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47 views

Jackson's theorem to optimize mean queue length of a traffic model

The following question I posted in mathematics stack exchange one month ago[http://math.stackexchange.com/questions/1307077/jacksons-theorem-to-optimize-mean-queue-length-of-a-traffic-model] but ...
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0answers
59 views

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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0answers
22 views

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 ...
4
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1answer
107 views

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 ...
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0answers
161 views

Repeatedly changing queue behavior

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 ...
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1answer
166 views

Matrix Generator for M/M/1 Queue Waiting Time Distribution

I "believe" that generator, $\bf W$, of the waiting time distribution for the M/M/1 queue is given by the following (I'm not sure if this is even correct): ${\bf W} =\left( \begin{array}{ccccc} 0 ...
4
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1answer
189 views

Concurrency related problems in $n$ independent, parallel $M/M/1$ queues

Queueing Model: Consider $n$ independent, parallel $M/M/1$ queues with identical arrival rate $\lambda$ and service rate $\mu$. For each $M/M/1$ queue, we use the FCFS (First Come First Served) ...
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1answer
77 views

Minimal variance for phase-type distributions?

Let $\mathcal{D}(m)$ be the set of phase-type distributions constructed from $m+1$-state Markov chains. Recall that the coefficient of variation of a distribution $D$ is the ratio of the standard ...
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1answer
175 views

A queuing process where customers must be detected

Imagine a scenario where customers arrive in some queue according to a Poisson process with rate parameter $\lambda_{arr}$, and where the process of responding to the customers has a kind of ...
0
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1answer
147 views

M/G/1 queue - probability that waiting time is zero

so: I have a M/G/1-queue with Poisson arrivals with rate lambda=1 and the service time being the sum of two exp-distributed variables vith rates u1=1 and u2=2. If we let Wq be the time an average ...
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0answers
235 views

Wiener-Hopf Integral/Lindley's Equation

Lindley's equation is well known within queueing theory and is as follows $F(y) = - \int_0^\infty F(x)dH(y-x)$ However, many textbooks only consider the case where 0 $\le$ y $\le \infty$ (which ...
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2answers
294 views

If Mean Residual Lifetime is approximately constant, Residual Lifetime is Approximately Exponential in a Strong Sense

Suppose the "mean residual lifetime," $\mathbb{E}[X-x|X≥x]$ is approximately constant for large $x$. Then, I believe that the conditional tail distribution is approximately exponential, in the sense ...
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0answers
184 views

Comparing two Markov chains

I thought that this question is more appropriate for math.stackexchange, where I asked it, but seeing how I got no response, here it goes: I am interested in the question of the positive recurrence ...
5
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1answer
513 views

Are there interesting problems involving arbitrarily long time series of small matrices?

Are there well-known or interesting applied problems (especially of the real-time signal processing sort) where arbitrarily long time series of small (say $d \equiv \dim \le 30$ for a nominal bound, ...