Models have been developed to help managers make better decisions about waiting line operations. Waiting line models use mathematical formulas to determine performance measures like average wait times and number of customers in the system. Burger Dome wants to study its single-server waiting line to reduce wait times and improve service. Waiting line models can indicate when improvements, like adding servers, are needed. Spreadsheets can easily implement waiting line models to analyze systems.

2. Chapter11
Waiting line models

3. Waiting line models that have been develop to help managers
make better decision concerning the operation of waiting
lines.
We also showed how an economics analysis of the waiting
line could be conducted by developing a total cost model that
includes the cost associated with units waiting for services
and the cost required to operate the service facility.

4. Models have been develop to help managers understand
and make better decisions concerning the operation of
waiting lines.
In management science terminology ,a waiting lines is also
known as queue and the body of knowledge dealing with
waiting lines is known as queueing theory.

5. Waiting line models- consist of mathematics formulas and
relationships that can be used to determine the operating
characteristics (performance measures)for a waiting line.
Operating characteristics of interest include these:
1.The probability that no units are in the system (I,e the
system is idle)
2.The average number of units in the waiting line.

6. 3.The average number of units in the system(the number
of units in the service time)plus the number of units being
served).
4.The average time a unit spend in the waiting line.
5.The average time a unit spend in the system (the waiting
time plus the service time).
6.The probability that an arriving unit as to wait for service.

7. Structure of a waiting line system
Burger Dome is concerned that the methods currently
used to serve customers are resulting in excessive
waiting times and a possible loss of sale.
Management wants to conduct a waiting line study to
help determine the best approach to reduce waiting
times and improve service

8. Single –serve waiting line
each customer entering the Burger Dome restaurant is
served by a single order-filling station that handles order
placement ,bill payment and food delivery.
Distribution of Arrivals –Defined the arrival process for a
waiting line involves determining the probability distribution
for the number of arrivals in a given period of time.

9. Distribution of Service Times-is the time a customer spends as the
service facility once the service has started.
Exponential probability distribution- Formulas are available for
providing useful information about the operation of the waiting line.
Queue Discipline-(FCFS) –First come and First served basis.
For example ,when people board an airplane the last passengers to
board are typically the first to deplane since many airlines have the
passengers with seat assignment in the back of the plane board
first.

10. Steady-State Operation- the beginning or startup period is
referred to as the transient period.
The transient period ends when the system reaches the
normal or steady-state operation.
Waiting line models describe the steady-state operating
characteristics of a waiting line.
Managers’ Use of waiting line models -This condition
indicates a fairly high probability that Burger Dome will
experiences some long waiting lines if it continues to use the
single –server operation.

11. Improving the waiting line operation-
Waiting line models often indicates when improvements in
operating characteristics are desirable.
1.Increasing the service rate by making a creative design change
or by using new technology.
2.Add one or more servers so that more customers can be served
simultaneously.
Excel Solution of Waiting Line Models-
Waiting line models are easily implemented with the aid of
spreadsheets.

12. Multiple-server waiting line- consists of two or more
server that are assumed to be identical in terms of service
capability.
For multiple-server systems there are two typical
queueing possibilities.
1.arriving customers wait in a single waiting line (called a
“pooled” or “shared” queue) and then move to the first
available server for processing.
2.Each server has a “dedicated” queue and an arriving
customer selects one of these lines to join(and typically is
not allowed to switch lines).

13. Economics Analysis of Waiting Lines- To conduct an economics
analysis of a waiting line we must obtain reasonable estimates of
the waiting cost and the service cost.
Constant Service Times- Such a waiting line can occur in
production and manufacturing environments where machine-
controlled service times are generally constant.
Waiting Line Models With Finite Calling Populations-Infinite calling
population –In technique terms when no limits is placed on how
many units seek service.

14. Finite calling population-In this situation the arrival rate for
the system change ,depending on the number of unity in the
waiting line.
1.The arrivals for each units follow a poison probability
distribution ,with arrival rate.
2.The service times follow an exponential probability
distribution with service rate .
3.The population of units that may seek service.

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