Concept explainers
a)
Interpretation:customer officer during time period.
Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.
a)
Answer to Problem 37P
The customer officer is busy 75% of the time.
Explanation of Solution
Given information:the scenario meets the assumptions of M/M/1 model
Explanation:
b)
Interpretation: average wait to speak to the officer andthe probability that someone will be able to speak immediately upon arrival.
Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.
b)
Answer to Problem 37P
average wait to speak to the officer 15 minutes.
the probability that someone will be able to speak immediately upon arrival is 0.25.
Explanation of Solution
Given information:
Explanation:
Average wait time to speak to the office,
The probability that someone will be able to speak immediately upon arrival is the same as the probability of there being no cars in the system. This probability
c)
Interpretation:the average cars present at the border crossing plaza during that time period.
Concept introduction:The M/M/1 queue assumes poison arrivals, exponential service times, and a single server serving customers in a FCFS fashion. Poisson arrivals are a reasonably good assumption for unscheduled systems. Further if there is a mix of many different types of jobs the exponential distribution can be realistic for service times. Otherwise it tends to be too variable of a distribution.
c)
Answer to Problem 37P
the average cars present at the border crossing plaza during that time period is 3 cars.
Explanation of Solution
Given information:
Explanation:
The average cars present at the plaza during that period, L is given using the below formula
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Chapter 5 Solutions
Practical Operations Management
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- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,