This document discusses queuing systems in project management. It defines a queue as a line waiting to be served and provides examples of queuing systems like vehicles waiting at toll booths or construction materials waiting to be unloaded. The key components of a queuing system are identified as the flow entity, arrival pattern, number of queues and servers, queue discipline, and service pattern. Performance is measured by criteria like average queue length and wait time. Attributes describe the system structure and performance. In summary, the document outlines queuing systems commonly found in project management and examines their components, performance measures, and descriptive attributes.

1. QUEUING
IN
PROJECT MANAGEMENT
Presented by:
Abdullah Al Mahmud
Student ID: MIT151326
MIT Program, IIT, University of Dhaka

2. Simply: A line waiting to be served
Queuing Systems
I
What is a Queue?

3. Examples of Queuing Systems in Everyday Life
 Vehicles waiting to be served at a toll-booth

4.  Individuals (in person) waiting to be served at
• various service counters,
• stations
• check-out lanes for groceries
• supermarkets, etc.
 Patients scheduled for use of hospital operation
theater
 Football fans waiting to get into stadium
 Operations of a vending machine
 Human urinary system
Queuing
Systems IExamples of Queuing Systems
In Everyday Life (cont’d)

5. PART 2
Resource Allocation for
Queues
Encountered in
Project Management

6. Examples of Queuing Systems in
Project Management
 Construction trucks waiting to be loaded with
raw materials

7. Examples of Queuing Systems in
Project Management (cont’d)
 Project vehicles waiting to unload finished
materials on site

8. Queuing Systems
I
Examples of Queuing Systems
in Project Management (cont’d)
 Vendors supply vehicles waiting to unload
Queuing in Project Management…
… is it a big deal?
 Yes and No

9. The flow entity (queuing unit) in a queuing system is
typically a discrete element,
and is represented by a discrete random variable
(trucks, cars, people, etc.).
But …
Queuing Systems
I
Queuing Units

10. …. queuing systems may also involve continuous flow
entities, (and hence, continuous random variables, such
as:
 Water (in gallons, say) in a large reservoir “waiting” to
be served daily to a project site
 Aggregates, cement, etc. in storage bins, “waiting” to
be shipped to site or to processing plants
Queuing Systems
I
Queuing Units (cont’d)

11. Queuing Systems I
Components
of a
Queuing System

12.  Flow Entity (vehicles, people, materials, etc.)
 Arrival Pattern (of the queuing units)
 Queue Multiplicity (No. of Queues)
 Queue Discipline
 Number of Servers
 Service Arrangement
 Service Pattern
Queuing Systems
I
Components of a Queuing System

13. Components of a Queuing System
Queuing Systems
I
Service
Facility
- Number of Servers
- Service Arrangement
-Service Pattern
Queue
Discipline
Arrival
Pattern
Queue Dissipation
(vehicles leaving
the queuing system
after being served)
Equipment for
Loading or
unloading

14.  Describes the way (usually a rate) in which the arrivals
enter the queuing system
 May be Frequency-based or Interval-based. That is,
arrivals can be described on the basis of:
 the number of arrivals that arrive in a given time
interval
 the average interval of time that passes
between successive arrivals.
Queuing Systems
I
A: Arrival Pattern

15. - Maybe deterministic or probabilistic:
(a) Deterministic: fixed number of arrivals per unit
time or fixed length of time interval between
arrivals
(b) Probabilistic: Stochastic number of arrivals per
unit time or stochastic length of time interval
between arrivals.
Queuing Systems
I
Arrival Pattern (cont’d)

16.  Probabilistic frequency of arrivals may be described
by Poisson distribution or other appropriate discrete
probability distribution
 Probabilistic interval of time between arrivals may
be described by the negative exponential distribution
or other appropriate continuous probability
distribution.
Queuing Systems I
Arrival Pattern (cont’d)

17. (i) Number of servers
(1 or more?)
(ii) Arrangement of servers
(parallel or series or combo?)
(iii) Service pattern
What distribution? How fast (average), etc.)
Queuing Systems I
B: Service Facility Characteristics

