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
具体的作业要求是在今天的讲座结束时，你应该解决排队分析的目的；排队理论的基本图；基本的排队术语；肯德尔的符号，以下是具体作业内容详情如果对于该作业有任何难题可扫码咨询客服：
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
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