# Questions tagged [queueing]

The mathematical study of waiting lines.

61 questions
2answers
143 views

### 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’...
2answers
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 ...
1answer
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 ...
1answer
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: ...
2answers
965 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 ...
1answer
133 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 ...
1answer
347 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 ...
3answers
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 ...
2answers
453 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%; ...
1answer
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 ...
1answer
1k views

### Distribution of arrival times to server for an M/M/1 queue (what the server experiences)

In an M/M/1 queue, we know that inter-arrival times are exponentially distributed, and that service times are the same. What is the distribution of to-server inter-arrival times (aka service start ...
1answer
138 views

### CDF of multiple exponential random variables

Assume we are are serviced by core $I$, where $I=i$ and $i=[0, n]$, with probability $p_i$. Also assume that the time needed by each $i$ in order to complete a job is an exponential random variable ...
1answer
415 views

0answers
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2answers
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### 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: ...
1answer
309 views

### How to predict and optimize a queue?

I am trying to determine if I can model my system as a M/M/1 queue and if so do the numbers I get from it help me at all. I can model my system like this: System Description A. I want to spec out ...
1answer
99 views