10. Customers arrive an average of 8 per hour and an average of 12 customers can beserved in an hour. Assume this is an M/M/1 model. (Noteshaper Quick Start #18 - #20)what is the system utilization?what is the average length of the line?what is the average number of customers in the system?what is the average amount of time spent waiting in the line?what is the average amount of time a customer spends in the system?what is the probability of no customers in the system?11. Customers arrive at a ferry ticket office at the rate of 18 per hour on Monday mornings.This can be described as a M/M/1 model. Selling the tickets and providing generalinformation takes an average of 2 minutes per customer. One ticket agent is on duty onMondays. (Noteshaper Scenario #34)a. What is the average length of the line on Monday mornings?b. On average, how long does a customer wait to buy a ticket on Monday mornings(in minutes)?c. How long does it take to successfully buy a ticket on Monday mornings (inminutes)? (This includes time waiting in line and purchasing from the agent.)d. What is the probability that an arriving customer has to wait to buy a ferry ticketon Monday morning?e. What is the probability of exactly four customers in the ferry ticket office? Thisincludes both customers waiting in line and those being served. Operating Characteristics of the M/M/1 Queuing ModelW refers to timeL refers to number of customersq refers to the queues refers to the system2= Lambda (average numberto arrive)u = Mu (average number served)System UtilizationProbability of NoCustomers in the SystemAverage Number ofCustomers in the QueueAverage Waiting Time inthe QueueW, =%3Dる=1-2Hu-ス)Probability of n Customersin the SystemAverage Number ofCustomers in the SystemAverage Length of Visit tothe SystemW, = W,+-%3!P, = P%3!ペ|さ

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Answered: 10. Customers arrive an average of 8…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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