1
vote
1answer
39 views

How would I find the PDF of one poisson variable in terms of another?

I am looking for the PDF of a Poisson variable. The setup is that pit crews are working on racecars on the track after the drivers reports trouble. The pit crew's expected work time is exponentially ...
0
votes
0answers
10 views

conditional mean of geometric RV

Say, there are three nodes: $S$, $R$, $D$. $S$ transmits to $R$, $R$ stores the packets, and later transmits to $D$. At any time, either $S$ or $R$ is selected to transmit according to some random ...
1
vote
0answers
52 views

Solving Probabilities for M/M/1 Queue Waiting Time Generating Function

I "believe" that generator, $\bf Q$, of the waiting time distribution for the $M/M/1$ queue is given by the following (I'm not 100% sure if this is even correct): $\bf Q$ = $\left( ...
1
vote
1answer
56 views

Which Queue to Join at the Super Market

Last night I started wonder about the fastest way to take a shopping trip with my university flat mates and was wonder about how we should queue for the check out. I have a feeling that queue theory ...
0
votes
0answers
17 views

Conditional Poisson PMF ~ the joint PMF not independent?

Let X denote the number of customers who arrive during a service time and Y the first service time. Customers arrive in a Poisson process with rate $\lambda$. Then: $P(X=x|Y=y)= e^{-(\lambda y)} ...
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votes
0answers
40 views

Probabilistic model of parallel web servers

Note: The following probabilistic model of parallel web servers is abstracted from an engineering project. I am not good at probability theory and I am seeking some evaluations and suggestions. ...
1
vote
1answer
202 views

Question on M/M/s queue

costumers arrive to a service station according to a poisson prossees and on average 2 during an hour.the service times and independent of the arrivals and internally independent with mean 45 minuts ...
0
votes
1answer
70 views

Proof of $ \text{Poisson}(\lambda p) $-arrivals.

We have a queue where people pass out of it with $ \text{Poisson}(\lambda) $ and they come in with probability $ p $. I understand that the arrivals follow $ \text{Poisson}(\lambda p) $, but how can ...
0
votes
2answers
235 views

M/GI/1 service time distribution

I want to compute the distribution of the waiting time and the number of jobs for M/GI/1 where the service time is Heavy-Tailed or more specifically Pareto. I found this paper ...
5
votes
2answers
5k views

What is the correct inter-arrival time distribution in a Poisson process?

Given a Poisson process (e.g. radioactive decay) with rate $\lambda$, then the expression $\exp(-\lambda t)$ is the probability of observing no counts in time interval $t$. This can be interpreted ...
2
votes
1answer
339 views

Find the probability that the second customer to arrive has to wait to be served if arrival time is exponential and serving time is uniform

Customers line up to be serviced according to a Poisson process at an average rate of five per hour. If the time it takes to serve one customer is a continuous uniform random variable on $[0,4]$, ...