1) A toll plaza has 5 booths, with each booth capable of servicing 50 cars per...

Question

Question

1) A toll plaza has 5 booths, with each booth capable of servicing 50 cars per hour. Cars arrive at the plaza at the rate of 225 cars per hour.

Make the standard assumptions of a Poisson distribution for arrivals, and an Exponential distribution for service times, and calculate the following:

a) What is the probability of zero cars in the toll plaza?

b) What is the average length (in cars) of the (total) queue?

Answer 1

Answer #1

Answer 2

Similar Homework Help Questions

Cars arrive at a toll booth at average rate of 60 per hour. The standard deviation...

Cars arrive at a toll booth at average rate of 60 per hour. The standard deviation of the time between arrivals is 0.8 minutes. What is the coefficient of variation of the interarrival times of cars?
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
The average number of cars per hour arriving at a toll booth is 57 while the...

The average number of cars per hour arriving at a toll booth is 57 while the standard deviation is 15. (a) Use Markov’s inequality to find an upper bound on the probability of having more than 200 cars arrive in an hour. (b) Use Chebyshev’s inequality to find an upper bound on the probability of having more than 200 cars arrive in an hour

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...
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?
Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate...

Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate of 51 per minute during the 5:00 to 6:00 p.m. hour (assume Exponential distribution). If an auto has just arrived, what is the probability that the next auto will arrive within 3 seconds? 1.00 0 0.284 0.922

Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate...

Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate of 51 per minute during the 5:00 to 6:00 p.m. hour (assume Exponential distribution). If an auto has just arrived, what is the probability that the next auto will arrive after 2 seconds? 0.000 1.000 0.183 0.632
Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate...

Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate of 51 per minute during the 5:00 to 6:00 p.m. hour (assume Exponential distribution). If an auto has just arrived, what is the probability that the next auto will arrive in the next 3 to 10 seconds? 0.078 0.024 1.000 0.000
Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate...

Automobiles arrive at a toll plaza located at the entrance to a bridge at a rate of 51 per minute during the 5:00 to 6:00 p.m. hour (assume Exponential distribution). If an auto has just arrived, what is the probability: a) That the next auto will arrive within 3 seconds? b) That the next auto will arrive in the next 3 to 10 seconds? c) That the next auto will arrive after 2 seconds?

During off hours, cars arrive at a tollbooth on the East-West toll road at an average...

During off hours, cars arrive at a tollbooth on the East-West toll road at an average rate of 0.6 cars per minute. The arrivals are distributed according to a Poisson distribution. What is the probability that during the next minute, three cars will arrive? What is the probability that during the next five minutes, three cars will arrive? What is the probability that during the next five minutes, three or less cars will arrive? IS THERE A WAY TO SHOW...