## 这是一篇来自英国的关于管理科学视频讲座A部分：排队系统的结构（Video Lecture Part A: Structure of a Queueing System）的管理科学作业代写

Objectives of Today’s Lecture

By the end of this lecture, you should:

• The purpose of queueing analysis;
• The fundamental diagram of Queueing Theory;
• Basic queueing terminology;
• Kendall’s notation.

Purpose of Queueing Models

Queueing Theory deals with the analysis and management of

waiting lines to:

➢Describe behavior;

➢Determine service levels;

➢Evaluate alternative service configurations.

Queueing Terminology

●Customer – person or item to be processed

●Server or Channel – resource that serves or“processes” customer

●Queue – customers waiting for service (not including any being served)

●System一all customers from moment of arrival to moment of departure.

●Arrival rate (L _ambda)=入per unit of time

●Service rate per server (mu)= μ per unit of time

●Queue discipline: FIFO (FCFS), LIFO, RIRO, PRP, NPRP

●Customer behaviour: Balking, Reneging, Jockeying

Arrival Process

●Arrival Rate = 1 1 Inter-Arrival Time

• Arrival Rate = λ per unit time; Inter-Arrival Time= 1/ λ tim

●Constant Arrivals (D)

• Exactly the same time between arrival

●Poisson Random Arrivals (M)

• Exponential (variable) times between arrivals

Service Process

●Service Rate = 1 / Service Time

• Service Rate = u per unit time; Service Time = 1/ μ time

●Constant Services (D)

• Exactly the same time for each service

●Random Services (M)

• Exponential (variable) times for each service

Operating Characteristics or Performance Measures

Typical operating characteristics of interest include:

U – Utilization factor, % of time that all servers are busy.

Lq- Avg number of units in line waiting for service.

L – Avg number of units in the system (in line & being served).

Wq- Avg time a unit spends in line waiting for service.

W – Avg time a unit spends in the system (in line & being served).

P0- Prob. that there are no units in the system.

Pn – Prob. of n units in the system.

Kendall Notation

●Queueing systems are described by 6 parameters:

●1/2/3/4/5/6

●1: Arrival Process (M or D)

●2: Service Process (M or D)

●3: Service Channels (S)

●4: Capacity of the Queue (C)

●5: Population size of Potential Arrivals (n to∞)

●6: Queue Discipline (FIFO, LIFO, etc)

●Example: M/D/3/10/∞/FIFO