Suppose vehicles arrive at a single toll booth according to a Poisson process with a mean...
Suppose vehicles arrive at a single toll booth according to a Poisson process with a mean arrival rate of 8.4 veh/min. Their service times are exponentially distributed. The mean processing rate is 10 veh/min.
a. What is the value of the utilization ratio?
b. What is the average length of the queue?
c. What is the average waiting time in the queue?
d. What is the average time spent in the system?
Homework Answers
The solution is based on the queuing theoy.
Given data:-
mean arrival rate (
)=
8.4veh./min.
mean service rate (
)=10veh./min.
Solutions:-
(a)utilization rate :-
formula for utili0ation rate =
i.e. u.r.=8.4/10 =.0.84
(b)avg. length of queue(Lq):-
formula for length of queue in terms of vehicles=
i.e. Lq=8.42/10(10-8.4)=4.41veh.
(c)avg. waiting time in the queue(Wq) :-
Formula =
Lq=8.4/10(10-8.4)=0.52 min.=31.5 seconds
(d) avg. time spent in the system(Ws) :-
Formula=
Ws=1/1.6=0.625 minutes=37.5 seconds
Add Answer to:
Suppose vehicles arrive at a single toll booth according to a
Poisson process with a mean...
QUESTION 26 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive...
QUESTION 26 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 900 veh/h, and at the booths, drivers take an average of 12 seconds to pay their tolls. Both the arrival and departure headways can be assumed to be exponentially distributed How would the average queue length change if a fifth toll booth were opened? a. The average queue length is reduced by 1.17 vehicles D.The average...
At 9 am, vehicles arrive at a toll booth facility at the rate of 8 vehicles/min....
At 9 am, vehicles arrive at a toll booth facility at the rate of 8 vehicles/min. Initially, the toll booth is closed from 9:00 am until 9:15 am. Then it opens from 9:15 with a service rate of 10 vehicles/min. Assuming D/D/1 queuing, determine: (1) At what time queue is disappears? (2) What is the total delay? (3) What is the maximum Queue length? (4) What is the queue length at time t=30? (5) What is maximum delay? (6) What...
I need matlab code for solving this problem Clients arrive to a certain bank according to a Poisson Process. There is a...
I need matlab code for solving this problem
Clients arrive to a certain bank according to a Poisson Process. There is a single bank teller in the bank and serving to the clients. In that MIM/1 queieing system; clients arrive with A rate 8 clients per minute. The bank teller serves them with rate u 10 clients per minute. Simulate this queing system for 10, 100, 500, 1000 and 2000 clients. Find the mean waiting time in the queue and...
answer the question number 3 as stated in the picture 2. Vehicles arrive at an entrance...
answer the question number 3 as stated in the picture
2. Vehicles arrive at an entrance to a recreational park. There is a single gate at which all vehicles must stop), where a park attendant distributes a free brochure. The park opens at 08:00 am, at which time vehicles begin to arrive at a rate of 480 veh/hr. after 20 minutes the arrival flow rate declines at 120 veh/hr, and it continues at that level for the remainder of the...
A toll booth on a turnpike is open from 8:00 AM until midnight. Vehicles start arriving...
A toll booth on a turnpike is open from 8:00 AM until midnight. Vehicles start arriving at 7:45 AM at a uniform rate of 6 veh/min. At 8:15 AM the rate drops to 2 veh/min. If vehicles are processed at a uniform rate of 6 veh/min, determine when the queue will end, the total delay, the maximum queue length, and the longest vehicle delay
Question: 2. Customers arrive to a single-server queue according to a Poisson process with mean rate...
Question: 2. Customers arrive to a single-server queue according to a Poisson process with mean rate 10 per hour. Customer service times have an exponential distribution with a mean of 5 minutes. Find: a. average number of customers in queue b. average number of customers in queue and being served Answer: 2. (a) 25/6 (b) 5.0 Professor gave answer, but I would like to see the steps on how to get the answer.
7.1. Cars arrive to a toll booth 24 hours per day according to a Poisson process...
7.1. Cars arrive to a toll booth 24 hours per day according to a Poisson process with a mean rate of 15 per hour. (a) What is the expected number of cars that will arrive to the booth between 1:00 p.m. and 1:30 p.m.? (b) What is the expected length of time between two consecutively arriving cars! (c) It is now 1:12 p.m. and a car has just arrived. What is the expected number of cars that will arrive between...
the determinstic rate of arrival of vehicles at a parking garage having a single toll booth...
the determinstic rate of arrival of vehicles at a parking garage having a single toll booth is A (t) =6.1-0.22t where A(t) is in vehicle per minute and t is in minute after the parking lot has opened.what should be the minimium constant departure rate needed after the opening of the parking lot to ensure that the queue length doesnt exceed 10 vehivles
1. Visitors arrive at the ticket booth at the Metropolitan Museum at the rate of 5...
1. Visitors arrive at the ticket booth at the Metropolitan Museum at the rate of 5 every 6 minutes. The average service time is 1 minute. The arrival rate is assumed to follow Poisson distribution and service times are exponentially distributed. e) What is the probability that there are no visitors at the window? f) What percentage of the time is the ticketing clerk busy? g) What is the probability that there are exactly 2 visitors in the ticketing area?...
An average of 90 cars per hour arrive at a single-server toll booth. The average service...
An average of 90 cars per hour arrive at a single-server toll booth. The average service time for each customer is a half minute, and both interarrival times and service times are exponential. For each of the following questions, show your work, including the formula that you are using. 1) On average, how many cars per hour will be served by the server
QUESTION 26 At an entrance to a toll bridge, four toll booths are open. Vehicles arrive at the bridge at an average rate of 900 veh/h, and at the booths, drivers take an average of 12 seconds to pay their tolls. Both the arrival and departure headways can be assumed to be exponentially distributed How would the average queue length change if a fifth toll booth were opened? a. The average queue length is reduced by 1.17 vehicles D.The average...
I need matlab code for solving this problem
Clients arrive to a certain bank according to a Poisson Process. There is a single bank teller in the bank and serving to the clients. In that MIM/1 queieing system; clients arrive with A rate 8 clients per minute. The bank teller serves them with rate u 10 clients per minute. Simulate this queing system for 10, 100, 500, 1000 and 2000 clients. Find the mean waiting time in the queue and...
answer the question number 3 as stated in the picture
2. Vehicles arrive at an entrance to a recreational park. There is a single gate at which all vehicles must stop), where a park attendant distributes a free brochure. The park opens at 08:00 am, at which time vehicles begin to arrive at a rate of 480 veh/hr. after 20 minutes the arrival flow rate declines at 120 veh/hr, and it continues at that level for the remainder of the...
7.1. Cars arrive to a toll booth 24 hours per day according to a Poisson process with a mean rate of 15 per hour. (a) What is the expected number of cars that will arrive to the booth between 1:00 p.m. and 1:30 p.m.? (b) What is the expected length of time between two consecutively arriving cars! (c) It is now 1:12 p.m. and a car has just arrived. What is the expected number of cars that will arrive between...
1. Visitors arrive at the ticket booth at the Metropolitan Museum at the rate of 5 every 6 minutes. The average service time is 1 minute. The arrival rate is assumed to follow Poisson distribution and service times are exponentially distributed. e) What is the probability that there are no visitors at the window? f) What percentage of the time is the ticketing clerk busy? g) What is the probability that there are exactly 2 visitors in the ticketing area?...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago