Questions tagged [queuing-theory]
The queuing-theory tag has no usage guidance.
16
questions
3
votes
1answer
41 views
Service probability for M/M/1 queue with reneging
Consider an M/M/1 queue with arrival rate $\lambda$ and service rate $\mu$, where participants renege after a random amount of time which follows an exponential distribution with mean $\tau$. We ...
12
votes
1answer
95 views
Model or State Uncertainty in Queueing Model due to uncertain arrival rate
Introduction
I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy via Value or ...
7
votes
1answer
124 views
The departure process of an $\rm M/M/\infty$ queue
Burke's theorem says that the output process of an $\rm M/M/1$, an $\rm M/M/C$, and a $\rm M/M/\infty$ queue with arrival rate $\lambda$ and service rate $\mu$ follows a Poisson with parameter $\...
2
votes
1answer
54 views
How do derive the steady state probabilities M/M/1/k queueing system?
How do I derive the steady state probabilities for the $M/M/1/k$ queueing systems with finite system capacity $k$?
3
votes
0answers
43 views
Two M/M/1 queues working independently
If two M/M/1 queues with arrival rate $\lambda$ and service rate $\mu$ are working independently. Is the system equivalent to a single M/M/1 queue with arrival rate $2\lambda$ and service rate $2\mu$?
1
vote
2answers
105 views
Waiting time in M/M/n queue
I was able to numerically "show" that an M/M/n queue is concave increasing in the number for $n$ servers, which makes intuitive sense. However is there a formal analytical proof for it? Where can I ...
5
votes
0answers
18 views
Approximate average waiting time when a m\m\1 queue shows transient behavior
I have an m/m/1 queue and a set of arrival rate $\{\lambda_{t_1}, \lambda_{t_2} ...., \lambda_{t_n}\}$ and a fixed service rate $\mu$. I want to calculate the average waiting time during each time ...
1
vote
0answers
62 views
Combining Two Different Queues
I am trying to create an optimization model for a problem that involves two different types of queues. Given Poisson demand (for both), there is a queue with constant service time and another queue ...
6
votes
0answers
33 views
MPX Queuing Software for Manufacturing with the GTHUBS Case
I'm teaching an Operations Management Class. A long time ago, there was a simple DOS-based product called MPX. It was based on queuing theory and let you model manufacturing processes. There was ...
11
votes
1answer
119 views
Queuing Theory with Learning Perspective
I am willing to work on queuing models but in classical queuing models, it is assumed the probability distributions of arrival and service are known or at least the rate is known. However, I am ...
10
votes
2answers
345 views
Current Issues of Interest
What are some current issue of interest in Operations Research? I am interested in current topics that experts in the field are interested in researching.
4
votes
2answers
254 views
Queuing models in R, $\lambda$ Little
It's noted that the number of folks in a stationary system will maintain an average equal to the rate of arrival multiplied by the mean of the service distribution.
The formula $L = \lambda w$ is ...
9
votes
1answer
242 views
Convexity/Concavity of Average Number of Jobs in M/M/1 Queue?
I am working on a problem involving the average number of jobs $L$ in an M/M/1 queue with arrival rate $\lambda$, service rate $\mu$. For traffic intensity $\rho = \frac{\lambda}{\mu}$,
$$
L = \frac{\...
3
votes
1answer
82 views
Queuing Theoretic Model with Memory
Consider a telephone company which receives call request at some arrival rate and serves each request with some service rate. This can be modeled using a Poisson Process. However I wish to model the ...
4
votes
1answer
97 views
Question about a queueing problem
Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The length of phone calls is assumed to be distributed exponentially, ...
14
votes
5answers
1k views
Good textbook for queueing theory and performance modeling
Can someone recommend a good self-study textbook for queueing theory and performance modeling? My interest is in applying this to understanding the behavior of some real-world server networks, ...
