Question: Need help with this urgently 3. Consider a single-server queue with Poisson rate 2 arrivals and Exponential rate u > > service times, but make

Need help with this urgently

3. Consider a single-server queue with Poisson rate 2 arrivals and Exponential rate u > > service times, but make the following modification: Fix some a E (1 /u, 1). When a service time is complete, with probability 1 - a the customer rejoins the end of the queue instead of leaving the system as usual. (a) By relating the modified queue to a certain M/M/1 queue, find the stationary distribution for the number of customers in the system. [2] (b) Using Little's formula, L = AW, find the long run average time spent in the queue until being served for the first time. [2]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Section 2 1) Machines in a factory break down at an exponential rate of six per hour. There is a single repairman who fixes machines in 10 minutes. Find the average waiting time and average queue...

3 Answer Sheet Due by midnight December 3rd 2015. Copy and paste the part of this answer sheet below the dotted into a Course Message titled Assignment 3 Answer Sheet. Enter the letter of the best...

Queuing theory question,thanks Exercise 3.1. Amy and Bill simultaneously write a bid on a piece of paper. The bid can only be either $2 or $3. A referee then looks at the bids, announces the amount...

1.Consider a single-server queue with Poisson arrivals and exponential service times having the following variation: Whenever a service is completed a departure occurs only with probability . With...

Section 1 : Queuing Theory Question 1: Travelers arrive at an airline smart check-in with a mean rate of 50 travelers per hour. Based on the FCFS service discipline, a traveler is served every 1...

tackle the following with a thorough explanation...... 1 Short Answer Questions 1. The price eluticity of demand for gasoline is -2%%. If the government wants to reduce gasoline consumption by 20%%...

Three Hills Power Company provides power to a large city. The company is concerned about generator failures because it incurs two added costs when one fails. When a generator breaks down, Three Hills...

Computer Systems Modelling Consider a birth death model with birth rates n in states n = 0, 1, . . . and death rates n in states n = 1, 2, . . .. (a) State the detailed balance conditions for the...

Please answer questions 9-15 as it is a part of the same problem. If you are unable to answer then please don't attempt. I will give a thumbs up to whomever answers! 13.5. A company has a central...

The overall theme or concept had three parts that are synergetic with each other diversity, ethics, and social responsibility. These three principles of the modern company are essential for having a...

Explain two ways that can be used to monitor level of physical exertion.

Yesterday, Galaxy Corp. released its annual report on the company's website. While reading the report for her boss, Mia came across several terms about which she was unsure. She leaned around the...

Describe in brief email marketing analytics and how it is done. What platforms work best for such marketing?

5. Give examples of binary thinking.

2. In this chapter, the reader should reflect on the following concepts: Social facts, concrete fallacy, constructs, overestimation error.

1. Explain the following statements: a) Objective reality is always subjectively interpreted. b) What we know depends on whom we got to know it from.