Modeling Algorithm (vii)--Queuing theory model

(i) Basic concepts

I. General presentation of the queuing process

All the objects that require service are called customers, and those who serve the customer are called waiters.

Ii. the composition and characteristics of the queuing system

Mainly by the input process, the queuing rules, the service process is composed of three parts

Three, the symbolic representation of the queuing model

1, X: Indicates customer arrival flow or customer arrival interval time distribution

2, Y: Service time distribution

3. Z: Number of service desks

4, A: System capacity limits

5, B: number of customer sources

6, C: Service Rules FCFS first to first service LCFS after service

IV. operational indicators of the queuing system

1. Average captain: The mathematical expectation of the number of customers in the system (including the customers who are being served and the customers waiting for service), remember to do LS

2, the average platoon captain: refers to the system waiting for the customer number of mathematical expectations, remember to do LQ

3. Average length of stay: The mathematical expectation of the customer's stay within the system (including the waiting time and the time to be served), the WS

4, average waiting time: refers to a customer in the queuing system waiting for the amount of time the mathematical expectation, remember to do Wq

5, average busy period: refers to the service organization continuous peak time (the customer arrives at the idle service organization, to the service organization again idle time) The mathematics expectation of the length, remember to do TB

6, the state of the system: refers to the number of customers in the system

(ii) Distribution of input processes and service times

When the input process is a Poisson flow, the time interval T must follow the exponential distribution when the customer arrives successively

(iii) The process of birth and death

First, the definition

(iv) M/M/S waiting system queuing model

One, single service desk model

1. Definition

2, the distribution of the captain

Ii. several important quantitative indicators

1. Average Captain

2. Average Queue Length

3. Average length of stay

4. Average Waiting time

5. Important Relationship

6. Busy and busy periods

Average stay time equals average busy period

Three, multi-service desk model (m/m/s/∞)

Modeling Algorithm (vii)--Queuing theory model