A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution. How much of that time is spent waiting for service?

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution. How much of that time is spent waiting for service?

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 26P

See similar textbooks

Similar questions

A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 11 customers per hour and an average service rate of 14 customers per hour. The average length of time customers will spend in the system is: a. 15.71 minutes b. 20 minutes c. 0.2619 minutes d. 0.3333 minutes
At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average time that a vehicle must wait to get through the system? (Round your answer to 2 decimal places.) c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)
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
A drive-through at a Fast Food serves 424 customers over a 10-hour day. On average, a customer spends 3 minutes waiting in line, 7 minutes placing the order, and 4 minutes completing the order before leaving the drive-through. How many customers on average are "in" the drive-through (i.e., from the time they enter to the time they exit the drive-through) on a typical day? (Specify your answer in two decimal points)
Trucks using a single-server loading dock have a mean arrival rate of 14 per day. The loading/unloading rate is 19 per day. What is the probability that the truck dock will be idle? What is the average number of trucks waiting for service? What is the average time a truck waits for the loading or unloading service? What is the probability that a new arrival will have to wait? What is the probability that more than three trucks are waiting for service?
A graphics reproduction firm has four units of equipment that are automatic but occasionally become inoperative because of the need for supplies, maintenance, or repair. Each unit requires service roughly twice each hour, or, more precisely, each unit of equipment runs an average of 30 minutes before needing service. Service times vary widely, ranging from a simple service (such as pressing a restart switch or repositioning paper) to more involved equipment disassembly. The average service time, however, is five minutes. Equipment downtime results in a loss of $20 per hour. The one equipment attendant is paid $6 per hour.Using finite queuing analysis, answer the following questions: a. What is the average number of units in line? b. What is the average number of units still in operation? c. What is the average number of units being serviced?d. The fi- rm is considering adding another attendant at the same $6 rate. Should the firm do it?
At a border inspection station, vehicles arrive at the rate of 10 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 15 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? (Round your answer to 2 decimal places.) b. What is the average total time it takes for a vehicle to get through the system? (Round your answer to 2 decimal places.) c. What is the utilization of the inspector? (Round your answer to 1 decimal place.) d. What is the probability that when you arrive there will be three or more vehicles ahead of you? (Round your answer to 1 decimal place.)