At the bus station, there are six lines for arriving passengers, each staffed by a single worker. The arrival rate for passengers is 108 perhour and each passenger takes (on average) 3.1 minutes for a worker to process. The coefficient of variation for arrival time is 1.5 andthe coefficient of varlation for service time is 11.(Round your answer to three decimal places.)On average, how many customers will be waiting in the queue?passengers

Answered: On average, how many customers will be…

Business

Operations Management

On average, how many customers will be waiting in the queue?

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 30P

See similar textbooks

Related questions

Q: Describe at least 4 operating characteristics you can determine by performing queue analysis. What…

A: Queue Analysis: Queue analysis is very important for every business model nowadays…

Q: In an M/MA queueing system, the arrival rate is 4 customers per hour and the service rate is 6…

A: Given data Arrival rate λ = 4 customer per hour Service rate μ= 6 customer per hour

Q: If the restaurant runs a sale and the customer arrival rate increases by 20 percent how would this…

A: The restaurant needs to develop new strategies if the customer arrival rate increases by 20 percent…

Q: a. Customers queue at the express aisle of a supermarket checkout at the rate of 16 per hour.…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: In a queueing system, customers arrive once every 4 minutes (standard deviation = 7) and services…

A: Queuing systems are basic mathematical models that are used to explain traffic bottlenecks. A…

Q: A post office has a single line for customers waiting for the next available postal clerk. There are…

A: Given: λ = 13×60= 20/hourμ = 12×60=30/hour c = number of servers = 2 Multiple server queues model…

Q: A remote bank with one teller on average has a customer arrive every 10 minutes, and on average…

A: WE ARE GIVEN ARRIVAL TIME (LAMDA) = 10 MINS SERVICE TIME (AMU) = 10 PER HOUR = 10/60 = 1 PER MIN WE…

Q: a) On the average, how many machines are waiting for service? The average number of machines waiting…

A: Service rate is the measurement rate at which the customer service is measured in the supply…

Q: An average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential),…

A: a). M/M/5 system with λ = 90 customers/hr and μ = 20 customers/hour. P(j≥5) = .76. Then Wq =…

Q: A small COVID testing location has a single reception desk. The time between two arriving people…

A: Given data, Arrival rate, = (1/3.5) × 60 = 17.14285714285 per hour Service rate, = 27 per hour

Q: Trucks arrive at a warehouse at a rate of 15 per hour during business hours. Crews canunload the…

A: Given Information: Arrival Rate = 15 per hour Service (Unloading) Rate = 5 per hour Crew and Dock…

Q: A server operates with 75 percent utilization. The average processing time istwo minutes and the…

A: Utilization of Server = ρ=0.75 Average processing time = 2 minutes Service rate = μ = 12×60 = 30…

Q: The queuing models assume that customers are served in what order?

A: There are various assumptions with respect to the order of service in queuing models. These are:…

Q: For the first two hours of the day, the arrival rate at the donut shop is 10 customers per hour. The…

A: Given:Time interval(t) = 2 hrArrival rate ( λ)= 10 hrServing rate(μ) = 8 hr

Q: In a queueing system, customers arrive once every 6 seconds (standard deviation = 5) and services…

A: Given data Arrival rate λ=16 Service rate μ=15 Coefficient of variations of the arrival time…

Q: In what kind of situations is queuing analysis most appropriate?

A: The mathematical analysis of the congestion and delays of waiting in line is the queuing theory.…

Q: Drivers who come to get their licenses at the Department of Motor Vehicles have their photograph…

Q: In an M/MA queueing system, the arrival rate is 3 customers per hour and the service rate is 5…

A: Service rate is the rate at which the customers are being served in the company’s system by the…

Q: Consider the baggage check-in process of a small airline. Check-in data indicate thatfrom 9 a.m. to…

A: Formula:

Q: What is the number of customers waiting in the queue on average?

A: Arrival Rate (Lambda) = 12 per hour Average Service Rate (Mu) = 60/4 = 15 per hour

Q: A small popular restaurant at an interstate truck stop provides priority service to truckers. The…

A: Below is the solution:-

Q: At a ride in an amusement park, customers form a line to wait for their turn to get a ride. Only one…

A: Operations management is all about overseeing the activities related to the manufacturing of goods…

Q: One field representative services 5 customers for a computer manufacturer. Customers request…

Q: Five drilling machines at Al Hamriya steel is maintained by Lumina maintenance service with 2…

Q: At a fashion retailer, there are 3 cashiers providing On average, customers arrive at the checkout…

A: A Small Introduction to Retailers Retail is an agreement where the dealer offers little amounts of…

Q: Do: 12-21 Truck drivers working for Juhn and Sons (see Problems 12-19 and 12-20) are paid a salary…

A: Given information: Truck drivers salary=$20 per hour on average Fruit loaders receive $12 per hour…

Q: The Draper Clinic has two general practitioners who seepatients daily. An average of 6.5 patients…

A: Given Average arrival Rate = 6.5/hour Average service rate per server = 4/hour M=number of servers…

Q: How much time, on average, would a server need to spend on a customer to achieve a service rate of…

A: Queuing theory helps to solve the issue of economics of waiting lines and helps managers in better…

Q: A new customer walks into SLC Barber Shop every 60 minutes on average, with a standard deviation of…

A: Service time is the total time in which a customer is served after their arrival in a system.

