# Tagged Questions

2answers
130 views

### When does the next bus come?

People arrive at a bus stop according to a Poisson process at rate $\lambda$ per minute. The bus leaves every $n$ minutes, but you have no idea when the last bus left. You observe that there are $k$ ...
0answers
119 views

### Boundedness of expected reward Markov chain (may be related to discret $M/M/\infty$ queue)

[EDIT]: I read a bit on $M/M/\infty$ queue and it may not be the right comparison and my notation may be confusing (I'm in discrete time and $\lambda,\mu$ look likes rates when they are probability). ...
0answers
87 views

### Is Queueing Theory dead? [closed]

I was studying queueing theory for my class and noticed that we are now able to either solve with certainity most queiening problems or simulate them. is queueing a dead research area? I read this ...
0answers
43 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 ...
1answer
113 views

### Markov Chain Transition Intensity Conversion

I have a question about converting a 3-state discrete state, continuous-time, markov chain to a 2-state. My 3-state model has states: Well (state 1), Ill (state 2) and Dead (state 3). ...
1answer
145 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 $[0,4]$, ...
0answers
46 views

### Probability that a presentation will be on time

I'm visiting a grand conference soon which has 30 lectures in a single day. Unfortunately they don't say when each of the lectures will be held. Only that each will be held in the order written ...
2answers
512 views

### One vs multiple servers - problem

Consider the following problem: We have a simple queueing system with $\lambda%$ - probabilistic intensity of queries per some predefined time interval. Now, we can arrange the system as a single ...
1answer
100 views

### Queueing Theory - Probability that all jobs have been served?

Suppose I have M/M/1 system with $\lambda = 4$ per hour and $\mu = 5$ per hour. How can I find out if all jobs have been served after, say, 8 hours? At first I thought about doing $P(n > 40)$ since ...
2answers
254 views

### The processing time of an M/M/1 queue

Suppose I have a queue with $\lambda$ and $\mu$. I can calculate the probability that there are 2 objects in the queue trivially, but how can I compute, for example, the probability that it takes an ...
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