11
votes
Accepted
Significant bias introduced into simple simulation
You have fallen victim to the renewal paradox, a.k.a. inspection paradox, a.k.a. length-biased sampling.
$F_{\Delta}$ is the distribution of service time for the kth customer, but it is NOT the ...
- 13.8k
9
votes
Accepted
Convexity/Concavity of Average Number of Jobs in M/M/1 Queue?
Your calculations (factoring and simplification) are incorrect. $L$ is neither convex nor concave as a function of $\lambda$ and $\mu$.
This can be concluded by examining the eigenvalues of the ...
- 13.8k
9
votes
Accepted
MPX Queuing Software for Manufacturing with the GTHUBS Case
Sure thing, you can download from archive.org. You need to run it in DOSBOX.
- 106
8
votes
Queuing Theory with Learning Perspective
Certainly, and to take the problem's structure into account, one could model the queue knowing - or guessing - prior information about the queue's structure and/or parameter distribution and use ...
- 1,687
7
votes
Current Issues of Interest
This is an attempt at an answer, based on my current understanding:
Background:
Operations Research is an interdisciplinary field. You go from business administration and economics to theoretical ...
7
votes
Good textbook for queueing theory and performance modeling
Unfortunately, much of the performance analysis and transient approximations for time-varying systems with non-Markovian (non-exponential) properties are not easily obtained in book form (see note at ...
- 1,895
7
votes
Queuing models in R, $\lambda$ Little
Not directly answering your question of how to code it manually but for discrete simulation of queues in R I would strongly recommend the simmer package. The ...
- 1,343
6
votes
Accepted
The departure process of an $\rm M/M/\infty$ queue
The following proof approach for Bruke's Theorem was given in this Lecture by Richard Clegg:
Definition: A chain is called time-reversible if $p_{ij} = p^*_{ij}$ for all $i$ and $j$. This occurs if ...
- 8,677
4
votes
Good textbook for queueing theory and performance modeling
I enjoyed Performance Modeling and Design of Computer Systems: Queueing
Theory in Action (Amazon link) by Mor Harchol-Balter, which sounds
like it fits your bill pretty well. I have it on my desk.
...
- 141
4
votes
Good textbook for queueing theory and performance modeling
I have used Stochastic Modeling: Analysis and Simulation by Barry Nelson and found it to be a pretty gentle introduction. It covers stochastic processes, queuing, and simulation.
- 13.2k
4
votes
Model or State Uncertainty in Queueing Model due to uncertain arrival rate
After having read Chapter 5.3 of Decision Making Under Uncertainty by Mykel J. Kochenderfer, I have come to some conclusions.
We are dealing with model uncertainty, in which case we can formulate a ...
- 463
4
votes
Accepted
How would I model the following problem concerning customer service via FCFS vs Appointment Scheduling
Since you are unfamiliar with OR, I would recommend using discrete event simulation, which I think is the easiest approach for a newcomer (although it may require some programming chops, depending on ...
- 40.1k
4
votes
Current Issues of Interest
On the solving side, some hot topics include:
presolving techniques
GPU-powered algorithms
algorithms designed for problems that consume a lot of memory
algorithms for distributed architectures
...
4
votes
Accepted
Waiting time in M/M/n queue
Dyer and Proll (1977)1 showed that for an M/M/c queue, the mean waiting time is a strictly decreasing and convex function of c.
Reference
[1] Dyer, M. E., Proll, L. G. (1977). On the Validity of ...
- 5,452
4
votes
Significant bias introduced into simple simulation
Note: This answer is intended to show what I have learned from the valuable answer provided by @Mark L.Stone. His post answered my question of why the simulation is biased. Hence, this post provides ...
- 463
3
votes
Elevator Traffic (Queueing Theory) Papers
I am not an expert in elevator traffic system simulation, but by googling you could find lots of related papers and literature. Some of them are as follows:
Modelling of Elevator Traffic Systems ...
- 9,248
3
votes
Accepted
The impact of utilization rate of a queueing system on its average queue time
I do not agree with the assertion that "both high and low utilization rate mean we are going to have a long average queue time". If $\rho$ is low (close to 0), $E[QT]$ is close to 0. Low ...
- 40.1k
3
votes
Accepted
If $x=\min\{f(\mathbf{a}),1-\epsilon\}$, how can we model and partition $x$?
Start with the constraints $$x \le f(\mathbf{a})$$ and $$x \le 1-\epsilon.$$ If the nature of the problem is that larger values of $x$ are always preferable in objective terms to smaller values of $x$,...
- 40.1k
3
votes
Accepted
Average time between two dispatches in a taxi fleet (probably a batch processing queuing system)
Let $\tau$ represent the average time between dispatches.
I'm skeptical about $\frac{\lambda T}{t}$ as a possible value of $\tau$ because it fails dimensional analysis. $\tau$ is in units of time. $T$ ...
- 40.1k
3
votes
Question about a queueing problem
This is a $M/M/1$ queue with Poisson arrival distribution with $\lambda =1/10$ and Exponential service distribution with $\mu=1/3$. The proportion of the time that the system is busy can be calculated ...
- 8,677
3
votes
Accepted
Confusion with Expected Queue Length (Lq) Formulas for M/M/s Model in Queuing theory
They are the same, with the caveat that the two sources are using slightly different notation. All symbols other than $\rho$ are the same in both places, but Hillier and Lieberman use $\rho = \frac{\...
- 40.1k
2
votes
Accepted
Service probability for M/M/1 queue with reneging
The steady-state probability of being served for an M/M/1 queue with exponential reneging times and no balking is
$$
p_s=\frac{1+z}{1+r(1+z)}
$$
where $r=\lambda/\mu$ is the service intensity, and
$$
...
- 2,117
2
votes
How do derive the steady state probabilities M/M/1/k queueing system?
There are a couple of ways to derive the steady state probabilities for a $M/M/1/k$ queuing system with Markovian* arrivals (the first $M$), exponential service time distribution (the second $M$), a ...
- 1,895
2
votes
Queuing Theoretic Model with Memory
Since you are assuming infinite capacity, this sounds like an $M/M/\infty$ queueing system.
- 40.1k
2
votes
Good textbook for queueing theory and performance modeling
I learned from Quantitative System Performance
Computer System Analysis Using Queueing Network Models by Lazowska, et.al. Unfortunately, it is no longer published, but it is available for free online....
- 121
2
votes
Good textbook for queueing theory and performance modeling
Introduction to queueing theory and stochastic teletraffic models$^1$.
The aim of this textbook is to provide students with basic knowledge of stochastic models
that may apply to ...
- 8,677
2
votes
MPX Queuing Software for Manufacturing with the GTHUBS Case
Edit: Grunchy delivers the perfect answer to your question.
However, if you want to try out something else, see my answer below:
====
I recommend SIMIO if you just want to play around and visualize ...
- 81
2
votes
Departure process of M/G/1 queue with hyper-exponential service times
It is not true. You can refer to the following two papers, which provide a general method to analyze the departure process.
The Departure Process of the GI/G/1 Queue and Its MacLaurin Series.
...
- 21
1
vote
Modeling an assembly line as a batch processing $M/D^{(b,b)}/r$ queue
t= start of service to end of service. The t for return will be part of average wait time for the queue.
- 3,513
1
vote
Queueing model without steady state
Most of the formulas I have come across in queueing theory assume steady state, and I don't know of a purely mathematical approach for all cases. So let me show you a simple simulation approach.
Using ...
- 141
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