Questions tagged [queueing]

The mathematical study of waiting lines.

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6
votes
1answer
381 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 ...
11
votes
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 ...
14
votes
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 ...
2
votes
3answers
108 views

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 ...
4
votes
1answer
418 views

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^{-...
4
votes
1answer
88 views

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. $\...
8
votes
2answers
971 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 ...