What is the probability that the system is empty

Reference no: EM131930292

Question: An agent in a train station sells tickets and provides information to travelers. An average of two travelers approach the agent for assistance each minute. Their arrival is distributed according to a Poisson distribution. The agent is able to meet the travelers' needs in approximately 20 seconds, distributed exponentially.

(a) What is the probability that there are more than two travelers in the system? More than three? More than four?

(b) What is the probability that the system is empty?

(d) What is the expected number of travelers in the queue?

(e) What is the average number in the system?

(f) If a second agent is added (who works at the same pace as the first), how will the operating characteristics computed in parts (b), (c), (d), and (e) change? Assume that travelers wait in a single line and go to the first available agent.

Reference no: EM131930292

Questions Cloud

Find average number of patients waiting for nurse to arrive : County General Hospital's cardiac care unit (CCU) has seven beds, which are virtually always occupied by patients who have just undergone heart surgery.

What is the average time spent in the shop : Sal's International Barbershop is a popular haircutting and styling salon near the campus of the University of New Orleans.

What average number of callers waiting to make reservation : A restaurant's reservation agent takes reservations for dinner by telephone. If he is already on the phone when a patron calls to make a reservation.

What is the average time per truck in the system : The wheat harvesting season in the U.S. Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a twoweek.

What is the probability that the system is empty : An agent in a train station sells tickets and provides information to travelers. An average of two travelers approach the agent for assistance each minute.

How fast does the computer have to process jobs : A computer processes jobs on a first-come, first served basis in a time-sharing environment. The jobs have Poisson arrival rates.

What percentage of the time is the ticket window busy : Find the average number of patrons waiting in line to purchase tickets. What percentage of the time is the ticket window busy?

Find the utilization rate of the service system : Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of l = 3 per day (approximately Poisson in nature)

Find probability that no cars are in the system : From historical data, Harry's Car Wash estimates that dirty cars arrive at a rate of 10 per hour all day Saturday. With a crew working the wash line.

User Account

All Pages