Queueing server with exponential+deterministic stages

  • Context: Graduate 
  • Thread starter Thread starter lahanadar
  • Start date Start date
  • Tags Tags
    Server
Click For Summary
SUMMARY

This discussion focuses on modeling the probability density function (PDF) of a queuing system with two parallel servers: one with an exponential service rate (μ) and the other with a deterministic service rate (k). The first server is chosen by customers with probability p, while the second is chosen with probability 1-p. Participants suggest using a linear combination of the individual servers' PDFs to represent the overall system and recommend Monte Carlo simulation as a verification method, although the primary goal is to derive the PDF through computation.

PREREQUISITES
  • Understanding of queuing theory concepts, specifically M/M/1 and M/D/1 systems.
  • Familiarity with probability density functions and their applications in queuing models.
  • Knowledge of Monte Carlo simulation techniques for statistical modeling.
  • Experience with Markovian processes and their relevance in queuing systems.
NEXT STEPS
  • Research how to derive PDFs for M/M/1 and M/D/1 queuing systems.
  • Learn about linear combinations of probability density functions in queuing theory.
  • Explore Monte Carlo simulation methods for validating queuing models.
  • Study Markovian queue models and their applications in complex systems.
USEFUL FOR

Queueing theorists, operations researchers, and systems engineers looking to model and analyze complex queuing systems with mixed service rates.

lahanadar
Messages
22
Reaction score
2
Hi, does anyone know how to model probability density function, b(x), of a system that has two parallel servers:

-The first is selected by the customer with probability p, it has an exponential rate of \mu.
-The second server is selected by the customer with probability 1-p, it has a deterministic rate of k.
-When a customer chooses a server, another servers waits until the customer being served leaves.

If the second server were an exponential rate server, it would simply be an M/Er=2/1 system but now I don't know how to model this. Can anyone help me, please?
 
Physics news on Phys.org
Hey lahanadar.

Are you allowed to use Monte-Carlo simulation to simulate the process so that you get a PDF (by stipulating a large enough number of simulations)?
 
Hey lahanadar.

Are you allowed to use Monte-Carlo simulation to simulate the process so that you get a PDF (by stipulating a large enough number of simulations)?
 
Not really, I should find it by computation. I think one way could be representing the over all server pdf by linear combination of individual servers' pdfs, while first has an exponential pdf and second unit step function. Do you think this works?
 
Last edited:
Have you constructed a Markovian system for your queues (if you can't use simulation)?

Even if you do it analytically, I would suggest you use simulation to double check your work and get into the habit of double checking things in this way for the future.
 

Similar threads

Graduate Solving Queueing Problem: Population to Queue to Server
  • · Replies 2 ·
Replies
2
Views
2K
Comp Sci What is the idle time of each server in three server systems?
  • · Replies 0 ·
Replies
0
Views
2K
Graduate Calculating Waiting Time with Weighted Servers in Queueing Theory
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Queueing Models: Generator Matrix for M/M/2/2 & M/M/2/4
  • · Replies 18 ·
Replies
18
Views
3K
MHB Could use help, know the answers but with the process and equations
  • · Replies 2 ·
Replies
2
Views
3K
How Is Queueing Theory Applied in a Busy Store's Christmas Sale?
  • · Replies 6 ·
Replies
6
Views
2K
Statistics Bernoulli single-server queuing process with ATMS
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Understanding permutations and combinations in a coin toss experiment
  • · Replies 6 ·
Replies
6
Views
1K
Graduate Exponential Distribution Problem
  • · Replies 5 ·
Replies
5
Views
8K
Graduate Is Discarding the Higher Random Number in a Stochastic Queue Simulation Correct?
  • · Replies 4 ·
Replies
4
Views
1K