Customer waiting time and response time confidence interval prediction method for G/G/1 queuing system

Abstract

The invention discloses a customer waiting time and response time confidence interval prediction method for a G / G / 1 queuing system. The method comprises the steps of: sampling m random samples obeyingservice time of an experience distribution function for customers of an ID number i; calculating samples of m waiting time and response time of the customer with the ID number i and a mean value of the samples; calculating B Bootstrap samples of the waiting time mean value of the customer with the ID number i, and the mean value and the standard deviation of the B Bootstrap samples; calculating BBootstrap samples (B is an integer greater than or equal to 100) of a response time mean value of the customer with the ID number i, and a mean value and a standard deviation of the B Bootstrap samples; and determining a standard Bootstrap confidence interval, a quantile confidence interval, a deviation correction quantile confidence interval and a pivot confidence interval of waiting time and response time of which the customer confidence level of the ID number i is 1-[alpha]. According to the method for predicting the confidence interval of the waiting time and the response time of each customer in the n customers based on the G / G / 1 queuing system, prediction of the confidence interval of the waiting time and the response time of the customers has higher practical value.

Description

technical field [0001] The invention relates to the technical fields of computer science, statistics and queuing theory, more specifically to a confidence interval prediction of customer waiting time and response time in a G / G / 1 queuing system based on service time empirical distribution function and Bootstrap method. Background technique [0002] At present, there are queuing machines in various hospitals, banks, government service halls, etc. After the customer takes the number, he only knows his position in the queue, but he cannot know how long he will have to wait to get the service, nor can he know how long it will take to get the service. It takes a long time to end the service. Although there are some patents such as the patent No. 200710027670.2 "An Intelligent Queuing and Calling System", the patent No. 201210242019.8 "A Queuing Processing System for Estimated Business Processing Time and Queuing Machine Scheduling Method", the patent No. is 201410231288.3's paten...

AI Technical Summary

Problems solved by technology

[0002] At present, there are queuing machines in various hospitals, banks, government service halls, etc. After the customer takes the number, he only knows his position in the queue, but he cannot know how long he will have to wait to get the service, nor can he know how long it will take to get the service. long time to end service

Although there are some patents such as the patent No. 200710027670.2 "An Intelligent Queuing and Calling System", the patent No. 201210242019.8 "A Queuing Processing System for Estimated Business Processing Time and Queuing Machine Scheduling Method", the patent No. is 201410231288.3's patent "A Method for Predicting Waiting Time for Queuing Machines" etc. discloses different methods of predicting customer waiting time, but there are the following deficiencies: (1) the existing patent predicts the point estimation of customer waiting time; but Due to the influence of various random factors, the waiting time of customers usually changes within a certain range, so predicting the confidence interval of customer waiting time is more in line with objective reality, and it is also convenient for customers to arrange other affairs reasonably; (2) Patent No. 2007100 27670.2 Although the patent predicts the time interval of the customer's second queuing return time period, the interval is not a confidence interval in the statistical sense, and the M / M / n queuing model is used instead of the more general G / G / 1 queuing model

However, these documents all discuss the average performance index or distribution calculation method of n customers, but do not involve the confidence interval of predicting the waiting time and response time of each customer in n customers in the queuing system

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