A vending machine dispenses hot chocolate or coffee. Service time is 15 seconds per cup and is constant. Customersarrive at a mean rate of 55 per hour, and this rate is Poisson-distributed.a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.)Average number of customerb. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round youranswer to 2 decimal places.)Average timeminutesc. Determine the average number of customers in the system. (Do not round intermediate calculations. Round youranswer to 2 decimal places.)

A discrete probability distribution that shows the likelihood of an event within a specified time is…

Answered: b. Determine the average time customers…

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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One field representative services 5 customers for a computer manufacturer. Customers request assistance at an average (Poisson-distributed) rate of once every 1.5 working days. The field representative can handle an average (Poisson-distributed) of 1.0 call per day. Determine: Use Table 1. a. The expected number of customers waiting. (Round "X" value to 2 decimal places. Round your answer to 3 decimal places.) Expected number of customers waiting b. The average length of time customers must wait from the initial request for service until the service has been completed. (Round your answer to 2 decimal places.) Average length of time days c. The percentage of time the service rep will be idle. (Round your answer to 1 decimal place.) Percentage of Idle time d. By how much would your answer to part a be reduced if a second field rep were added? (Round your answer to 3 decimal places.) Reduced number of customer(s)
The office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. b.) What proportion of time are both clerks idle? c.) Counting each person being served and the people in line, on average, how many customers would be in this system?
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and isconstant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed. Determine the following:a. The average number of customers waiting in lineb. The average time customers spend in the systemc. The average number in the system
A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 76 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customer b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes c. Determine the average number of customers in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average number customers
Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copierrepairs come in at a mean rate of three per eight-hour day (assume Poisson).A) Identify the Queuing Model and sketch the system.B) What is the arrival rate?C) What is the service rate?D) What is the average number of customers awaiting repairs?
At a fashion retailer, there are three cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It is estimated that the customer arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 15 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer? Note: 1. Keep 2 decimal places for your final answer. Either use Excel for your calculation, or keep at least 4 decimal places for your intermediate numbers. 2. The Poisson arrival process has exponentially distributed inter-arrival times.

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