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?

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?

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

See similar textbooks

Similar questions

A grocery store has three open checkout counters. There is a single queue leading up to these three counters. On average, 45 shoppers arrive at this queue. The coefficient of variation of the interarrival time is equal to 1. The average service capacity of each of the three servers is 18 customers per hour, and the coefficient of variation of service time distribution for each server is 3. (a) (3 points) What is the percentage decrease in capacity utilization when one more checkout lane is added to the system? (b) (7 points) On average, how many customers are waiting in the queue?
Podunk University Operations Research Departmenthas two phone lines. An average of 30 people per hour tryto call the OR Department, and the average length of aphone call is 1 minute. If a person attempts to call whenboth lines are busy, he or she hangs up and is lost to thesystem. Assume that the time between people attempting tocall and service times is exponential.a What fraction of the time will both lines be free?What fraction of the time will both lines be busy? Whatfraction of the time will exactly one line be free?b On the average, how many lines will be busy?c On the average, how many callers will hang up eachhour?
The Seaboard Shipping Company has a warehouse terminalin Spartanburg, South Carolina. The capacity of each terminal dock is three trucks. As trucks enter the terminal, the drivers receive numbers, and when one of the three dock spacesbecomes available, the truck with the lowest number entersthe vacant dock. Truck arrivals are Poisson distributed, andthe unloading and loading times (service times) are exponentially distributed. The average arrival rate at the terminalis five trucks per hour, and the average service rate per dockis two trucks per hour (30 minutes per truck).a. Compute L, Lq, W, and Wq.b. The management of the shipping company is considering adding extra employees and equipment to improvethe average service time per terminal dock to 25 minutes per truck. It would cost the company $18,000 peryear to achieve this improved service. Managementestimates that it will increase its profit by $750 per yearfor each minute it is able to reduce a truck’s waitingtime. Determine…
1. A multiple channel queuing system with a Poisson arrival rate, and an exponential service time distribution has an average arrival rate of 2.5 customers per hour and an average service time of eighty minutes per customer. A queuing system is described as unstable or overloaded if its utilization rate is greater than, or equal to one. For the system just described, what is the minimum number of servers required to retain stability i.e., to avoid overloading? A. 2 B. 3 C. 1 D. 4
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places.P0 = fill in the blank 1 What is the probability that one customer is receiving a haircut and no one is waiting? If required, round your answer to four decimal places.P1 = fill in the blank 2 What is the probability that one customer is receiving a haircut and one customer is waiting? If required, round your answer to four decimal places.P2 = fill in the blank 3
Assume that an average of 125 packets per second ofinformation arrive to a router and that it takes an average of.002 second to process each packet. Assuming exponentialinterarrival and service times, answer the followingquestions.a What is the average number of packets waiting forentry into the router?b What is the probability that 10 or more packets arepresent?
A small bank is trying to determine how many tellers toemploy. The total cost of employing a teller is $100 perday, and a teller can serve an average of 60 customersper day. On average, 50 customers arrive per day at thebank, and both service times and interarrival times areexponentially distributed. If the delay cost per customerday is $100, how many tellers should the bank hire?
A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customersper hour arrive at the facility (interarrival times are assumed to be exponential). The system capacity isthree customers: two waiting and one being served.a. On average, how many potential customers enter the system each hour?b. What is the probability that the server is busy at atypical point in time?