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A Calculation Method of Steady State Probability Matrix for Queuing Lines with Two Heterogeneous Service Types

A service type and matrix calculation technology, which is applied in complex mathematical operations, inspection devices, instruments, etc., can solve the problems of ill-conditioned matrices and increase the computational complexity of solving steady-state probability, so as to improve queuing efficiency, reduce computational complexity, cost reduction effect

Active Publication Date: 2022-06-21
FUJIAN UNIV OF TECH
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Problems solved by technology

[0002] For a large-scale heterogeneous service queuing system, the existing technology or traditional iterative algorithm will generate a large number of boundary states and the number of stages of the quasi-birth-death process when calculating the steady-state probability of the system, which will lead to an ill-conditioned matrix when calculating the rate matrix, which is extremely Greatly increases the computational complexity of solving the steady-state probability

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  • A Calculation Method of Steady State Probability Matrix for Queuing Lines with Two Heterogeneous Service Types
  • A Calculation Method of Steady State Probability Matrix for Queuing Lines with Two Heterogeneous Service Types
  • A Calculation Method of Steady State Probability Matrix for Queuing Lines with Two Heterogeneous Service Types

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[0057] The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings.

[0058] The present invention provides a steady-state probability matrix calculation method with two heterogeneous service types. After the threshold δ, the proportion of customers assigned to the first service type queue line is p 1 (δ), the number of servers configured for the first type of service is c 1 , the average service rate is μ 1 ; while the proportion of customers assigned to the second service type queue line is 1-p 1 (δ), the number of servers configured for the second type of service is c 2 , the average service rate is μ 2 ; Then, define the steady-state probability vector π of the queuing system with two heterogeneous service types queuing lines, construct the state transition probability matrix Q, and the steady-state probability vector π, and then calculate the performance index of the queuing system, that is, the averag...

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Abstract

The invention relates to a method for calculating a steady-state probability matrix with two queuing lines of heterogeneous service types. By constructing an embedded Markov chain, constructing a two-dimensional Markov chain system state queuing and waiting system, a queuing model steady-state probability calculation algorithm is proposed, which can be directly applied to service systems and computer systems with two heterogeneous service-type queuing lines 1. Solve the steady-state probability in the medical system to reduce the computational complexity of the steady-state probability; in addition, the method of the present invention can be used to solve the performance index of a large-scale heterogeneous service queuing system, improve system queuing efficiency, and reduce system cost.

Description

technical field [0001] The present invention relates to a steady-state probability matrix calculation method with two heterogeneous service type queuing lines. Background technique [0002] For a large-scale heterogeneous service queuing system, the existing technology or traditional iterative algorithm will generate a large number of boundary states and the number of stages of the quasi-birth-death process when calculating the steady-state probability of the system, which will lead to an ill-conditioned matrix when calculating the rate matrix. Greatly increases the computational complexity of solving the steady state probability. To overcome this difficulty, the applicant proposes the present invention. SUMMARY OF THE INVENTION [0003] The purpose of the present invention is to provide a steady-state probability matrix calculation method with queuing lines of two heterogeneous service types, which can be used to solve the performance index of a large-scale heterogeneous...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/16G07C11/00
Inventor 王嘉宏吴晓晶
Owner FUJIAN UNIV OF TECH