# Questions tagged [queueing]

The mathematical study of waiting lines.

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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’...
19k views

### 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 ...
3k views

### 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 ...
807 views

### 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: ...
972 views

### 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 ...
135 views

### 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 ...
382 views

### 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 ...
7k views

### 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 ...
2k views

### 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 ...
465 views

### 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%; ...
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614 views

### 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 ?
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### How many random selections needed to be 90%, 95%, 99% confident that a specific selection occurred?

For example, let's say that I have a bag of 100 marbles labeled 1 to 100. A "selection" is randomly picking a marble from the bag and then placing it back into the bag. The marble selected is not ...
47 views

### Expected value of $e^{vS}$, where $S$ is an exponential

I am studying queueing theory and in particular I am dealing with priority queues with preemption. I found this very interesting paper that treats various topics of interest. The system is composed ...
204 views

### How to determine 'burstiness' of data?

This is both a Math- and an R-question. I have a vector of POSIXct dates and a I want to determine the characteristics of the data. Example with numbers: ...