Waiting Line Questions Render A waiting line meeting the M/M/1 assumptions has a
ID: 365748 • Letter: W
Question
Waiting Line Questions Render
A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour. What is the probability that the waiting line is empty?
A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour. What is the average time a unit spends in the system and the average time a unit spends waiting?
A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour. What is the average time a unit spends in the system and the average time a unit spends waiting?
A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour. What is the probability that the waiting line is empty?
A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of l = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of m = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a. What is the utilization rate for this service system?
b. What is the average time before the facility can return a breakdown to service?
c. How much of that time is spent waiting for service?
d. How many vehicles are likely to be in the system at any one time?
A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of l = 7 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of m = 11 vehicles per day with a repair time distribution that approximates an exponential distribution.
a. What is the utilization rate for this service system?
b. What is the average time before the facility can return a breakdown to service?
c. How much of that time is spent waiting for service?
d. How many vehicles are likely to be waiting for service at any one time?
A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of l = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of m = 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). What is the expected cost of this system?
A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of l = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of m = 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). Which is cheaper, the existing system with one service crew, or a revised system with two service crews?
A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic is uniformly busy with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.
a. What is the probability that the clinic is empty (except for the dentist)?
b. What percentage of the time is the dentist busy?
c. What is the average number of patients in the waiting room?
d. What is the average time a patient spends in the office (wait plus service)?
e. What is the average time a patient waits for service?
At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machines to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machines is at the rate of 140 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.
a. What is the utilization rate of the system?
b. What is the average number of packages waiting to be sorted?
c. What is the average number of packages in the sorting system?
d. How long must the average package wait until it gets sorted?
(FPS) Use the following to answer questions 68-71:
A bank of 5 machines requires regular periodic service. Machine running time and service time are both exponential. Machines run for an average of 44 minutes between service requirements, and service time averages 6 minutes per machine.
68. What is the probability that a machine will have to wait for service with two operators?
A) .654
B) .090
C) .076
D) .910
E) .016
69. What is the average machine downtime with two operators?
A) 1.71 minutes
B) 3.46 minutes
C) 6.25 minutes
D) 7.71 minutes
E) 9.46 minutes
70. What is the average number of machines down with one operator?
A) 1.49
B) 3.35
C) 4.40
D) 6.65
E) 8.51
71. If operators cost $15 per hour in wages and fringe benefits and machine downtime costs $75 per hour in lost production, what is the optimal number of operators for this bank of machines?
A) 1
B) 2
C) 3
D) 4
E) 5
Explanation / Answer
Answer 1:
Probability = 1 - / , Here is arrival rate and is service rate
= 1 - 4/12
= 8/12
= 0.667.
Answer 2:
Average time a unit spends in the system (Ws) = 1 / (- ), Here is arrival rate and is service rate
= 1 / (12 – 4)
= 1/8 or 0.125;
Average time a unit spends waiting (Wq) = / ( *(-)), Here is arrival rate and is service rate
= 4 / (12*8)
=4/96
= 1/24 or 0.0417.
Answer 3:
Average time a unit spends in the system (Ws) = 1 / (- ), Here is arrival rate and is service rate
=1/ (12-10)
=1/2
=0.50
Average time a unit spends waiting (Wq) = / ( *(-)), Here is arrival rate and is service rate
= 10/ (12*10)
=10/120
=1/12
=0.0833
Answer4:
Probability = 1 - /
= 1 - 10/12
= 2/12 or 0.1666
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