The traffic on the service road of a highway

Reference no: EM131130890

A truck driver is waiting to join the traffic on the service road of a highway. The truck driver blocks the service road for four seconds when he joins the traffic. Suppose that vehicles arrive according to a Poisson process and that six seconds elapse, on average, between two consecutive vehicles. Answer the following questions by assuming that the truck driver makes sure that he has enough time to perform his maneuver before merging into the traffic.

(a) What is the probability that the truck driver is able to join the traffic immediately on his arrival at the intersection with the service road?

(b) What is the mathematical expectation of the gap (in seconds) between the truck and the nearest vehicle when the truck driver merges into the traffic?

(c) Calculate the average number of vehicles that the truck driver must let go by before being able to merge into the traffic.

Reference no: EM131130890

Questions Cloud

What are the main ethical concerns for court personnel : Conduct library and Internet research to support your response. Explain your responses and source your ideas with in-text APA citations and corresponding reference list entries at the end

City buses arrive at a certain street corner : City buses arrive at a certain street corner, between 5 a.m. and 11 p.m., according to a Poisson process with rate λ = 4 per hour. Let T1 be the waiting time, in minutes, until the first bus (after 5 a.m.), and let M be the total number of buses be..

What do the following two quotes have in common : My wages are going up 5 percent a year. If only inflation weren t 5 percent a year, I would be rich.

What is the rate of return on this investment : What is the rate of return on this investment? Assuming the investor wants to earn at least 12 percent, is this investment an attractive one?

The traffic on the service road of a highway : A truck driver is waiting to join the traffic on the service road of a highway. The truck driver blocks the service road for four seconds when he joins the traffic.

Find terminal stock price using benchmark pe ratio : In practice, a common way to value a share of stock when a company pays dividends is to value the dividends over the next five years or so, then find the “terminal” stock price using a benchmark PE ratio. Suppose a company just paid a dividend of $1...

What is the difference between explicit and implicit cost : What is the difference between explicit and implicit cost? Explain your answers. How would we determine if a cost is a fixed cost or a variable cost?

Are you over benefited or underbenefited in the relationship : Are you over benefited or underbenefited in the relationship or do feel you are equals? - What behaviors do you use to maintain your relationship?

Specific activities organization can engage in to accomplish : Suppose firm XYZ has AR (Accounts Receivable) = 500, Sales = 3000, Inventory = 300, Cost of Goods Sold = 1200, and AP (Accounts Payable) = 100. How much cash does firm XYZ save if it reduces its Days Sales Outstanding by 10 days? What are specific ac..

User Account

All Pages