18. Queuing Systems
I
B: Service Facility Characteristics (cont’d)
(i) Number of Servers:
Single Server:
Examples: Only one counter open at bank
Candy dispenser,
Coke vending machine
Single truck loader at project site
Multi-server:
Examples: Several counters open at bank
Multi-lane freeway toll booth
Multiple truck loader at project site

19. (ii) Arrangement of servers
Parallel arrangement of servers
e.g., Bank counters
Serial arrangement of servers
e.g., Some McDonald drive-thrus
S1- PLACE ORDER
S2- PAY MONEY
S3- COLLECT FOOD
Queuing
Systems I
B: Service Facility Characteristics (cont’d)
S1
S2
S3
S1 S2 S3

20. Queuing Systems
I
(ii) Arrangement of servers (cont’d)
Combination of
Parallel and Serial
Arrangements
S3 S2
S4S3

21. Queuing Systems
I
(ii) Arrangement of servers (cont’d)
Combination of Parallel and Serial Arrangements
2 channels and 2 phases
S3 S2
S4S3
Arrivals
Departures
Departures
Channel 1
Channel 2

22. Queuing Systems
I
(ii) Arrangement of servers (cont’d)
Combination of Parallel and Serial Arrangements
2 channels and 2 phases
S3 S2
S4S3
Arrivals
Departures
Departures
Phase 1 Phase 2

23. Queuing Systems
I
(ii) Arrangement of servers (cont’d)
Combination of Parallel and Serial Arrangements
2 channels and 2 phases
S3 S2
S4S3
Arrivals
Departures
Departures
Phase 1 Phase 2
Channel 1
Channel 2

24. 1Arrivals Departure
Server
Single Phase, Single Channel
Queuing Systems
I

25. 1Arrivals Departure
Server
Single Phase, Single Channel
Multiple Phase, Single Channel1Arrivals Departure
Server
2 3
Queuing Systems
I

26. 1Arrivals Departure
Server
Single Phase, Single Channel
Multiple Phase, Single Channel
Single Phase, Multiple Channel
1Arrivals Departure
Server
2 3
2Arrivals Departures
Servers
3
1
Queuing Systems
I

27. 1Arrivals Departure
Server
Single Phase, Single Channel
Multiple Phase, Single Channel
Single Phase, Multiple Channel
Multiple Phase, Multiple Channel
1Arrivals Departure
Server
2 3
2Arrivals Departures
Servers
3
1
4Arrivals Departures
7
1
5
8
2
6
9
3
Queuing Systems
I

28. (iii) Service Pattern
Describes the way (usually a rate) by which arrivals are
processed
 May be frequency-based or interval-based. That is, service
can be described based on:
 The number of arrivals that are served in a given
time interval
 The average interval of time that is used to serve
the arrivals
Queuing Systems
I
B: Service Facility Characteristics (cont’d)

29. - Maybe deterministic or probabilistic:
(a) Deterministic: fixed number of served arrivals per unit
time or fixed length of time interval between services
(b) Probabilistic: Stochastic number of servings per unit
time or stochastic length of time interval between
servings
Queuing Systems
I
(iii) Service Pattern

30. Refers to the number of queues being served simultaneously
 Single queue (Examples: most drive thrus, banks, narrow toll
bridges, traffic green lights serving only one lane)
 Multiple queue (assuming no preference between each queue)
Examples: Most dining counters, toll booths traffic green light
serving two or more lanes)
Typically number of queues ≤ number of servers, but when
number of queues > number of servers, then some extra rules
for queue discipline are needed
Queuing
Systems I
C: Queue Multiplicity

31. Queuing Systems
I
1 queue, 1 server
S1
Some Queuing Configurations

32. Queuing Systems I
1 queue, 2 servers
S1
Some Queuing Configurations
S2

33. Queuing Systems
I
2 queues, 2 servers
S1
Some Queuing Configurations
S2

34. 2 queue, 5 servers
Queuing Systems
I
S4
Some Queuing Configurations
S3
S2
S1
S5

35. 4 queues, 1 server
Queuing Systems I
S1
Some Queuing Configurations

36. This refers to the rules by which the queue is served
Relates serving priority to:
a. Order of arrival times, or
b. Order of arrival urgencies
c. Order of expected length of service time
d. Order of “desirability” of arrival of specific flow
entities
Queuing Systems
I
D: Queue Discipline

