solve all parts 3c. Customers arrive at a Starbucks that has 1 barista and they wait in line on a first-come, first-served basis. Customers arrive according to a Poisson process with a rate of 12 per hour. It takes onaverage 3.5 minutes for a customer to be served by the barista. No customer leaves without gettingcoffee. The standard deviation of the service time is 2.25 minutes.1. What is the average utilization of the barista? [Select]2. What is the average time (in minutes) a customer spends in line waiting?[Select]minutes3. How many are waiting in line, on average? [Select]people4. The manager is thinking of adding more baristas, and would like to add as many as needed to getthe probability of delay to a value less than or equal to 1/3. How many baristas are needed forthis? (Assume all baristas have identical service rates.)[Select]

Given, Arrival rate,λ =12 per hour Service rate, μ=60/3.5 =17.14 customers per hour Standard…

Answered: 3c. Customers arrive at a Starbucks…

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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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.
Customers enter the camera department of a store at an average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation.a. As a casual observer, how many people would you expect to see in the camera department (excluding the clerk)? How long would a customer expect to spend in the camera department (total time)?b. What is the utilization of the clerk?c. What is the probability that there are more than two people in the camera department (excluding the clerk)?d. Another clerk has been hired for the camera department who also takes an average of six minutes to serve each arrival. How long would a customer expect to spend in the department now?
Customers enter the camera department of a store at the average rate of six per hour. The department is staffed by one employee, who takes an average of six minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distributed service time situation. a. As a casual observer, how many people would you expect to see in the camera de- partment (excluding the clerk)? How long would a customer expect to spend in the camera department (total time)? b. What is the utilization of the clerk? c. What is the probability that there are more than two people in the camera department (excluding the clerk)? d. Another clerk has been hired for the camera department who also takes an average of six minutes to serve each arrival. How long would a customer expect to spend in the department now?
A supermarket has more than one server servicing at counters. The customer arrives in a Poisson fashion at the rate of 10 per hour. The service time for each customer is expected with a mean of 4 minutes. Find the probability of a customer has to wait for the service, average queue length, the average time spent by a customer in the queue.
Please do not give solution in image formate thanku. λ= 4 customers per hour; μ = 5 customers per hour; M= 1 An average of 20 customers arrive at a service center each hour. There are two servers on duty, and each can process 12 customers per hour. a) What is the system utilization? b) What is the average waiting time for customers who actually have to wait? c) What is the average time customers wait in line for service?
13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.
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)
An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed byone ticket agent. It is estimated that requests for tickets and information will average15 per hour and requests will have a Poisson distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggeststhat mean service time should average about three minutes per request. Determine each ofthe following:a. System utilizationb. Percentage of time the server (agent) will be idlec. The expected number of customers waiting to be servedd. The average time customers will spend in the systeme. The probability of zero customers in the system and the probability of four customersin the system.

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