The mathematical study of waiting lines.
Questions tagged [queueing]
90 questions
16
votes
2 answers
Why is the Poisson distribution chosen to model arrival processes in Queueing theory problems?
When we consider Queueing theory scenarios where individuals arrive to a serving node and queue up, usually a Poisson process is used to model the arrival times. These scenarios come up in network routing problems. I'd appreciate an intuitive…
Vighnesh
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Distribution to reflect situation where some waiting leads us to expect more waiting
In reading Blake Master's notes on Peter Thiel's lecture on start ups, I came across this metaphor of the technology frontier:
Picture the world as being covered by ponds, lakes, and oceans. You’re
in a boat, in a body of water. But it’s…
Andy McKenzie
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12
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1 answer
A hair dresser's conundrum
My hairdresser Stacey always puts on a happy face, but is often stressed about managing her time.
Today Stacey was overdue for my appointment and very apologetic. While getting my haircut I wondered:
How long should her standard appointments be?…
Nick
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12
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1 answer
Monte carlo simulation in R
I am trying to solve the following exercise but I actually have no clue on how to start doing this. I've found some code in my book that looks like it but it's a completely different exercise and I don't know how to relate them to eachother. How can…
user3485470
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9
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2 answers
General approaches to model car traffic in a parking garage
a friend of mine has asked me to help him with predictive modelling of car traffic in a medium sized parking garage. The garage has its busy and easy days, its peak hours, dead hours opening hours (it is opened during 12 hours during weekdays and…
David D
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7
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Queuing theory for elevators
It's been a while since I had my probability course based on Sheldon Ross' book "Probability Models", and while I never went into econometrics, I was very interested in the queuing theory section. I thought about this problem, and figured it has a…
AdamO
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7
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Finite state machine with gamma distributed waiting times
I have a state machine with positive and negative inputs. The time between positive inputs follows a gamma distribution ($X_+ \sim \Gamma(k_+, \theta_+)$), and the time between negative inputs follows a different gamma distribution ($X_- \sim…
mwoods
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7
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1 answer
The Number of Exponential Summands in a Fixed Interval is Poisson
What is the most clever way to prove that the number of independent exponential summands in a fixed interval is distributed as a Poisson random variable? I can do it one way, but I would like to know if there is another way that gets more style…
Taylor
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7
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Dynamics of birth-death process with discouraged arrivals (alternatively, M/M/1 queue with balking customers)
Take a continuous-time birth-death process, where $k \in \{0,1,\ldots\}$ is the count and
the arrival rate of death is $\mu \geq 0$ for $k = 1, 2, \ldots$
the arrival rate of births is $\alpha_k > 0$ for $k = 0,1,\ldots$. For extra simplicity,…
jlperla
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6
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Exponential Service Times When a Minimum Service Time is Reasonable
In many queuing models it is assumed that the service time follows an exponential distribution with parameter $\mu=1/\lambda$, where $\lambda$ is the average rate of service. An example might be a bank teller who, on average, is able to service…
tjnel
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6
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3 answers
Assumption for an M/M/1 queue
When a queueing system is modeled as an M/M/1 queue, it is assumed that the arrival time of jobs has Poisson distribution and the service rate has exponential distribution. I am wondering what features a system should have in order to model the…
Javad
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5
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1 answer
Mean length of time spent queueing in $M/E_2/1$ system?
Context: Consider a $M/E_2/1$ queueing system, where the customer arrival rate is $\lambda$ and the service time distribution has a gamma distribution with parameters $2$ and $\mu$, i.e. with p.d.f. $\mu^2te^{-\mu t}$ , $t ≥ 0$
Question: Assuming…
Clair Crossupton
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5
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1 answer
Mean service time of a $M/E_2/1$ queueing system?
Consider a $M/E_2/1$ queueing system, where the customer arrival rate is $\lambda$ and the service time distribution has a gamma distribution with parameters $2$ and $\mu$, i.e. with p.d.f. $\mu^2te^{-\mu t}$ , $t ≥ 0$
(1) How can I determine the…
Clair Crossupton
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5
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2 answers
Poisson distribution problem - traffic problem
Hi So I have this question below. I know I need to model each lane as a separate Poisson distribution. The possible answers are:
a) 11.4%; 22.4%; 33.4%; 44.4%; 55.4%
b) 2.74%; 4.74%; 12.74%; 34.74%; 64.74%
but obviously I need to know how to get to…
Kyle
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5
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1 answer
Why is the exponential distribution chosen to model service time in Queuing theory?
Why is the exponential distribution chosen to model service time in Queuing theory ?
user3914897
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