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### A question about intuition of fluid limit in queuing system

This is a question about intuition in understanding the fluid limit queuing system. Assume we have a sequence of queuing systems $\{S^N\}_{N=1}^{\infty}$ with N servers and each server has unit ...
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### Analyzing a multiple-queue single-server model

Consider the following multiple-queue single-server model of a packet network problem. At each discrete time $t=0,1,\ldots,n$, a packet may arrive at the server R with probability $1-\epsilon_1$. The ...
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### Problem of random scheduling of queues of tasks

Consider $L$ queues in a discrete time system. At each time $n=0,1,2,\ldots$, one task would arrive at one of the queues with equal probability $\frac{1}{L}$. Immediately after that, a task scheduler ...
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### Expected finite time Queue Length in Birth-Death process

Consider a Birth-death process $Q(t)$ with reflection at zero with geometric arrival and departure. With probability $\lambda$ there is an arrival at each time-slot. At the end of each time-slot there ...
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### Customers and Anti-Customer Queueing Problem: What is the Customer delete probability

Hello may I ask for your help? First the setting: I have got a problem with some queueing theory. The whole problem would be a grid of nodes, all nodes have an operation intensity $\mu_{i,j}$. ...
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### Average queue-length optimal queuing system

Consider a time-slotted queuing system which has two servers and two users. At each time slot, a packet for user $1$ arrives with probability $\lambda _1$, while a packet arrives for user $2$ with ...
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### Continuity of the stationary distribution of $M/G/1$ queue w.r.t. the input rate

Let $(\lambda_n)_{n\geq0}$ be a sequence of positive numbers such that $\lambda_n\rightarrow \lambda$ as $n\rightarrow +\infty$. These $\lambda_n$ are the parameters of a sequence of Poisson Processes ...
I'm not sure if this question is suited to MO. I will happily delete if not. Situation Consider a general queueing system $\mathscr{S}$, whose customer arrival times are independent, and whose ...