On renewal processes relating to counter models: the case of phase-type interarrival times

1993 ◽  
Vol 30 (1) ◽  
pp. 175-183 ◽  
Author(s):  
Edward P. C. Kao ◽  
Marion Spokony Smith

The Type I and Type II counter models of Pyke (1958) have many applications in applied probability: in reliability, queueing and inventory models, for example. In this paper, we study the case in which the interarrival time distribution is of phase type. For the two counter models, we derive the renewal functions of the related renewal processes and propose approaches for their computations.

1993 ◽  
Vol 30 (01) ◽  
pp. 175-183 ◽  
Author(s):  
Edward P. C. Kao ◽  
Marion Spokony Smith

The Type I and Type II counter models of Pyke (1958) have many applications in applied probability: in reliability, queueing and inventory models, for example. In this paper, we study the case in which the interarrival time distribution is of phase type. For the two counter models, we derive the renewal functions of the related renewal processes and propose approaches for their computations.


1972 ◽  
Vol 62 (2) ◽  
pp. 493-507 ◽  
Author(s):  
Harsh K. Gupta ◽  
B. K. Rastogi ◽  
Hari Narain

abstract The behavior of earthquakes near the artificial lakes at Kariba, Kremasta, and Koyna, where earthquakes of magnitude exceeding 6 have occurred, is examined. Foreshock-aftershock patterns of these earthquake sequences correspond with Mogi's type II model, whereas the normal earthquakes of these regions belong to type I. Three similar relations could be fitted in the time distribution of aftershocks of the main earthquakes. Quite contrary to normal earthquakes, foreshock b values are found to be comparable with the aftershock b values in the frequency-magnitude relations. Focal mechanisms of the largest earthquakes of these sequences have been determined and compared. Dip-slip components of the motion are such that the lakes are situated on the downthrown blocks. These regions are characterized by a volcanic past and the presence of rocks such as limestones and red boles which are easily affected by water. These findings are useful in distinguishing the reservoir-associated earthquakes from normal earthquakes and suggest that the artificial lakes are responsible for changing the mechanical properties of the strata and releasing the accumulated strains.


1985 ◽  
Vol 25 (05) ◽  
pp. 693-703 ◽  
Author(s):  
Laurent Prouvost ◽  
Gary A. Pope ◽  
Bruce Rouse

Abstract A thermodynamic model is presented for modeling the partitioning of amphiphilic species between the different partitioning of amphiphilic species between the different phases of systems typically used for chemical flooding. phases of systems typically used for chemical flooding. The model, an extension of the pseudophase model by Biais et al. that can analyze only a four-component system, can work with five-component systems, including two partitioning amphiphilic species (e.g., two alcohols or one alcohol and a partitioning cosurfactant species). The self-association of alcohol in the organic phases, which results in a variable alcohol partition coefficient, is considered. Experiments to determine thermodynamic constants (which are entered into the model) are described for four-component systems, including one alcohol. The salinity dependence of these parameters is also studied. Brine/decane/isobutanol/TRS 10–410 as well as brine/nonane/ isopropanol/TRS 10–80 systems are considered. Some computations of pseudophase compositions for the five-component model and for various overall compositions are included. This partitioning model has been included in the chemical-flooding simulator developed at the U. of Texas; the results of this model have been presented in another paper. The model used for the presented in another paper. The model used for the binodal surface that is required to calculate phase compositions from pseudophase compositions is presented in this paper, as well as comparisons with experimental data for both four- and five-component systems. Reservoir simulation results are presented in Ref. 3. Introduction The possibility of reaching very low interfacial tensions (IFT) during the displacement of oil by surfactant solutions has been the subject of intense interest for some time. Because the decrease in IFT can be as much as several orders of magnitude, almost all the contacted oil can be mobilized by this process. However, the recovery rate has proved to be very sensitive to many parameters, and the process has to be designed carefully to achieve a good oil recovery. It is commonly recognized that the phase behavior is one of the most critical features for the phase behavior is one of the most critical features for the design of chemical oil-recovery processes. Many investigators have studied phase behavior of systems with various combinations of brine, oil, surfactants, and cosurfactants. Winsor introduced a very convenient classification of phase behavior for such systems. Type I is a lower-phase microemulsion (surfactant-rich phase) in equilibrium with an oleic phase; Type II is an phase) in equilibrium with an oleic phase; Type II is an upper-phase microemulsion in equilibrium with an aqueous phase, and Type III corresponds to a middle-phase microemulsion in equilibrium with both aqueous lower phase and oleic upper phase. The number of phases and their composition determined IFT's, viscosity, relative permeabilities and other hydrodynamic parameters on permeabilities and other hydrodynamic parameters on which the efficiency of the process is directly dependent. Components present in the reservoir during chemical flooding include water, electrolytes, oil, polymer, and the amphiphilic species surfactant and cosurfactant. From the viewpoint of chemical thermodynamics, the number of chemical species is very large if we consider every species of which oil, surfactant, and cosurfactant are made. Fortunately, some of these species behave collectively, so they can be considered a single pseudocomponent in the phase behavior description, thereby pseudocomponent in the phase behavior description, thereby making the study more tractable. For example, Vinatieri and Fleming considered brine a good pseudocomponent, which means that the ratio of salt to water is about the same in each phase. McQuigg et al.'s experiments yield similar conclusions. Even crude oil has been shown to be a good pseudocomponent with a fairly acceptable accuracy. Dealing with amphiphilic species is far more difficult. In some laboratory studies, surfactant can be a chemically pure component, but for field applications it is usually a complex blend, such as petroleum sulfonates. In the case of petroleum sulfonates, different monosulfonated or polysulfonated species are present with varied carbon polysulfonated species are present with varied carbon tails. Commercial nonionic surfactants, which generally are ethoxylated alcohols, show a broad distribution of ethylene oxide number (EON). In both cases, investigators have shown that these commercially available surfactants do not behave collectively but in some situations partition selectively between the phases. The cosurfactant generally is an alcohol or an ethoxylated alcohol. Although many research programs currently are devoted to the design of alcohol-free systems to avoid some of the drawbacks induced by its presence (lower solubilization parameters, higher IFT's), most of the commonly used systems include alcohol or even a blend of alcohols with different carbon chain lengths and/or branching. SPEJ P. 693