37. (i) Serving priority by order of arrival times
FIFO (First in, first out)
First come, first served
Last in, last out
e.g., Truck in front is always served first.
FIFO is a non-discriminatory queue discipline, very fair
LIFO (Last in, first out)
e,g., Truck at tail end of queue always served first
e.g., Candy dispenser
e.g., Often crowded elevator mostly serving 2 floors
LIFE is not fair!
Queuing Systems
I
D: Queue Discipline (cont’d)
LIFO

38. (ii) Serving priority by order of arrival urgencies
Trucks needing attention most urgently is served first,
regardless of when they arrived
Examples in everyday life:
 Scheduling patients for surgery in order of
sickness severity
 Giving way to fire trucks at intersections
Queuing
Systems I
D: Queue Discipline (cont’d)

39. (iii) Serving priority by order of expected service period
Trucks whose service will take shorter times are
served first, regardless of the time they joined the
queue
Examples:
 Express lanes at supermarkets (shoppers with
less than 5 items)
 Trucks taking away items that take a very
short time to load
 Trucks delivering items that take very short
time to unload
Queuing
Systems I
D: Queue Discipline (cont’d)

40. Queuing Systems
I
Performance
of
Queuing Systems

41. Class Questions:
 How would you assess the performance of a
queuing system?
 That is, what criteria would you use?
Queuing Systems I
Performance of Queuing Systems

42. Performance of Queuing Systems
Performance of a Queuing System Is Measured by:
•Average queue length (Lq) - average number of
customers in the waiting line.
•Average number of customers in the system (L).
•Average waiting time in the queue (Wq).
•Average staying time in the system (W).
•Utilization rate of servers ( ).
•Probability that n customers in the system (Pn).
ρ
[Source: Handbook of Industrial and Systems Engineering, Second Edition, by Adedeji
B. Badiru, Ch-48]

43. Performance of Queuing Systems
 Service Rate,
- number of customers that can be served per unit time
 Arrival Rate,
(number of customers per unit time)
Server Utilization or Traffic Intensity,
 = / m
µ
λ
ρ
ρ λ µ
[Source: Handbook of Industrial and Systems Engineering, Second Edition, by Adedeji
B. Badiru, Ch-48]

44. [Source: Handbook of Industrial and Systems Engineering, Second Edition, by Adedeji
B. Badiru, Page#1036]
Performance of Queuing Systems

45. Performance criteria for queuing systems:
 Average queue length
 Maximum queue length
 Average waiting period per truck
 Maximum waiting period per truck
 % of time each server is idle
 Physical and operating cost of the
queuing systems
 Number of customers served per unit time
Queuing Systems I
Measure of Evaluation(MOE)
Minimize this,
or
truck time is
wasted
Minimize this,
or project
resources
are wasted
Maximize this,
or
Both truck time
and project resources
are wasted

46. Attributes of a
Queuing System
Queuing
Systems I

47. QUEUING SYSTEM ATTRIBUTES
- These describe the way the system is structured, its operating
procedure, and how well it performs.
- Consists of system components, and other attributes:
Physical System Components
 Flow Entities (trucks), Queues, Servers (serving
facilities/equipment)
Operational System Components
Pattern of Arrivals, Number of Queues, Pattern of Service,
Number of Servers, Queue Discipline, Queue Capacity
System Performance
 Queue length, waiting time, server idle time, etc.
Queuing
Systems I

48. Summary
Queuing in Project Management:
 Examples of Queuing Systems
 Components of a Queuing System
 Flow Entity, Arrival Pattern, Queue Multiplicity,
 Queue Discipline, Number of Servers,
 Service Arrangement, Service Pattern
 Queuing System Performance
 Measure of Evaluation
 Attributes of a Queuing System

49. Acknowledgements
 Dr. Samuel Labi , Purdue University
 Dr. Fred Moavenzadeh, Massachusetts Institute of Technology
(MIT)
 Dr. Md. Mahbubul Alam Joarder, Institute of Information
Technology, University of Dhaka.

50. ….QUESTIONS?