For the M/M/N/o system, the probability that an arrival will find all servers busy and will be forcedto wait in queue is an important measure of performance of the M/M/N/∞ system. This probabilityis given byPQN!(1 – p/N)|and is known as the Erlang C formula. Please derive the equation. What is the expected number ofcustomers waiting in the queue (not in service)?

Given information: PQ=P0·ρNN!·1-ρN

Answered: For the M/M/N/∞ system, the probability…

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

Show work for every step. Two types of customers (Preferred and Regular) call a service center. Preferred customers call with rate 3 per hour, and Regular customers call with rate 5 per hour. The interarrival times of the calls for each customer type are exponentially distributed. If the call center opens at 8:00 AM, what is the probability that the first call (regardless of customers type who calls) is received before 8:15 AM?
You are allowed to take a certain test three times, and your final score will be the maximum of the test scores. Your score in test k, where k = 1, 2, 3, takes one of the values from k to 10 with equal probability 1/(11 − k), independently of the scores in other tests. What is the PMF of the final score?
A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?
Suppose you are fitting a survival model and the outcome of interest is time to the diagnosis of cancer (T). A subject entered the study at t=0 and the diagnosis of cancer did not occur by the end of the study period, what kind of event is that? It is an interval-censored observation because an event happened between time of entry and the exit. It is a right-censored observation because no event will be observed during the study period. It is a left-censored observation where the event of interest happened before the study starts. It is a right-censored observation because the event has already occurred.
You are planning to go fishing with two friends. The time (in hours) before you catch a fish is exponentially distributed with parameter 6. How long do you need to arrange for the fishing so that there is a 95% probability that everyone catches at least one fish? [Assume that the events that each person catches a fish are independent.]
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS