Concept explainers
a)
To determine: The average number of cars waiting for drive-through window.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
b)
To determine: The average number of cars to be served per hour.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
c)
To determine: The average time will it take before receiving the food.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
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Chapter 12 Solutions
Practical Management Science
- Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes.Arrivals tend to follow a Poisson distribution, and service times follow anexponential distribution. We need to analyze this waiting-line system. (g) Should the retail store consider creating a second cashier lane?(h) A cash machine manufacturer has offered an advanced system that willreduce service time to 2 minutes per customer. The cost of the newmachine would be the same as opening a second cashier lane, so theowner has decided to buy the new system only if it reduces wait timesover the two-cash option. Evaluate the two options (advanced cash or atwo-cash system) and suggest which option you would choose.arrow_forwardAssume that at a bank teller window the customers arrive in their cars at the average rate of twenty per hour according to a Poisson distribution. Assume also that the bank teller spends an average of two minutes per customer to complete a service, and the service time is exponentially distributed. Customers, who arrive from an infinite population, are served on a first-come-first-served basis, and there is no limit to possible queue length.a. What is the expected waiting time in the system per customer?b. What is the mean number of customers waiting in the system?c. What is the probability of zero customers in the system?d. What value is the traffic intensity?arrow_forwardA teller works at a rural bank. Customers arrive to complete their banking transactions on average one every 10 minutes; their arrivals follow a Poisson arrivalprocess. Because of the range of possible transactions, the time taken to serve eachcustomer may be assumed to follow an exponential distribution with a mean timeof 7 minutes. Customers wait in a single queue to get their banking done and nocustomer leaves without service.a. Calculate the average utilization of the teller.b. Calculate how long customers spend on average to complete their transactionsat the bank (time in queue plus service time). What percentage of that time isspent queueing?arrow_forward
- An average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a singleline for the first available clerk. The average time for a clerkto service a patron is 3 minutes (exponentially distributed).Clerks earn $10 per hour, and the hotel assesses a waitingtime cost of $20 for each hour that a patron waits in line.a Compute the expected cost per hour of the currentsystem.b The hotel is considering replacing one clerk with an Automatic Clerk Machine (ACM). Management esti-mates that 20% of all patrons will use an ACM. An ACM takes an average of 1 minute to service a patron.It costs $48 per day (1 day 8 hours) to operate anACM. Should the hotel install the ACM? Assume thatall customers who are willing to use the ACM wait in asingle queue.arrow_forward12-17 Automobiles arrive at the drive-through window at a post office at the rate of four every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. a. What is the average time a car is in the system? b. What is the average number of cars in the system? c. What is the average time cars spend waiting to receive service? d. What is the average number of cars in line behind the customer receiving service? e. What is the probability that there are no cars at the window? f. What percentage of the time is the postal clerk busy? g. What is the probability that there are exactly two cars in the system?arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,