Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. consider a single server system with a limit of 3

Consider a single server system with a limit of 3 jobs (an M/M/1/3 system). Let ?...

80.2K

Verified Solution

Question

Advance Math

Consider a single server system with a limit of 3 jobs (anM/M/1/3 system). Let ? be the mean arrival rate and ? be the meanservice rate.
(a) Use the singleton subset partition method to derive asystem of balance equations (note the last equation is theprobability norming equation):
?p0??p1 =0 ?p0+?p2?(?+?)p1 =0 ?p1+?p3?(?+?)p2 =0 ?p2??p3=0
p0+p1+p2+p3 =1.
(b) Use the subset partition between successive nodes toderive a system of balance equations.
(c) Solve for each pi in terms of p0 for each set of balanceequations (a and b) to establish that they yield the samesolution.

Answer & Explanation Solved by verified expert
4.4 Ratings (619 Votes)
SolutionaSince this system can have at most 3 jobs there are 31possible states representing the number of jobs in the system Interest is indeveloping the steadystate distribution    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Programming
1.2K views

You have been requested to design a schema (as an E/R diagram) for the contact-tracing database....

Civil Engineering
1.2K views

A disk rolls along a flat surface at a constant speed of 10m/s. Diameter is 0.5m....

Mechanical Engineering
1.2K views

Using this sample matlab code: clear all; clc A= ????????; B= ????????; AUG=[A B]; for L=1:size(A,2) %Pivoting starts for k=L:size(AUG,1) for m=k+1:size(AUG,1) if abs(AUG(k,L))

Accounting
1.2K views

Seattle Coffee Limited's bank statement for the month of November 30, 2020 showed a balance per...

Biology
1.2K views

which of the following is a role of the lymphatic system O brings microbes antigens...

Physics
1.2K views

Q 40 Magnetic field due to 0 1 A current flowing through a circular coil...

Statistics
1.2K views

0 05 0 15 0 2 0 3 0 1 0 2 0 3 4...

Algebra
1.2K views

11 1 point The domain of the graph of this equation is all real numbers...

Accounting
1.2K views

Determine whether the following items included in Wong Company's January bank reconciliation will require adjustments...

Accounting
1.2K views

A. The depreciation of national currency most likely increases profit of: 1. Government-owned company...

Accounting
1.2K views

In January year 1, the Under Mine Corporation purchased a mineral mine for $3,400,000 with...

Finance
1.2K views

Tonys Racing Engines, Inc. wants to replace a 10-year-old cylinder boring machine with a new...