Queuing theory model

1. brief introduction

We use six symbols to represent the queuing model , Separate the symbols with a slash , Write it down as X/Y/Z/A/B/C . The first symbol X Indicates the distribution of customer arrival flow or customer arrival interval ; The second symbol Y Represents the distribution of service time ; The third symbol Z Indicates the number of service desks ; Fourth symbol A Is the system capacity limit ; The fifth symbol B Is the number of customer sources ; Sixth symbol C It represents a service rule , For example, first come first serve FCFS, Last come first serve LCFS etc. .

2. Little（ Little ） The formula

In the queuing theory model , You can use the average captain L_s , Average platoon length L_q Average waiting time W_q, Average length of stay W_s​ These basic quantitative indicators judge the performance of the system .

2.1 Definition

Little ( Little ) The law can be applied to a stable 、 In a non preemptive system . The definition for ：

• In a stable system （L） in , The average number of customers observed for a long time is equal to the effective arrival rate observed for a long time （\lambda） Multiply by the average customer waiting time in the system （W）; Expressed in an algebraic expression as ：

\begin{array}{c} L = \lambda W \end{array}

use \lambda Indicates the average number of customers arriving in a unit time ,\mu It indicates the average number of customers leaving after receiving the service in a unit time , The average arrival time of two adjacent customers can be obtained 1 / \lambda, Average service time per customer 1 / \mu, according to Little The laws of , We can get the following Little The formula ：