Opersea reporting waiting lines and Queuing theory

1. WAITING LINES and QUEUING
THEORY MODELS
Isaac Lawrence Yvan C. Andaya

2. INTRODUCTION
• The Foundation of modern
queuing theory is based on
studies about automatic
dialing equipment made in
the early part of the 20th
century by Danish
telephone engineering “A.K.
ERLANG”.

3. QUEUING THEORY
• The Planning and Analysis of service capacity.
• It is the study of Waiting Lines.
• Three basic components of a queuing process
are arrivals, service facilities and the actual
waiting line.
• Queuing theory has been used for
operations research, manufacturing
and system analysis.

4. Applications of Queuing Theory
• Telecommunications
• Traffic Control
• Determining the sequence of computer
operations
• Airport traffic, airline ticket sales
• Predicting computer performance

5. • Waiting lines tends to form even though a
system is basically under loaded. For
example: a fast food restaurant may have
the capacity to handle an average of 100
orders/hour but may experience waiting
lines even though the average number of
orders is only 75/hour. The operative word
is “AVERAGE”.

6. • In real situation, customers arrive at
random intervals rather than at evenly
spaced intervals, also some orders take
longer to fill than the others. In short both
arrivals and service time exhibit a high
degree of variability, w/c results to
temporary overloading – waiting lines.

7. Implication of Waiting Lines
There are Reasons why managers have to be concerned
with waiting lines:
1.The cost of providing a waiting space.
2.Should customers leave the line before being served or
refuse to wait at all, the possible business loss should be
considered.
3.A possible loss of goodwill.
4.Probable reduction in customer satisfaction.
5.The resulting congestion may interrupt other business
operations and or customers.

8. WAITING LINE COSTS
• The Main goal of waiting line analysis
is to minimize costs. There are two
type of cost in a queuing scenario;
those costs relating to customers
waiting for service and those relating
to capacity.

9. Capacity costs
• Is defined as the costs of maintaining
the ability to provide service. Capacity
is lost when a service facility is idle,
since capacity cannot be stored.

10. • Meanwhile the cost of customer waiting for
service could include: the salaries paid to
employees while they wait, the cost of
space for waiting and any loss of business
due to customers refusing to wait and or
going elsewhere. This loss of business is
oftentimes called as ”Opportunity Loss.”

11. • Queuing costs and service level
*
Optimal
Service
Level
Cost
Service Level
Cost of Providing Service
Total Expected Cost
Cost of Waiting Time

12. Characteristics of a Queuing
System
• There are three parts to a queuing system
1. The arrivals or inputs to the system (sometimes
referred to as the calling populationcalling population)
2. The queue or waiting line itself
3. The service facility
• These components have their own
characteristics that must be examined before
mathematical models can be developed

13. Arrival Characteristics
• Arrival Characteristics have three major
characteristics, sizesize, patternpattern, and behaviorbehavior
– Size of the calling population
• Can be either unlimited (essentially infiniteinfinite) or
limited (finitefinite)
– Pattern of arrivals
• Can arrive according to a known pattern or can
arrive randomlyrandomly
• Random arrivals generally follow a PoissonPoisson
distributiondistribution

14. • The Poisson distribution is
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16. Behavior of arrivals
– Join the Queue,Join the Queue, Most queuing models assume
customers are patient and will wait in the queue until
they are served and do not switch lines
– BalkingBalking refers to customers who refuse to join the
queue
– RenegingReneging customers enter the queue but become
impatient and leave without receiving their service
– That these behaviors exist is a strong argument for
the use of queuing theory to managing waiting lines

17. – Waiting lines can be either limitedlimited or unlimitedunlimited
– Queue discipline refers to the rule by which
customers in the line receive service
– The most common rule is first-in, first-outfirst-in, first-out (FIFOFIFO)
– Other rules are possible and may be based on
other important characteristics
– Other rules can be applied to select which
customers enter which queue, but may apply FIFO
once they are in the queue
Waiting Line Characteristics

18. Service Facility Characteristics
• Service systems are classified in terms of the number of
channels, or servers, and the number of phases, or
service stops
• A single-channel systemsingle-channel system with one server is quite
common
• MultichannelMultichannel systemssystems exist when multiple servers are fed
by one common waiting line
• In a single-phase systemsingle-phase system the customer receives service
form just one server
• If a customer has to go through more than one server, it
is a multiphase systemmultiphase system

19. Service Time Distribution
– Service patterns can be either constant or random
– Constant service times are often machine controlled
– More often, service times are randomly distributed
according to a negative exponential probabilitynegative exponential probability
distributiondistribution
– Models are based on the assumption of particular
probability distributions
– Analysts should take to ensure observations fit the
assumed distributions when applying these models

20. Performance Measure of
Queuing systems
Managers observed these five factors when evaluating
existing or proposed service systems.
•The Average number of customers waiting, either in line or in the
system.
•The Average time customers wait or spend in the cue, either in line or
in the system.
•Average length of the cue.
•System Utilization – refers to the percentage of capacity utilized.
•The implied cost of a given level of capacity and its related waiting
line.
•The probability that an arrival will have to wait for service.
•Probability that the service will be idle.

21. SINGLE CHANNEL EXPONENTIAL
SERVICE TIME MODEL
• This model involves a system that has one
server and there is no limit on length of queue.
1.Queue discipline: FIFO
2.No Balking or Regening
3.Independent arrivals
4.Arrivals: Poisson distributed
5.Service times: negative exponential
6.Average service rate . Average arrival rate