A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customers per hour arrive at the facility (interarrival times are assumed to be exponential). The system capacity is three customers: two waiting and one being served. What is the probability that the server is busy at a typical point in time? If needed, round your answer to a whole percentage. The excel formula breaks the answer down to 0.8769. However 0.87 or 1% is showing as wrong answer.
A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customers per hour arrive at the facility (interarrival times are assumed to be exponential). The system capacity is three customers: two waiting and one being served. What is the probability that the server is busy at a typical point in time? If needed, round your answer to a whole percentage. The excel formula breaks the answer down to 0.8769. However 0.87 or 1% is showing as wrong answer.
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...
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A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customers per hour arrive at the facility (interarrival times are assumed to be exponential). The system capacity is three customers: two waiting and one being served. What is the probability that the server is busy at a typical point in time? If needed, round your answer to a whole percentage.
The excel formula breaks the answer down to 0.8769. However 0.87 or 1% is showing as wrong answer.
Transcribed Image Text:Inputs
Unit of time
hour
Arrival rate
3
customers/hour
Service rate
Number of servers
2
customers/hour
Calculate steady-state
quantities
Maximum customers in system
3
customers
Maximum queue length
2
customers
Outputs
Steady-state probabilities
Summary measures
Pn
0 0.1231
1 0.1846
Expected number in system
1.985
customers
Expected number in queue
1.108
customers
Expected time in system
1.132
hours
2 0.2769
Expected time in queue
0.632
hours
3 0.4154
Entering rate
Percentage who don't wait in queue
1.754
customers/hour
12.3%
Probability server is busy
0.8769
Transcribed Image Text:* CENGAGE MINDTAP
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The following problem is based on the limited queue and limited source models in the Limited Queue Template.xlsm and Limited Source Template.xlsm files.
A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customers per hour arrive at the facility (interarrival
times are assumed to be exponential). The system capacity is three customers: two waiting and one being served.
a. On average, how many potential customers enter the system each hour?
needed, round your answer to one decimal digit.
1.7
b. What is the probability that the server is busy at a typical point in time? If needed, round your answer to a whole percentage.
1
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