Question: A computer consists of three processors. Their main task is to execute jobs from users. These jobs arrive according to a Poisson process with rate

A computer consists of three processors. Their main task is to execute jobs from users.

These jobs arrive according to a Poisson process with rate 15 jobs per minute. The execution time is exponentially distributed with mean 10 seconds. When a processor completes a job and there are no other jobs waiting to be executed, the processor starts to execute maintenance jobs. These jobs are always available and they take an exponential time with mean 5 seconds. But as soon as a job from a user arrives, the processor interrupts the execution of the maintenance job and starts to execute the new job. The execution of the maintenance job will be resumed later (at the point where it was interrupted).

(i) What is the mean number of processors busy with executing jobs from users?

(ii) How many maintenance jobs are on average completed per minute?

(iii) What is the probability that a job from a user has to wait?

(iv) Determine the mean waiting time of a job from a user.

Step by Step Solution

★★★★★

3.58 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

To solve this problem well need to model the system using queueing theory Lets address each part stepbystep i Mean number of processors busy with exec... View full answer

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!

A computer consists of a processor and an I/O device D connected to main memory M via a shared bus with a data bus width of one word. The processor can execute a maximum of 106 instructions per...

A computer consists of a CPU and an I/O device D connected to main memory Mvia a shared bus with a data bus width of one word. The CPU can execute a maximum of 106 instructions per second. An average...

Cabs pass your workplace according to a Poisson process with a mean of five cabs per hour. (a) Determine the mean and standard deviation of the number of cabs per 10-hour day. (b) Approximate the...

A computer consists of three processors. Their main task is to execute jobs from users. These jobs arrive according to a Poisson process with rate 15 jobs per minute. The execution time is...

Provide a summary technical report with your own words about Pipelined Execution which is also named as Instruction Level Parallelism, addressing mainly the following areas: 1. What is Pipelined...

Provide a summary technical report with about Pipelined Execution which is also named as Instruction Level Parallelism, addressing mainly the following areas: 1. What is Pipelined Execution and its...

Portray in words what transforms you would have to make to your execution to some degree (a) to accomplish this and remark on the benefits and detriments of this thought.You are approached to compose...

can i get a solution to this question please. Value: Document (include your file name) 15% of final grade How to complete: 1. Read the following Anniversary Party scheduling problem: As the project...

answer the following questions: What are your moral obligations as professionals to prevent such things from happening? What guidance do the professional codes provide (cite specific code sections in...

Discuss how regional and local tax strategy regarding property, value-added, inventory and income taxes can influence supply chain design.

To be done with Excel Solver . The mayor of Gatorville has decided to completely revamp thecitys fire services. Towards this end, the mayor has dividedGatorville into seven population areas and...

Solve the system of equations by using the addition method. 0 . 6 x 0 . 1 y = 0 . 3 3 x - 0 . 4 y = 0 . 6 { 1 3 , 1 } { ( 1 , 1 ) } { ( 0 , 3 ) } { ( 1 , - 2 4 ) }

Using the information in Exercise 5, prepare journal entries to record the transactions assuming a periodic inventory system. In Exercise 5 Feb. 1 Sold merchandise with a cost of $1,500 for $2,100;...

Why might a company be interested in investing in an operation in a foreign country (foreign direct investment)?

Desiree Clark is a licensed CPA. During the fi rst month of operations of her business, the following events and transactions occurred. May 1 Clark invested $20,000 cash in her business. 2 Hired a...

Journalize each of the following transactions assuming a perpetual inventory system. Jan. 5 Sold merchandise to a customer for $6,800; terms 1 /10, n/30 (cost of sales $4,080). 7 Made a cash sale of...

Acker Inc. bought 40% of Howell Co. on January 1, 2010 for $576,000. The equity method of accounting was used. The book value and fair value of the net assets of Howell on that date were $1,440,000....

The market for hot dogs begins at equilibrium. Then most of the hamburger vendors decide to sell hot dogs instead. This causes hamburger prices to increase and more hot dog vendors to enter the...

Consider a closed system in which 4 terminals submit jobs to a computer system. Each terminal submits jobs according to a Poisson process with a rate = 1 job every 2 seconds. Once a terminal submits...

Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...

This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What are these trees called? [1 mark] (ii) If one were building a grammar for English...

answer all questions as instructed below. make sure you have attended all questions .Comparative Architectures (a) Describe the organisation of a two-level branch predictor that makes use of a global...

COST ACCOUNTING. QUESTION 3 Mercer Asbestos Removal Company removes potentially toxic asbestos insulation and related products from buildings. There has been a long-simmering dispute between the...

Tina is a manager in the Business Advisory and Assurance Services division of a national public accounting firm. She has been given the job of managing the audit of Simply Steam, Co., which provides...