Continuous Time Frame Research Articles

A multi-class discrete-time queueing system under the FCFS service discipline

The problem with the FCFS server discipline in discrete-time queueing systems is that it doesn’t actually determine what happens if multiple customers enter the system at the same time, which in the discrete-time paradigm translates into ‘during the same time-slot’. In other words, it doesn’t specify in which order such customers are served. When we consider multiple types of customers, each requiring different service time distributions, the precise order of service even starts to affect quantities such as queue content and delays of arbitrary customers, so specifying this order will be prime. In this paper we study a multi-class discrete-time queueing system with a general independent arrival process and generally distributed service times. The service discipline is FCFS and customers entering during the same time-slot are served in random order. It will be our goal to search for the steady-state distribution of queue content and delays of certain types of customers. If one thinks of the time-slot as a continuous but bounded time period, the random order of service is equivalent to FCFS if different customers have different arrival epochs within this time-slot and if the arrival epochs are independent of customer class. For this reason we propose two distinct ways of analysing; one utilizing permutations, the other considering a slot as a bounded continuous time frame.

Application of Petri Nets in Bone Remodeling

Understanding a mechanism of bone remodeling is a challenging task for both life scientists and model builders, since this highly interactive and nonlinear process can seldom be grasped by simple intuition. A set of ordinary differential equations (ODEs) have been built for simulating bone formation as well as bone resorption. Although solving ODEs numerically can provide useful predictions for dynamical behaviors in a continuous time frame, an actual bone remodeling process in living tissues is driven by discrete events of molecular and cellular interactions. Thus, an event-driven tool such as Petri nets (PNs), which may dynamically and graphically mimic individual molecular collisions or cellular interactions, seems to augment the existing ODE-based systems analysis. Here, we applied PNs to expand the ODE-based approach and examined discrete, dynamical behaviors of key regulatory molecules and bone cells. PNs have been used in many engineering areas, but their application to biological systems needs to be explored. Our PN model was based on 8 ODEs that described an osteoprotegerin linked molecular pathway consisting of 4 types of bone cells. The models allowed us to conduct both qualitative and quantitative evaluations and evaluate homeostatic equilibrium states. The results support that application of PN models assists understanding of an event-driven bone remodeling mechanism using PN-specific procedures such as places, transitions, and firings.

Solution to a Problem of Infinitely Many Time Conversions

This paper considers an investment decision problem in continuous-time frame work, in which a firm can switch between a risky investment and a riskless investment. In this paper, I proposes a method to derive a closed-form solution to this (S, s) control problem. As a result, I derive the values of the conversion options and the critical thresholds analytically. The values of the conversion options are very helpful for us to interpret conversions between operations as exercises of the options. OR Subject Classification: Applications (Dynamic Programing), Investment (Financial Institutions), Maintenance/Replacement (Inventory/Production)

Dynamic approach to human resources planning for major professional companies with a peak-wise demand

Human resource planning has always been a key issue to professional companies. To help professional firms cope with demands, a dynamic approach for planning human resources in a continuous time frame is proposed. We analytically determine an exact and globally optimal solution to a firm's human resources by explicitly considering its hierarchical structure, costs of recruiting and hiring, workload, contract delays, loss of revenues, and an over-capacity issue. Managerial implications of this study are also discussed.

Comparison of Car-Following Models for Simulation

Presented in this paper are the car-following methods and algorithms of the NETSIM, INTRAS, FRESIM, CARSIM, and INTELSIM models. Moreover, the car-following performance of these models is compared with the field data. NETSIM, INTRAS, FRESIM, and CARSIM car-following models first move the leader and then update the follower in one simulation time step. Because of this approach, these car-following models cannot be used to command vehicles in real-time intelligent transportation systems applications. Moreover, brake reaction times are limited by the simulation time step because of this method of updating the vehicles. INTELSIM was developed to overcome these deficiencies. INTELSIM moves vehicles simultaneously and produces solutions for a continuous time frame. INTELSIM produced the best agreement with the field data and required the least amount of calibration effort.

Dynamic Modeling of an Individual's Discrete Choice Behavior on Continuous Time Frame Using Panel Data: Toward Dynamic Demand Analysis without the Assumption of Equilibrium*

A dynamic model of an individual's commute mode switching behavior along a continuous time dimension is presented. The model is specified as a semi-Markov process model of commute mode use. Its parameters are estimated using discretetime panel data. Parameter estimates indicate that the duration of carpooling to commute is shorter than those of the other commuting modes. The average speed of each commute mode has effects on commute-mode switching behavior. A sample enumeration study using this dynamic behavioral model offers estimates of the dynamic characteristics of aggregate commute-mode shares, and the time it will take for the market to reach an “equilibrium.” The numerical study thus reveals that the market is not in equilibrium even for commute travel modes.

Engineering Aspects of PETT VI

PETT VI is a circular ring, multislice positron emission tomograph designed for small field studies. Features such as wobble and rotate motions, bimodal resolution, cesium flouride scintillators, fast timing circuits and dual buffer histogram memories allow a flexible data acquisition environment. Efficient modularized software concepts are implemented to facilitate concurrent tasks of data acquisition, processing and display. The ability to effectively manage high count rate situations and collect continuous time frames makes PETT VI ideally suited for dynamic studies.

ENGINEERING ASPECTS OF PETT V

PETT VI is a circular ring, multislice positron emission tomograph designed for small field studies. Features such as wobble and rotate motions, bimodal resolution, cesium flouride scintillators, fast timing circuits and dual buffer histogram memories allow a flexible data acquisition environment. Efficient modularized software concepts are implemented to facilitate concurrent tasks of data acquisition, processing and display. The ability to effectively manage high count rate situations and collect continuous time frames makes PETT VI ideally suited for dynamic studies.