An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed byone ticket agent. It is estimated that requests for tickets and information will average15 per hour, and requests will have a Poisson distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggeststhat mean service time should average about three minutes per request. Determine each ofthe following:a. System utilizationb. Percentage of time the server (agent) will be idlec. The expected number of customers waiting to be servedd. The average time customers will spend in the systeme. The probability of zero customers in the system and the probability of four customersin the system Performance MeasureEquationAverage number in line(18–6)H(H – 1)(-)Probability of zero units in the systemPo= 1-(18–7)Probability of n units in the systemP,= Po(18–8a)--G)'Probability of less than n units in the systemP =(18–8b)I This notation is commonly used to specify waiting-line models. The first symbol refers to arrivals, the second toservice, and the third to the number of servers. M stands for a rate that can be described by a Poisson distribution or,equivalently, a time that can be described by an exponential distribution. Hence, M/M/1 indicates a Poisson arrivalrate, a Poisson service rate, and one server. The symbol D is used to denote a deterministic (i.e., constant) servicerate. Thus the notation M/D/1 would indicate the arrival rate is Poisson and the service rate is constant. Finally, thenotation M/M/S would indicate multiple servers.

Answered: Image /qna-images/answer/00722f82-2380-4749-aded-670b86ae1f75.jpg

Answered: Performance Measure Equation Average…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

See similar textbooks

Related questions

Concept explainers

Question

An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed by
one ticket agent. It is estimated that requests for tickets and information will average
15 per hour, and requests will have a Poisson distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggests
that mean service time should average about three minutes per request. Determine each of
the following:
a. System utilization
b. Percentage of time the server (agent) will be idle
c. The expected number of customers waiting to be served
d. The average time customers will spend in the system
e. The probability of zero customers in the system and the probability of four customers
in the system

Performance Measure
Equation
Average number in line
(18–6)
H(H – 1)
(-)
Probability of zero units in the system
Po= 1-
(18–7)
Probability of n units in the system
P,= Po
(18–8a)
--G)'
Probability of less than n units in the system
P =
(18–8b)
I This notation is commonly used to specify waiting-line models. The first symbol refers to arrivals, the second to
service, and the third to the number of servers. M stands for a rate that can be described by a Poisson distribution or,
equivalently, a time that can be described by an exponential distribution. Hence, M/M/1 indicates a Poisson arrival
rate, a Poisson service rate, and one server. The symbol D is used to denote a deterministic (i.e., constant) service
rate. Thus the notation M/D/1 would indicate the arrival rate is Poisson and the service rate is constant. Finally, the
notation M/M/S would indicate multiple servers.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.

Similar questions