Reference no: EM131130509
We consider a queueing system with two servers. The customers arrive according to a Poisson process with rate λ = 1, and the system capacity is equal to four customers. The service times are independent random variables having an exponential distribution. Each server is able to serve two customers at a time. If a server attends to only one customer, he does so at rate 𝜇 = 2, whereas the service rate is equal to 1 when two customers are served at the same time.
Indication, If two customers are served together, then they will leave the system at the same time. Moreover, if there are two customers in the system, then one of the servers may be free.
(a) Write the balance equations of the system.
(b) Let T* be the total time that a given customer entering the system will spend in it.
(i) Calculate, in terms of the limiting probabilities, and supposing that no customers arrive during the service period of the customer in question, the distribution function of T*,
(ii) Under the same assumption as in (i), does the random variable T* have the memoryless property? Justify.
|
Will transportation affect other transportation business
: "Will transportation affect other transportation business" and then make a outline for a presentation about this topic.
|
|
Why the company does not pay bribes when its foreign compet
: Is there a conflict between maximizing shareholder wealth and never paying bribes when doing business abroad? If so, how might you explain the firm’s position to shareholders asking why the company does not pay bribes when its foreign competitors in ..
|
|
The accrual of interest and the discount amortization
: The payment of interest and the discount amortization on July 1, 2010, assuming that interest was not accrued on June 30.
|
|
What is the function of cholesterol in plasma membranes
: What is the function of cholesterol in plasma membranes? Which of the following is an example of an aliphatic hydrocarbon? What examples describe the second law of thermodynamics? Select all that apply.
|
|
Consider a queueing system with two servers
: Indication, If two customers are served together, then they will leave the system at the same time. Moreover, if there are two customers in the system, then one of the servers may be free.
|
|
Why an apparently innocent speech would create such reaction
: Some commentators attacked him as not being sufficiently vigilant against inflation. Use the idea of credibility to explain why an apparently innocent speech would create such a reaction. (Related to Application 2 on page 339.)
|
|
An arbitrary customer goes to server
: Customers arrive according to a Poisson process with rate λ = 5 per hour in a system with two servers. The probability that an arbitrary customer goes to server no. 1 (respectively, no. 2) is equal to 3/4 (resp., 1/4).
|
|
Sports-general, types of fans or influence on culture
: Sports-general, types of fans, or influence on culture and genres of movies, television shows, or video games
|
|
Why might the company refuse to split its shares to make
: The share price of BRKA has never been spilt. Why might the company refuse to split its shares to make them more affordable to average investors?
|