Cycle Time Distribution Research Articles

Cycle-time and residence-time density approximations in a stochastic model for circulatory transport.

The concentration of a drug in the circulatory system is studied under two different elimination strategies. The first strategy--geometric elimination--is the classical one which assumes a constant elimination rate per cycle. The second strategy--Poisson elimination--assumes that the elimination rate changes during the process of elimination. The problem studied here is to find a relationship between the residence-time distribution and the cycle-time distribution for a given rule of elimination. While the presented model gives this relationship in terms of Laplace-Stieltjes transform., the aim here is to determine the shapes of the corresponding probability density functions. From experimental data, we expect positively skewed, gamma-like distributions for the residence time of the drug in the body. Also, as some elimination parameter in the model approaches a limit, the exponential distribution often arises. Therefore, we use Laguerre series expansions, which yield a parsimonious approximation of positively skewed probability densities that are close to a gamma distribution. The coefficients in the expansion are determined by the central moments, which can be obtained from experimental data or as a consequence of theoretical assumptions. The examples presented show that gamma-like densities arise for a diverse set of cycle-time distribution and under both elimination rules.

Cycle-time and residence-time density approximations in a stochastic model for circulatory transport

The concentration of a drug in the circulatory system is studied under two different elimination strategies. The first strategy—geometric elimination—is the classical one which assumes a constant elimination rate per cycle. The second strategy—Poisson elimination—assumes that the elimination rate changes during the process of elimination. The problem studied here is to find a relationship between the residence-time distribution and the cycle-time distribution for a given rule of elimination. While the presented model gives this relationship in terms of Laplace-Stieltjes transform, the aim here is to determine the shapes of the corresponding probability density functions. From experimental data, we expect positively skewed, gamma-like distributions for the residence time of the drug in the body. Also, as some elimination parameter in the model approaches a limit, the exponential distribution often arises. Therefore, we use Laguerre series expansions, which yield a parsimonious approximation of positively skewed probability densities that are close to a gamma distribution. The coefficients in the expansion are determined by the central moments, which can be obtained from experimental data or as a consequence of theoretical assumptions. The examples presented show that gamma-like densities arise for a diverse set of cycle-time distributions and under both elimination rules.

The cycle time distribution in a cycle of Bernoulli servers in discrete time

In a cycle of Bernoulli servers in discrete time the equilibrium distribution for a customer's round-trip time is shown to be of product-form and is given in explicit formulas. The results are used to obtain the equilibrium flow time distribution for an open tandem of queues.

A stochastic model for circulatory transport in pharmocokinetics

A new stochastic model for the residence time distribution of a drug injected instantaneously into the circulatory system is proposed and analyzed. The properties of the residence time are derived from the assumptions made about the cycle time distribution and the rule for elimination. This rule is given by the probability distribution of the number of cycles needed for elimination of a randomly selected molecule of the drug. Only the geometric distribution has been previously used for this purpose. Its transformation is applied here to get a boundary for the residence time. Other discrete distributions are applied with a view to describing different experimental situations. Suitable continuous probability distributions for the cycle time description are discussed.

Limiting Factors In Mechanized Tree-Planting

Certain properties of continuously advancing planting machines restrict their speed, thereby limiting their capacities. The cycle time of the planting device is predetermined by the design and is therefore difficult to alter. It is easier to influence the cycle timeof the seedling feed system, especially by changing the technical properties of the seedlings. In the case of pneumatic feed systems, air flow and hose diameter are also important physical factors. In cases where the seedling is not delivered to the planting device when required, the device will have to wait, and there will be a corresponding fall in productivity. Consequently, it would be advantageous if we could predict the likelihood of such a delay occurring. To be able to do this, we need to know the statistical distribution of the feed cycle times for different combinations of the physical variables. One hypothesis is that feed cycle times exhibit a chi-square distribution. If this is true, future work should focus on developing transformations between physical properties and statistical parameters.

Distribution of cell cycle times amongst the leukemia cells within individual patients with acute myelogenous leukemia

Seventeen patients with AML received infusions of BrdUrd to permit measurement of the cell parameters of leukemia cells in vivo. The range of S-phase times was measured by using a two color BrdUrd/PI analysis to determine the range of BrdUrd incorporation into cells which had been in S-phase throughout the entire duration of BrdUrd administration. These data were, in turn, used to calculate the range of cell cycle times amongst the leukemia cells present within individual patients. The range of cell cycle times amongst the leukemia cells present within individual patients differs between patients, with some leukemia cell populations characterized by narrow and others by broad ranges. In general, the longer the mean cell cycle time (between 27 and 112h) the broader the range of cell cycle times. These differences may help to explain, in part, the differences in response to therapy among patients whose mean leukemia cell kinetic parameters are similar.

