large as that in the closed system and the attenuation rate of cohesion is even 4 times of that in the closed system. These differences reveal that the deterioration effect of freeze-thaw cycles on soil strength is aggravated after water supply. These findings indicate that soil structure damage and moisture content increase is the dominant factor affecting engineering properties of the soil in the open system.

scholarly journals Spatial Variations of Radiocarbon in the Coastal Aquifer of Israel—Indicators of Open and Closed Systems

Radiocarbon ◽  
2001 ◽  
Vol 43 (2B) ◽  
pp. 783-791 ◽  
Author(s):  
Debbie Bruce ◽  
Gerald M Friedman ◽  
Aaron Kaufman ◽  
Yoseph Yechieli
Keyword(s):  
Spatial Variation ◽  
Open System ◽  
Closed System ◽  
Coastal Aquifer ◽  
Spatial Variations ◽  
Calcite Dissolution ◽  
Closed Systems

The spatial variation in radiocarbon concentration was studied in the Coastal Aquifer of Israel. Lower concentrations were found in the western section of the aquifer (55–70 pMC) as compared to the eastern section (80–100 pMC). Since no correlation was found between the tritium and radiocarbon values, these variations could not simply be explained by a difference in ages, or by a difference in the degree of old calcite dissolution as similar δ13C values were found throughout the aquifer. The results are best explained when viewing the differences in 14C values within the same coastal aquifer, where the eastern section of the aquifer is a more open system and the western section is a more closed system. In general, the age of the groundwater in the coastal aquifer was found to be less than 50 years old (14C >55 and measurable tritium).

scholarly journals On Open Systems

2004 ◽  
Vol 24 (1) ◽  
pp. 3-17 ◽  
Author(s):  
VICTORIA CHICK
Keyword(s):  
General Theory ◽  
Open System ◽  
Closed System ◽  
Open Systems ◽  
Economic Factors ◽  
Economic Theories ◽  
Different Dimensions

ABSTRACT To many, economics is seen as increasingly divorced from reality. I shall argue that one of the causes of this divorce is the attachment to closed-system theorising, and advocate instead the method of open systems with partial and temporary closures. Definitions of closed and open systems are examined. It is evident that there are many different criteria which may define open systems. Theorists differ in their emphasis on one or other criterion. There are also different dimensions of openness: openness to non-economic factors; the openness of economic theories themselves; the interplay of micro- and macro-economics; and the treatment of time. These are explored, using Keynes’s General Theory as a case study of an open system.

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