2004 ◽  
Vol 41 (04) ◽  
pp. 1171-1181 ◽  
Author(s):  
M. Vlasiou ◽  
I. J. B. F. Adan ◽  
J. Wessels

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley's equation for the waiting time in the PH/U/1 queue. Although the latter equation has no simple solution, we show that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the PH/U/1 queue depends on the complete interarrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution.


2004 ◽  
Vol 41 (4) ◽  
pp. 1171-1181 ◽  
Author(s):  
M. Vlasiou ◽  
I. J. B. F. Adan ◽  
J. Wessels

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley's equation for the waiting time in the PH/U/1 queue. Although the latter equation has no simple solution, we show that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the PH/U/1 queue depends on the complete interarrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution.


Author(s):  
Ronald S. Weinstein ◽  
N. Scott McNutt

The Type I simple cold block device was described by Bullivant and Ames in 1966 and represented the product of the first successful effort to simplify the equipment required to do sophisticated freeze-cleave techniques. Bullivant, Weinstein and Someda described the Type II device which is a modification of the Type I device and was developed as a collaborative effort at the Massachusetts General Hospital and the University of Auckland, New Zealand. The modifications reduced specimen contamination and provided controlled specimen warming for heat-etching of fracture faces. We have now tested the Mass. General Hospital version of the Type II device (called the “Type II-MGH device”) on a wide variety of biological specimens and have established temperature and pressure curves for routine heat-etching with the device.


Author(s):  
G. D. Gagne ◽  
M. F. Miller ◽  
D. A. Peterson

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.


Author(s):  
T.A. Fassel ◽  
M.J. Schaller ◽  
M.E. Lidstrom ◽  
C.C. Remsen

Methylotrophic bacteria play an Important role in the environment in the oxidation of methane and methanol. Extensive intracytoplasmic membranes (ICM) have been associated with the oxidation processes in methylotrophs and chemolithotrophic bacteria. Classification on the basis of ICM arrangement distinguishes 2 types of methylotrophs. Bundles or vesicular stacks of ICM located away from the cytoplasmic membrane and extending into the cytoplasm are present in Type I methylotrophs. In Type II methylotrophs, the ICM form pairs of peripheral membranes located parallel to the cytoplasmic membrane. Complex cell wall structures of tightly packed cup-shaped subunits have been described in strains of marine and freshwater phototrophic sulfur bacteria and several strains of methane oxidizing bacteria. We examined the ultrastructure of the methylotrophs with particular view of the ICM and surface structural features, between representatives of the Type I Methylomonas albus (BG8), and Type II Methylosinus trichosporium (OB-36).


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