A snack stand with one seller is set in a university campus. Customers arrive at the snack standat an average of one every 5 minutes following Poisson distribution. The service of the sellerfor each customer can be described by an exponential distribution with a mean of 4 minutes.Q2.1 How long is the average waiting time in queue?Q2.2 What is the probability that there are at least four customers in the system?Q2.3 If the waiting cost for each customer is $200/h and the cost for each seller is $240/h, is itnecessary to hire more sellers? If yes, how many new sellers should be hired?Q2.4 If one snack selling machine is set to replace the snack stand, the service time for eachcustomer is constant (2 minute). What is the average time a customer spends in the system afterthe machine is used?

Given, Arrival rate, λ= 1÷5=0.2 customers per minute Service rate, μ =1÷4=0.25 customers per minute…

Answered: A snack stand with one seller is set in…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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A bank teller takes 24 minutes on average to serve a customer. What would be the hourly servicerate used in the queuing formulas?
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 9 customers per hour and an average service rate of 13 customers per hour. The probability of 6 customers in the system is : a. 0.9661 b. 0.8899 c. 0.3077 d. 0.03388
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Customers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?
4.) The DMV Licensing 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. a.) What percentage of the total available service time is being used? b.) Due to Covid restrictions, only two customers are allowed in the office at the same time. What percent of the time will there be customers waiting outside?
3 The M/M/1 Queue During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23 per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via a simple extension of the mean queue size formula) the effect of highly-variable service times on our familiar queuing metrics. The diagram below stylizes the queuing system: Waiting Service Calculate the marginal probability P (T > oT). a. O b. 0.25 O c. 0.63 O d. 0.75 Calculate the mean time a customer spends at the bank (waiting time plus service time) in minutes. O a. 30 minutes O b. 27.6 minutes O c. 2.4 minutes O d. 7 minutes
A post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk? 1.143 minutes 3.429 minutes 1.929 minutes 0.643 minute

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