(Sennott, 1989a) Consider an infinite-horizon countable-state version of the service rate control…

(Sennott, 1989a) Consider an infinite-horizon countable-state version of the service rate control model of Sec. 3.7.2, in which the service rate distribution is Bernoulli with probability pb, where b is chosen from a finite set E and p+= maXbeB pb < 1 and p-= minbeB pb > 0. This means that the probability of a service completion in a single time slot equals pb when action 6 is chosen. The cost of serving at rate p6 for one period equals ~(6). There is no cost associated with changing the service rate. The revenue R = 0 and the holding cost h(s) is linear in s. The objective is to determine a service rate policy which minimizes the long-run average expected cost.

a. Give the optimality equations for the discounted model.

b. Using Theorem 8.10.7, show that, if the second moment of the arrival distribution is finite and the mean arrival rate p is less than p&#39;, there exists a lim inf average optimal stationary policy.

c. Show that (8.10.9) holds with equality if, in addition, p

d. Provide conditions for the existence of a stationary lim inf average optimal policy and for the optimality equation to hold under the assumption that h(s) is quadratic in s.

e. Determine the structure of an optimal policy under the linear holding cost assumption.

Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
The price is based on these factors:
Academic level
Number of pages
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
error: Content is protected !!