Please provide detail steps as to how you solved the problem below. A server handles critical requests that come according to a Poisson process, on average once every hour. Suppose that at midnight the server will undergo a maintenance that will last for half an hour, and requests that arrive during this period will be lost. What is the probability that no requests will be lost? What is the expected number of requests that will be lost? Suppose that for two hours after the maintenance the server will be in a “warm-up” state and will not be able to process more than 2 requests total, and the rest will be lost. What is the probability that no requests will be lost from midnight till 2:30am?

Please provide detail steps as to how you solved the problem below. A server handles critical requests that come according to a Poisson process, on average once every hour. Suppose that at midnight the server will undergo a maintenance that will last for half an hour, and requests that arrive during this period will be lost. What is the probability that no requests will be lost? What is the expected number of requests that will be lost? Suppose that for two hours after the maintenance the server will be in a “warm-up” state and will not be able to process more than 2 requests total, and the rest will be lost. What is the probability that no requests will be lost from midnight till 2:30am?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Please don't copy
Jamuna future park has one parking counter. From previous experience, it is estimated that cars arrive according to Poisson distribution at a rate of 2 every 5 minutes and that there is enough space to accommodate a line of 3 cars. Other arriving cars can wait outside the space, if necessary. It takes 1.5 minutes on an average to serve a customer. However, the service time usually varies according to exponential distribution. Requirements: i. Determine the average time that the counter is free on an 8-hour working day. Determine the probability of having 5 cars in the queue. Determine the probability that a customer shall wait for more than 4 minutes in the queue. Determine the probability that an arriving car will have to wait outside the directed space. Now, Jamuna future park is planning to install automation servicing system that will reduce service time from 1.5 minutes to 1 minute, but increase the cost by TK. 30 per day. Should Jamuna future park introduce the automation…
Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 45 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 52 seconds. To help determine the amount of space needed for the line at the drive-up window, answer the following questions. a. What is the average waiting line length (in cars)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) b. What is the average number of cars in the system (both in line and at the window)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. What is the expected average time in the system, in minutes? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
We know that Jenny has a 70% chance to be active in 2020, and the yearly retention rate is 90% (i.e., the likelihood of being active in the next year, given that a customer is active in a particular year is 90%). What is th likelihood that Jenny will still be active in 2022 (choose the closest number)?
The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. What is the probability that there are no calls within a one-hour interval?
Customers arrive at a check-out counter in a supermarket in a Poisson fashion at a rate of 8 customers per hour. The supermarket has one cashier only. The check-out time is exponentially distributed with a mean of 3.204 minutes. Assume the queue discipline is first in first out (FIFO). Use Arena to simulate the system, run one replication for 10,000,000 minutes (10 million minutes), use minutes as the base time unit. Choose the nearest answer for the following. Note: No need to upload your Arena Model The server utilization Choose. + The average time in the queue; Choose. The probability that the server is idle Choose. The average number of cars in the queue; Choose. The average number of cars in the system Choose. The average time in system Choose.
It is known from past experience that in a certain plant there are on the average 4 incidents per month. Find the proba- bility that in a given year there will be less than 4 accidents. Assume Poisson distribution.
The average number of collisions in a week during the summer months at a particular intersection is 2. Assume that the requirements of the Poisson distribution are satisfied. What is the probability that there will be exactly one collision in a week?
Some previous studies have shown a relationship between emergency-room admissions per day and level of pollution on a given day. A small local hospital finds that the number of admissions to the emergency ward on a single day ordinarily (unless there is unusually high pollution) follows a Poisson distribution with mean = 2.0 admissions per day. Suppose each admitted person to the emergency ward stays there for exactly 1 day and is then discharged. The hospital is planning a new emergency-room facility. It wants enough beds in the emergency ward so that for at least 95% of normal-pollution days it will not need to turn anyone away. What is the smallest number of beds it should have to satisfy this criterion? Answer the previous question for a random day during the year.
Please solve very soon completely
A service company receives on average 4 service requests per day. The requests are received randomly according to Poisson process. The company has 2 service engineers and sends one engineer to attend each request. 1 An engineer needs an exponentially distributed service time with the mean of day(s). 2 The company's policy is to have maximum of 2 requests waiting in the queue If this number is reached, all incoming requests are rejected (sent to a competitor). Answer the following questions based on the information provide above: (a) Using the Kendall's notation, indicate what type of queueing system it is: (b) Compute the system state probabilities (provide at least 3 decimals): Po = P1= P2 = P3 = Pa = (c) Compute the expected total number of customer requests (waiting and served) in the system. ELL] = (d) Compute the expected number of accepted requests. Aaccepted = (e) Compute the expected total processing time (waiting + being served) for the accepted requests. E[Time] =
Top Cutz International Barbershop is a popular haircutting and styling salon . Four barbers work full-time and spend an average of 15 minutes on each customer. Customers arrive all day long at an average rate of 12 per hour. When they enter, they take a number to wait for the first available barber. Arrivals tend to follow the Poisson distribution, and service times are exponentially distributed. REQUIRED (c) What is the average time spent in the shop?