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Published in Sunderesh S. Heragu, Facilities Design, 2022
Assume that a system has Nt = n customers at time t, the pdf of the remaining time until the next arrival (birth) and the pdf of the remaining time until the next service completion (death or departure) are exponential with parameters λn, μn, respectively, for n = 0, 1, 2, …. Further, assume that only one event (either a birth or a death) can occur in any period Δt. Although the birth and death rates are independent of each other, they are state dependent, that is, the rate at which birth occurs is dependent upon the state (number of customers) of the system. However, because of the exponential assumption, birth and death occur randomly. While the birth–death process may be finite or infinite, Figure 15.2 shows an infinite birth–death process in which birth and death rates are state dependent. Such a diagram that shows the possible transitions into and out of each state is called a rate diagram. Analysis of most birth–death processes is computationally feasible only when the system has reached steady state. Until steady state is reached, the system is said to be in a transient state and its analysis is difficult. Therefore, this section only deals with steady-state analysis.
Electrothermal analysis of a TEC-less IR microbolometer detector including self-heating and thermal drift
Published in Quantitative InfraRed Thermography Journal, 2023
M. Felczak, T. Sosnowski, R. Strąkowski, G. Bieszczad, S. Gogler, J. Stępień, B. Więcek
In order to verify the simplified modelling presented above, the 2D numerical model of the microbolometer detector was made in the ANSYS environment using FEA. The software is an extensive and effective tool for engineers and researchers from various fields of science. One can perform strength analysis, vibration hydrodynamics and thermal analysis as well as many others. The analysis can be performed for steady or transient states. The aim of the simulations presented in this research was to obtain the more detailed results concerning bolometric detector self-heating during the integration and processing of radiation signal. Signal integration in resistive microbolometer requires powering the sensor. In result, it causes self-heating that can degrade FPA performance.
Routing and staffing in emergency departments: A multiclass queueing model with workload dependent service times
Published in IISE Transactions on Healthcare Systems Engineering, 2023
Siddhartha Nambiar, Maria E. Mayorga, Yunan Liu
An important future direction of research could consider the use of transient analysis instead of fluid approximations to analyze the complex queueing models we developed in this article. While fluid approximations are useful in analyzing the average behavior of the system, it does not account for any of the stochastic behavior. Most real systems rarely settle into a steady-state, and the ability to analyze a system in its transient state is often computationally intractable. Furthermore, the results of a transient analysis is a function of the initial conditions of the system, something that a steady-state analysis does not consider. Studying the model developed in this article in its transient state could be a potential future direction of research.