# Questions tagged [queueing-theory]

Queueing theory is the mathematical study of waiting lines, or queues.

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### Non-standard Queuing Theory problem (Modified M/M/1)

Haven't see anything like it in queueing theory, the problem appears to be M/M/1 but with a twist? Description: The server starts serving calls only when the number of customers in the system becomes ...
• 35
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### Intersections of line segment with discs distributed as blue noise?

My question Suppose that we have discs of radius $r$ in the plane, where the discs' centres are distributed as blue noise with a minimum centre-to-centre distance $d$ with $2r < d$; equivalently (...
• 1,020
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### Queue system with 2 parallel servers that works one at a time. Mean waiting time?

Consider a queueing system where customers arrive according to a Poisson process with rate $\lambda$, but the service facility consists of two parallel servers. A customer upon entry into the service ...
• 101
1 vote
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### Expected idle time of a server in an M/M/N queue

Consider a standard M/M/N queue where the jobs' arrival rate is $N\lambda$, the service rate of each of the $N$ servers is $1$, and $\lambda < 1$. When a new job arrives, assign it to an idle ...
• 1,433
1 vote
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### Percentage Jobs drop in $M/M/1 K$ Queue with Finite Queue Length

In my simulation of the $M/M/1 K$ Queue, the arrival rate $\lambda$ is $2.7\ \mathrm{ jobs/s}$ while the service rate $\mu$ is $3 \ \mathrm{ jobs/s}$. The capacity $K$ of the buffer is $5$. I am ...
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### Can you explain the queueing question/answer in this MBA exam?

In the paper that describes how ChatGPT could pass an MBA exam there is a question and associated answer relating to queueing that seems intuitively wrong. I copy the question and the answer the ...
• 157
1 vote
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### A strategy for photographer using limited camera and films to take photos for all houses

I was asked a question about developing strategy for a photographer. This guy has a camera which can take maximum $n$ photos. And he hangs on the street consisting $p$ houses. He wants to take photos ...
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### Number of departures in queues as an integral

In a queue with unit mean Poisson service times the number of departures are given by $$D(t)=\int_0^t \mathcal N(ds)$$ where $\mathcal N$ is the unit mean Poisson process. How should I think of this ...
• 405
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### Erlang B formula to solve a probability problem

I am trying to solve this problem where I need to express a probability problem as a queueing problem. I'm having troubles getting the distributions right. Here's the problem: There are $n$ keys, only ...
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### Simple process equivalent definitions

How do I prove that the two definitions of a simple process are equivalent? Definition 1. Let arrival process $\xi(t)$ satisfy the Markov property. Let the probability of $k$ arrivals within the time ...
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### M/M/c queue is it time sliced or discrete?

I am using a queuing model based on an M/M/C queuing calculation. I am interested to know if it is generally a time slice model and not discrete? I'm not able to provide the calculation being used, ...
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### Question about Markov Chain's - Queueing Theory

Consider a Markov chain $X_n$, for $n=0, 1, 2, \ldots$, with states 0, 1, 2, whose transition probability matrix is P = \begin{bmatrix} 0 & 1/2 & 1/2\\ 1/2 & 1/2 & 0\\ 1 & 0 & ...