Statistics Queue problem: M/M/2

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SUMMARY

The discussion centers on solving an M/M/2 queue problem with parameters λ=11.98, μ=7, and s=2. The user seeks assistance in calculating the steady-state probabilities and performance metrics, specifically ∏0, Lq, L, and W. The provided answers include p=0.8557, π0=0.2826, Lq=0.13527, L=1.8467, and W=0.1541, but the user is unclear on the formulas required to derive these values. The conversation emphasizes the need for clarity on the mathematical approach to queuing theory.

PREREQUISITES
  • Understanding of M/M/s queue theory
  • Familiarity with the arrival rate (λ) and service rate (μ)
  • Knowledge of performance metrics in queuing systems, including Lq, L, and W
  • Basic proficiency in probability and statistics
NEXT STEPS
  • Study the derivation of steady-state probabilities in M/M/s queues
  • Learn how to calculate Lq, L, and W using queuing theory formulas
  • Explore the use of software tools for simulating queuing systems
  • Review case studies on M/M/2 queue applications in real-world scenarios
USEFUL FOR

Students and professionals in operations research, particularly those studying queuing theory, as well as anyone involved in optimizing service systems and performance metrics in various industries.

caliboy
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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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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?
 

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