Q: In a queueing system, customers arrive once every 4 hours (standard deviation = 7) and services take…

Q: A supermarket manager notices that there are 20 customers at the checkouts andalso knows that…

A: Given that,

Q: what is the average time spent waiting in the queue and the average time in the system

A: In the above question, the percentage of time used by the machine is 44% and the average length of…

Q: The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests,and…

A: λ =7.5 cabs/hrμ= 7.05 cabs/hrIn finite que system the guest are service providers and cabs are…

Q: What is queuing model in the service operations? Explain different configurations of the service…

A: Queuing theory deals with problems that involve waiting (or queuing).• It is quite common that…

Q: Buses arrive at the downtown bus stop and leave for themall stop. Past experience indicates that 20%…

Q: A cashier at a supermarket is able to deal with on average, 480 customers per 8 hour shift.…

A: ANSWER IS AS FOLLOWS:

Q: Trucks arrive at the loading dock of a wholesale grocer at the rate of 1.2 per hour. A single…

A: Rate of arrival of Truck λ = 1.2 With 2 crew members Rate of Service μ = 60/30 = 2 per hour Number…

Q: ermediate calculation your ree decimai places.) What is the average number of customers in the…

A: THE ANSWER IS AS BELOW:

Q: A bank teller takes 24 minutes on average to serve a customer. What would be the hourly servicerate…

A: Provided Information: A customer is served by a bank teller in an average of 2.4 minutes.

Q: On average, a patient spends 5 minutes waiting and 15 minutes being treated at PSH Clinic. Given the…

A: Given, Average time in clinic Wq = Average time waiting + time being treated Wq = 5 + 15 = 20…

Q: Joe’s market is a small grocery store with only one checkout counter. Assume that shoppers arrive…

A: Given: Arrival rate= 15 customers/hour The Average order takes = 3 minutes The average waiting time…

Q: People arrive randomly at a bank teller at an average rate of 20 an hour. If the teller takes an…

A: Given data 60 customers per hour because the teller takes an average of 1 minute to serve each…

Q: The First American Bank of Rapid City has one outside drive-up teller. It takes the teller an…

Q: The office has a single line for customers waiting for the next available clerk. There are two…

A: Queuing theory is a mathematical study of the formation, function, and congestion of waiting lines…

Q: Snip

A: For any company in the market place, its main objective would be to satisfy customers and deliver…

Q: In a queueing system, customers arrive once every 6 minutes (standard deviation = 7) and services…

A: Given, a = 1 customer every 6 min = 1/6 s = 1 customer every 4 min = 1/4 Utilization = (1/6)/(1/4) =…

Concept explainers

Inventory Management

The supply chain is crucial to a firm's operations as it manages the inflow and outflow of products that are manufactured from the initial stage to the end product. It also considers the raw materials needed at different stages of production and when the work is in progress. Inventory management functions consist of ordering, storing, and procuring the organization's inventory like raw materials, factors, and finished products. It's also used for controlling the number of products for trade and helps manage the organization's inventory and stock. Inventory Management has been defined as having the right inventory, of the right volume, at the right cost.

Question

At the bus station, there are six lines for arriving passengers, each staffed by a single worker. The arrival rate for passengers is 108 per
hour and each passenger takes (on average) 3.1 minutes for a worker to process. The coefficient of variation for arrival time is 1.5 and
the coefficient of varlation for service time is 11.
(Round your answer to three decimal places.)
On average, how many customers will be waiting in the queue?
passengers

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 10

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.

Similar questions

A supermarket has four girls ringing sales at the counters. If the service time for each customer is exponential with mean 4 minutes, and if people arrive in a Poisson fashion at the rate of 10 per hour, calculate i. The average number of customers in the system. ii. The average time a customer spends in the system. iii. The average queue length iv. The average waiting time for customers. v. The expected percentage of idle time for each girl vi. The probability that at least a girl is waiting for the customer.
On average, 100 customers arrive per hour at theGotham City Bank. The average service time for eachcustomer is one minute. Service times and interarrivaltimes are exponentially distributed. The manager wantsto ensure that no more than 1% of all customers willhave to wait in line for more than five minutes. If thebank follows the policy of having all customers join asingle line, how many tellers must the bank hire?
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
Patients arrive to a small hospital emergency room according to a Poisson process with an average rate of 1.5 per hour. Because service times for these patients vary considerably, the service times are accurately described by an exponential distribution. Suppose that the average service time is 26 minutes. If there is only a single doctor working at any point in time, find the following measures of service for this emergency room:a. The expected total time in the system.b. The expected time each customer has to wait.c. The expected number of patients waiting for service.d. If the emergency room has a triage nurse who gives priority to more serious conditions, explain qualitatively how that would change your results to parts a, b, and c. What additional information would one need to know to analyze a system like this?
At the Smalltown post office, patrons wait in a singleline for the first open window. An average of 100 patronsper hour enter the post office, and each window can servean average of 45 patrons per hour. The post office estimatesa cost of 10¢ for each minute a patron waits in line andbelieves that it costs $20 per hour to keep a window open.Interarrival times and service times are exponential.a To minimize the total expected hourly cost, howmany windows should be open?b If the post office’s goal is to ensure that at most 5%of all patrons will spend more than 5 minutes in line,how many windows should be open?