Waiting Line Theory

Question 1

Someone or something that is in
need of some type of service

Answer 1

Customer or element

Question 2

a process or system that
performs the services to the
customer

Answer 2

Service facility

Question 3

represents any type of attention
to satisfy customer or element
needs

Answer 3

Service

Question 4

“The flow of customers from an infinite or finite population towards the service facility forms a queue or waiting line on account of lack of capability to serve all at a time.”

Answer 4

Service station

Question 5

Number of customers waiting to be serviced.

Answer 5

Queue

Question 6

A system having a service facility at which units of some kind (generically called “customers”) arrive for service

Answer 6

Queueing system

Question 7

• Danish telephone engineer who did the original work on queueing theory.
• Effects on fluctuation demand on the utilization of automatic dialing equipment.
• By the end of World War II, waiting line models were extended to other kinds of problems.

Answer 7

A.K. Erlang, 1905

Question 8

Four basic structures of waiting line theory

Answer 8

1. Single Phase, Multiple Channel
2. Single Phase, Single Channel
3. Multiple Phase, Single Channel
4. Multiple Phase, Multiple Channel

Question 9

2 possible situations for a customer to acquire the service needed

Answer 9

1. From customer to service center
2. From service center to customer

Question 10

When the customer is the one waiting…
- total number of customers > numher of facilities available
When the service center is the one waiting…
- total capacity of their system < total number of customers requiring service

Answer 10

Congestion

Question 11

theoretical analysis of the waiting
line problem in telephone calls

Answer 11

A.K. Erlang, 1903

Question 12

Developed the theory further

Answer 12

Mills and Thornton Fry, 1927

Question 13

systematic and mathematical
approach to waiting line problem

Answer 13

David George Kendall, 1951

Question 14

computerized reservation of
rail journey

Answer 14

1951 onwards

Question 15

Queue Process

Answer 15

Arrival -> Waiting line -> Units served -> Leaving the queue

Question 16

_____ __ ______ to the service system greatly depends on the nature of size of the population, which may be infinite or finite.

Answer 16

Size of arrivals

Question 17

Arrival time distribution, customers arrive in Poisson or Completely random fashion.

Answer 17

Constant or Random

Question 18

In queuing context, it refers to the space available for the arrivals to wait before being taken to service. The space available may be limited or unlimited.

Answer 18

Capacity of the Service System

Question 19

The length of the queue or the waiting time of a customer or the idle time of the service facility mostly depends on the ________ _______

Answer 19

Customer Behavior

Question 20

This behavior signifies that the
customer does not like to join the queue seeing the long length of it.

Answer 20

Balking

Question 21

Customer joins the queue and after waiting for a certain time loses his patience and leaves the queue

Answer 21

Reneging

Question 22

Customers may collaborate and only one of them may stand in the queue.

Answer 22

Collusion

Question 23

If there are a number of waiting lines
depending on the number of service
stations.

Answer 23

Jockeying

Question 24

Service Facility Design may be

Answer 24

Single channel or Multi channel

Question 25

Queue service discipline may be

Answer 25

FIFO, LIFO, SIRO, Service by priority (which may be preemptive or non-preemptive)

Question 26

probability distribution of queue length or the number of persons in the system at any point of time

Answer 26

Queue Length (Queueing Problem)

Question 27

time spent by a customer in the queue before the commencement of his service

Answer 27

Waiting time (Queueing Problem)

Question 28

- During the ____ _____, no customer is present in the system. - During his _____ ____, some more customers will arrive and will be served in their turn according to the system discipline.

Answer 28

Idle Time, Busy Time (Average Idle Time or Busy Time Distribution)

Question 29

the rate of arrivals of customers is less than the rate of service and both are **constant**

Answer 29

Steady State

Question 30

its operating characteristics or behavior are **dependent on time**

Answer 30

Transient State

Question 31

Arrival rate of the system is **larger** than its service rate. Queue length will **increase with time** and theoretically it could build up to infinity.

Answer 31

Explosive State

Question 32

(2) Common basic waiting line models

Answer 32

Poisson distribution and Negative Exponential distribution

Question 33

A certain fast-food restaurant gets an average of 3 visitors to the drivethrough per minute.

Answer 33

Poisson Distribution

Question 34

Representative of the Poisson process, but describes the time between arrivals and specifies that these time intervals are completely random.

Answer 34

Negative Exponential Distribution

Question 35

Corresponds to completely random arrivals and it is assumed that arrivals are completely independent of other arrivals as well as any condition of the waiting line.

Answer 35

Lamda (Arrivals per time unit)

Question 36

Mean time between arrivals

Answer 36

1/y

Question 37

the objective is to study the number of customers that enter the system, only arrivals are counted

Answer 37

Birth

Question 38

Is a generalization of pure birth process, and has two types of state transitions: '_____', which **increases** the current state variable by one, or '_____', which **decreases** the current state variable by one

Answer 38

Birth-Death Process, Birth, Death

Question 39

The reason for the common reference to rates in the discussion of arrivals and to times in the discussion of service is simply a _____ __ ________

Answer 39

Matter of practice

Question 40

Commonly used symbols

Answer 40

muu and u

Question 41

are single parameter distributions; that is, they are completely described by one parameter, the mean. For the ____ ____, the standard deviation is the **square root of the mean**, and for the _____ _____ _____, the standard deviation is **equal to the mean**

Answer 41

Poisson distribution and Negative exponential distribution

Question 42

It is to analyze and optimize systems that involve waiting lines

Answer 42

Queueing Model

Question 43

arrival and service rates are some *unknown random* variables.

Answer 43

Probabilistic Model

Question 44

arrival and service rates are **known and fixed**

Answer 44

Deterministic Model

Question 45

Either of the arrival and service rates is unknown random variable and other known and fixed.

Answer 45

Mixed Queueing Model

Question 46

Average number of customer in system L or E (n)

Answer 46

L or E (n) = p / 1-p

Question 47

Average number of time customer spends on the system W or E (v)

Answer 47

W or E (v) = L / y or = 1 / u - y

Question 48

Average number of customer in the queue E (L)

Answer 48

E (L) = p2 / (1 - p) or = y2 / u (u - y)

Question 49

Given: Arrival (y) Service (u)

Answer 49

Solution: Service (u) = 1 / WS (p) = y / u Ave. # of Customer in system L or E (n) = p / 1 - p Ave. # of time customer spends W or E (v) = L / y or 1 / (u - y) Ave. # of customer in the queue E (L) = p2 / (1 - p) or y2 / u (u - y)