# Tag Info

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
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
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

### 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

### 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 ...

### 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

### 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
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

### 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

### 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

### 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
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

### 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 ...
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

### 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

### 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
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
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
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

### 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
Accepted

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 ... 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. ... 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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