A Globally Gated Polling System with a Dormant Server

We study a globally gated polling system with a dormant server, which makes a halt at its home base when there are no customers present in the system. We derive an explicit expression for the cycle time distribution as well as for the waiting-time distribution at each of the queues. As a justification of the dormant server policy, we show the waiting time at each of the queues to be smaller (in the increasing-convex-ordering sense) than in the ordinary nondormant server case.

Drying Process on Inert Particles in Mechanically Spouted Bed Dryer

ABSTRACT Suspensions, slurries and paste-like materials can be dried in the Mechanically Spouted Bed ( MSB) dryer with men packing. The circulation of the men particles characteristic of classical spouted beds is provided with a houseless conveyor screw mounted in the vertical axis of the bed. Radioactive isotopic tracer technique was used for measurement of the cycle time distribution ( CTD) of the spherical inert particles as a function of the operational parameters of drying. The variances ( σ2) of the CTDs and the particle velocity m the various zones of the MSB dryer were calculated. The circulation of the mert particles can be characterised by nearly plug flow. According to the physical model of drying on inert packing the heat and mass transfer coefficients were calculated. Que to the relativeiy uniform film-like, wet coating formed on the surface of the spheical inert particles, the drying process may be characterised with the constant rate of drying. A method has been elaborated for calculation o...

A study of solid behavior in spouted beds using 3‐D particle tracking

AbstractA non‐invasive γ‐ray emission system, employing eight NaI detectors, has been developed to follow the motion of a single radioactive particle in a three‐dimensional spouted bed reactor. The count‐rates measured simultaneously by the detectors are converted into tracer coordinates (x, y, z) using a pre‐established calibration model which accounts for every physical and geometrical aspects involved in the spouting facility. Typically four hundred thousands successive coordinates, obtained over 3.5 hours of particle tracking, are used for determining the average particle velocity field and other hydrodynamic quantities such as the cycle time distribution, the spout shape and the solid exchange distribution at the spout boundary, which could not be evaluated accurately using any available techniques.

Cycle time distribution of cyclic networks with blocking

An algorithm is provided to compute the cycle time distribution for cyclic closed exponential queueing networks with N finite capacity nodes and blocking. The blocking phenomenon is due to the nodes with finite capacity queues which can be used to represent systems with limited resources. Moreover, a recursive algorithm is provided to evaluate the cycle time moments, and a closed form solution, both in terms of distribution and moments of the cycle time, is provided for the model under special constraints.

M/G/1/N vacation model with varying E-limited service discipline

We define and analyze anM/G/1/N vacation model that uses a service discipline that we call theE-limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied (i.e. exhausted) or a randomly chosen limit ofl customers has been served. The server then goes on a vacation before returning to service the queue again. The queue length distribution and the Laplace-Stieltjes transforms of the waiting time, busy period and cycle time distributions are found. Further, an expression for the mean waiting time is developed. Several previously analyzed service disciplines, including Bernoulli scheduling, nonexhaustive service and limited service, are special cases of the general varying limit discipline that is analyzed in this paper.

Proliferation of anchorage‐dependent contact‐inhibited cells: I. Development of theoretical models based on cellular automata

We report the development of new class of discrete models that can accurately describe the contact-inhibited proliferation of anchorage-dependent cells. The models are based on cellular automata, and they quantitatively account for contact inhibition phenomena occurring during all stages of the proliferation process: (a) the initial stage of "exponential" growth of cells without contact inhibition; (b) the second stage where cell colonies form and grow with few colony mergings; and (c) the final stage where proliferation rates are dominated by colony merging events. Model prediction are presented and analyzed to study the complicated dynamics of large cell populations and determine how the initial spatial cell distribution, the seeding density, and the geometry of the growth surface affect the observed proliferation rates. Finally, we present a model variant that can simulate contact-inhibited proliferation of asynchronous cell populations with arbitrary cell cycle-time distribution. The latter model can also compute the percentage of cells that are in a specific phase of their division cycle at a given time.

