M/G/C Queue Theory: Proving Results & Finding Sources

In summary, the speaker initially found some statements to be amazing and is now trying to find evidence for them. However, they mention that there are very few sources that discuss M/G/K or M/G/infinite queues, with most sources focusing on M/G/1 queues. The speaker then asks for mathematical demonstrations and proof of the statements, expressing frustration at the lack of support from the forum members. They acknowledge the abilities of the members and question why they are not willing to help.
  • #1
mertcan
345
6
upload_2016-12-8_18-40-28.png

hi, initially when I saw these statements , I got really amazed, and now I endeavor to find the proofs of these statements, bu I would like assure you of the fact that there are very very very few sources which evaluate M/G/K or M/G/infinite queue, mostly sources prefer to handle the subject of M/G/1 queue. Therefore, I am really asking you: Could you prove how these statements are possible to me using some mathematical demonstrations? Is there a proof of results above?
 
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  • #2
@Ray Vickson and other respectable forum members, Is there a incomprehensible, complex situation in my question? Why can't I get any support from you? I am absolutely aware that most of you are very capable of overcoming my question easily. Why don't you prefer to help me?
 

FAQ: M/G/C Queue Theory: Proving Results & Finding Sources

What is M/G/C Queue Theory?

M/G/C Queue Theory is a mathematical model used to study queuing systems, specifically those with multiple servers, general service times, and a finite capacity for waiting customers. It is a branch of queuing theory, which is a field of study that analyzes waiting lines and the behavior of systems with limited resources.

What are the main results of M/G/C Queue Theory?

The main results of M/G/C Queue Theory include the steady-state distribution of the number of customers in the system, the average waiting time for customers, and the probability of a customer being rejected due to the system being at full capacity. These results provide valuable insights into the performance of queuing systems and can be used to optimize their efficiency.

How are these results proven in M/G/C Queue Theory?

The results of M/G/C Queue Theory are proven using mathematical techniques such as Markov chain analysis and stochastic processes. These methods involve modeling the behavior of the queuing system and using probability theory to calculate the desired results. Computer simulations can also be used to validate the theoretical results.

What are some practical applications of M/G/C Queue Theory?

M/G/C Queue Theory has many practical applications in fields such as telecommunications, transportation, healthcare, and customer service. It can be used to analyze and optimize the performance of call centers, transportation systems, hospital emergency departments, and other systems that involve waiting lines and limited resources.

Where can I find more information about M/G/C Queue Theory?

There are many sources of information about M/G/C Queue Theory, including textbooks, research papers, and online resources. Some recommended sources include the book "Queueing Systems: Volume 2: Computer Applications" by Leonard Kleinrock, the research journal "Queueing Systems" published by Springer, and the website of the Institute for Operations Research and the Management Sciences (INFORMS).

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