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OMGT 101 (Midterms) > Waiting Line Theory > Flashcards

Waiting Line Theory Flashcards

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1
Q

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

A

Customer or element

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2
Q

a process or system that
performs the services to the
customer

A

Service facility

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3
Q

represents any type of attention
to satisfy customer or element
needs

A

Service

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4
Q

“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.”

A

Service station

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5
Q

Number of customers waiting to be serviced.

A

Queue

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6
Q

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

A

Queueing system

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7
Q
  • 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.
A

A.K. Erlang, 1905

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8
Q

Four basic structures of waiting line theory

A
  1. Single Phase, Multiple Channel
  2. Single Phase, Single Channel
  3. Multiple Phase, Single Channel
  4. Multiple Phase, Multiple Channel
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9
Q

2 possible situations for a customer to acquire the service needed

A
  1. From customer to service center
  2. From service center to customer
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10
Q

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

A

Congestion

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11
Q

theoretical analysis of the waiting
line problem in telephone calls

A

A.K. Erlang, 1903

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12
Q

Developed the theory further

A

Mills and Thornton Fry, 1927

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13
Q

systematic and mathematical
approach to waiting line problem

A

David George Kendall, 1951

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14
Q

computerized reservation of
rail journey

A

1951 onwards

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15
Q

Queue Process

A

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

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16
Q

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

A

Size of arrivals

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17
Q

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

A

Constant or Random

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18
Q

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.

A

Capacity of the Service System

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19
Q

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

A

Customer Behavior

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20
Q

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

A

Balking

21
Q

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

A

Reneging

22
Q

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

A

Collusion

23
Q

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

A

Jockeying

24
Q

Service Facility Design may be

A

Single channel or Multi channel

25
Q

Queue service discipline may be

A

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

26
Q

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

A

Queue Length (Queueing Problem)

27
Q

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

A

Waiting time (Queueing Problem)

28
Q
  • 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.
A

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

29
Q

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

A

Steady State

30
Q

its operating characteristics or behavior are dependent on time

A

Transient State

31
Q

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.

A

Explosive State

32
Q

(2) Common basic waiting line models

A

Poisson distribution and Negative Exponential distribution

33
Q

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

A

Poisson Distribution

34
Q

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

A

Negative Exponential Distribution

35
Q

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.

A

Lamda (Arrivals per time unit)

36
Q

Mean time between arrivals

A

1/y

37
Q

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

A

Birth

38
Q

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

A

Birth-Death Process, Birth, Death

39
Q

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

A

Matter of practice

40
Q

Commonly used symbols

A

muu and u

41
Q

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

A

Poisson distribution and Negative exponential distribution

42
Q

It is to analyze and optimize systems
that involve waiting lines

A

Queueing Model

43
Q

arrival and service rates are some unknown random variables.

A

Probabilistic Model

44
Q

arrival and service rates are known and fixed

A

Deterministic Model

45
Q

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

A

Mixed Queueing Model

46
Q

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

A

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

47
Q

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

A

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

48
Q

Average number of customer in the queue E (L)

A

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

49
Q

Given:

Arrival (y)
Service (u)

A

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)

OMGT 101 (Midterms) (6 decks)

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