Optimal headways for multiroute transit systems

AbstractThe problem considered is that of determining net‐benefit maximizing headways for multiroute transit systems which are subject to constraints on vehicle capacity, subsidy, and fleet size. Route demands are assumed to be independent of one another and to vary with the frequency of service, but details of route demand functions are assumed to be unknown. Conditions of optimality are derived for the unconstrained case and the various constrained cases. The relationship between conditions of optimality based on the assumption of fixed demand and those based on the assumption of variable demand is expressed by means of terms incorporating the elasticity of demand with respect to frequency of service. It is shown that the magnitude of discrepancies between the true conditions of optimality and fixed‐demand approximations of them depends on the elasticity of demand and on the distribution of ridership and cycle times among the various routes of the system. It is also shown that a trial‐and‐error search procedure based on fixed‐demand approximations should eventually converge to a stable schedule, although its use is not appropriate for all situations in which rescheduling might be considered. A case study is presented in which the maximum possible discrepancies between the variable‐demand and fixed‐demand conditions of optimality are found to be reasonable small, and an actual transit schedule is found to be generally similar to one indicated as optimal by the fixed‐demand approximation.

Laplace transform inversion and passage-time distributions in Markov processes

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certain weighted sums of these transforms is then solved by converting it into a linear first-order partial differential equation. The result may be used to find the density function of passage times between states in a Markov process and it is applied to derive an expression for cycle time distribution in tree-structured Markovian queueing networks.

Laplace transform inversion and passage-time distributions in Markov processes

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certain weighted sums of these transforms is then solved by converting it into a linear first-order partial differential equation. The result may be used to find the density function of passage times between states in a Markov process and it is applied to derive an expression for cycle time distribution in tree-structured Markovian queueing networks.

On the Cycle Time Distribution in a Two-Stage Cyclic Network with Blocking

On the Cycle Time Distribution in a Two-Stage Cyclic Network with Blocking

M/G/1/N Queue with vacation time and limited service discipline

A variant of an M/ G/1 queuing model with finite waiting room is studied in this paper. In this system, every busy period of the server at the queue is followed by the execution of additional tasks. The time spent by the server to perform these tasks is called a vacation time away from the queue. The server will begin a vacation from the queue if either the queue has been emptied or M customers have been served during the visit. The embedded Markov chain approach is used to obtain the steady state queue length distribution. The Laplace-Stieltjes transforms of the busy period and cycle time distributions are given. Using a combination of the supplementary variables and sample biasing techniques, the waiting time distribution, blocking probability and general queue length distribution are derived. Finally the results for the case of infinite waiting places are provided.

An extended technique for predicting the mixing times of high-viscosity liquid in a mixer. Mixing systems with molecular diffusion of solute.

This paper presents a technique for predicting the mixing time in a high-viscosity liquid mixing system where molecular diffusion is occurring in the mixture. In the technique, the diffusion differential equation and the model equation representing the decrease in scale of segregation with time are solved simultaneously. However, prior to prediction of the mixing time, the diffusion coefficient of the solute in the bulk liquid and the cycle time distribution of liquid in a mixer must be determined. From the concentration profile obtained by the technique proposed in this work, the macroscopic mixing time is predicted as the elapsed time until the local maximum concentrations of the solute become less than a chosen arbitrary criterion of mixing. Mixing experiments were carried out for helical screw/draft tube mixers and helical ribbon impeller mixers using corn syrup and PVA solutions of various viscosities. The mixing time was determined experimentally as the elapsed time until the segregation of tracer becomes uniform. The predicted mixing times were in good agreement with those determined experimentally.

Analytic models of cyclic service systems and their application to token-passing local networks

Using the framework of cyclic-service systems with a single server, two different token-passing models are investigated. The first model is approximate, obtaining the free-tokens cycle-time distribution on an asymmetric system with infinite capacity buffers and single-token operation. The second model is exact, yielding the cycle-time distribution of the free token on an asymmetric system with unit-capacity buffers, and single-token operation. The latter result is verified using known results for symmetric, unit-capacity buffer systems. To demonstrate the positive effects of buffering, a small variation of the unit-capacity buffering scheme is introduced. Computational results include performance measures such as throughput, utilization, loss probabilities, mean cycle times, cycle-time distributions, and a comparison of two buffering schemes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Multiqueue System with Non-Exhaustive Cyclic Service Modelled as a Linear-Programming Problem

In modern processor-controlled systems, it is common to find a central processor polling a number of message queues, where at most one message is processed from each queue during one polling cycle. This paper shows how one important parameter can be estimated quickly, namely the cycle-time distribution. This is the distribution of times taken for the cyclic server to perform one complete cycle in its continuous scan of a number of queues. The method of solution is to identify various constraints which will determine the cycle-time distribution, formulate them as linear inequality and equality constraints and, by determining an appropriate objective function, apply the simplex method to find upper and lower bounds on the values taken by the cycle-time distribution itself. A great strength of this technique is its overall simplicity, which enables it to be used to obtain important results very quickly and cheaply.