Statistics Queue problem: M/M/2

In summary, the problem at hand is a Queue type problem that is M/M/2. The given information includes λ=11.98, μ=7 and s=2. The desired values to solve for are ∏0, Lq, L, and W. The given answers are p=.8557, π0=.2826, Lq=0.13527, L=1.8467, W=0.1541. The writer is seeking help with the formulas to use in solving this problem and is expected to show their work.
  • #1
caliboy
15
0

Homework Statement


OK I am dealing with a Queue type problem that is M/M/2. I have already solved most of the problem but I can not figure out how to solve for ∏0, Lq, L, & W.
The information I am given is: λ=11.98, μ=7 and s=2.


Homework Equations





The Attempt at a Solution


I am trying to figure out how the book i am using solved the problem. The book does not demonstrate how to solve this type of queieing problem?? I do have the answers for everything I am looking for, just do not know how to find them.
p=.8557, π0=.2826, Lq=0.13527, L=1.8467, W=0.1541

Any help with formulas to use in solving this problem will be greatly appreciated.
 
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  • #2
caliboy said:

Homework Statement


OK I am dealing with a Queue type problem that is M/M/2. I have already solved most of the problem but I can not figure out how to solve for ∏0, Lq, L, & W.
The information I am given is: λ=11.98, μ=7 and s=2.


Homework Equations





The Attempt at a Solution


I am trying to figure out how the book i am using solved the problem. The book does not demonstrate how to solve this type of queieing problem?? I do have the answers for everything I am looking for, just do not know how to find them.
p=.8557, π0=.2826, Lq=0.13527, L=1.8467, W=0.1541

Any help with formulas to use in solving this problem will be greatly appreciated.

You are supposed to show your work. What have you done so far? Where are you stuck? That is: exactly what does the question say, what parts have you already done, and what did you get?
 

Related to Statistics Queue problem: M/M/2

1. What is the meaning of M/M/2 in the "Statistics Queue problem"?

In probability theory, M/M/2 is a notation used to represent a queuing system with two servers, where arrivals and service times follow a Markovian or exponential distribution. This means that the time between arrivals and the duration of service for each customer are both random and independent.

2. Why is the M/M/2 queuing system important in statistics?

The M/M/2 queuing system is commonly used in statistics because it is a simple yet powerful model for analyzing queuing systems. It allows for the calculation of important performance measures such as the average waiting time, average queue length, and the probability of a customer having to wait in the queue.

3. What are the assumptions made in the M/M/2 queuing system?

The M/M/2 queuing system assumes that the arrival rate of customers follows a Poisson distribution and the service times follow an exponential distribution. It also assumes that the system operates in a steady state, meaning that the arrival and service rates remain constant over time.

4. How is the M/M/2 queuing system solved?

The M/M/2 queuing system can be solved using various mathematical techniques, such as the Markovian method or the queuing network method. These methods involve calculating the probabilities of different states of the system and using them to determine the desired performance measures.

5. What are some real-world applications of the M/M/2 queuing system?

The M/M/2 queuing system has various applications in different fields, including telecommunications, computer networks, and manufacturing. For example, it can be used to analyze call centers and determine the optimal number of operators needed to minimize customer wait times. It can also be applied to study traffic flow and optimize transportation systems.

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