A certain highway with separate roadways

Reference no: EM131130689

At night, vehicles circulate on a certain highway with separate roadways according to a Poisson process with parameter λ = 2 per minute (in each direction). Due to an accident, traffic must be stopped in one direction. Suppose that 60% of the vehicles are cars, 30% are trucks, and 10% are semitrailers. Suppose also that the length of a car is equal to 5 m, that of a truck is equal to 10 m, and that of a semitrailer is equal to 20 m.

(a) From what moment is there a 10% probability that the length of the queue of stopped vehicles is greater than or equal to one kilometer?

(b) Give an exact formula for the distribution of the length of the queue of stopped vehicles after t minutes.

Indication, Neglect the distance between the stopped vehicles

Reference no: EM131130689

Questions Cloud

Opens new product line and requires initial outlay : A company is considering a 5-year project that opens a new product line and requires an initial outlay of $85,000. The assumed selling price is $97 per unit, and the variable cost is $63 per unit. Fixed costs not including depreciation are $20,000 pe..

How does acceptable risk affect injury reduction goals : The stated primary purpose of Z10 is to reduce the risk of occupational injuries, illnesses, and fatalities. As noted in the course text, zero risk is not likely to be achievable, so acceptable risk levels must be defined. What about a goal of zer..

Example of a different data collection method : Give one example of a different data collection method used in evidence based practice in Nursing. What variable was this method used to measure?

What should happen to the current level of taxes : Now suppose future spending increases are not inevitable and that, as a practical matter, you believe Congress will spend whatever revenue it collects. Would you still recommend tax smoothing?

A certain highway with separate roadways : At night, vehicles circulate on a certain highway with separate roadways according to a Poisson process with parameter λ = 2 per minute (in each direction).

What effect will this have on the housing market : As a reaction to problems in the subprime area, lenders are already tightening lending standards. What effect will this have on the housing market?

Significantly increase the flow of a certain river : During the rainy season, we estimate that showers, which significantly increase the flow of a certain river, occur according to a Poisson process with rate λ = 4 per day. Every shower, independently from the others, increases the river flow during..

What difference between avoiding a risk and accepting a risk : What are the differences between bottom-up and top-down estimating approaches? Under what conditions would you prefer one over the other?

Compare watson and arneson''s arguments : Compare Watson and Arneson's arguments. - Are they consistently applying consequentialist or deontological moral reasoning?

User Account

All Pages