Concept explainers
a)
Interpretation: Average length of the line.
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 34P
Average length of the line is 2.33
Explanation of Solution
Given information:
Explanation:
B)
Interpretation:customer wait to buy tickets.
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 34P
Customer wait to buy tickets is 7 minutes.
Explanation of Solution
Given information:
Average waiting time in queue = 10 min -service time
Explanation:
C)
Interpretation:time to buy tickets.
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 34P
10 minutes to buy tickets.
Explanation of Solution
Given information:
Explanation:
average waiting time to buy tickets
D)
Interpretation: probability of arriving customers wait
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.
D)
Answer to Problem 34P
0.7 probability of arriving customers wait
Explanation of Solution
Given information:Probability that there are zero customers in the system
Explanation:
Probability that there are zero customers in the system
E)
Interpretation: probability of having four customers.
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.
E)
Answer to Problem 34P
probability of having four customers is 0.07203
Explanation of Solution
Given information:
P = 4 customers
Explanation:
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Chapter 5 Solutions
Practical Operations Management
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,MarketingMarketingISBN:9780357033791Author:Pride, William MPublisher:South Western Educational Publishing