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Entropy02:39

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
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The Entropy as a State Function01:14

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Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
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Maximum entropy principle based estimation of performance distribution in queueing theory.

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This study models queuing systems as black boxes, deriving performance distributions using maximum entropy. This approach bypasses assumptions on arrival and service ratios, proving accurate with chi-square tests.

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Area of Science:

  • Operations Research
  • Applied Mathematics
  • Probability Theory

Background:

  • Traditional queuing system analysis often assumes known customer arrival and service ratios.
  • These assumptions limit the applicability of existing models to real-world scenarios.

Purpose of the Study:

  • To develop a novel method for deriving queuing system performance distributions.
  • To analyze queuing systems as black boxes, without assuming specific arrival or service ratio distributions.
  • To demonstrate the efficacy of the maximum entropy principle in this context.

Main Methods:

  • Applied the principle of maximum entropy to queuing systems.
  • Treated the queuing system as a black box, only assuming stability.
  • Derived performance distributions from accessible system indexes like capacity and mean server utilization.
  • Utilized the chi-square goodness of fit test for validation.

Main Results:

  • Successfully derived performance distributions for queuing systems without prior distribution assumptions.
  • Demonstrated the derivation of performance distributions from easily measurable system parameters.
  • Validated the accuracy and practical generality of the maximum entropy approach.

Conclusions:

  • The maximum entropy principle offers a robust method for analyzing queuing system performance.
  • This approach enhances the practical applicability of queuing theory by relaxing restrictive distributional assumptions.
  • The derived performance distributions are accurate and generalizable for real-world queuing systems.