0
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1answer
34 views

How do you find the probability of a certain state in Markov Chain?

This question appears without answer in an old exam I found (not a homework question) Suppose messages that enter a system need to be processed by two servers. They arrive at the system at a ...
0
votes
0answers
23 views

G/G/1 Queues - Book with Discrete Time Markov Chain examples

Need some book recommendation or links which have examples how to solve G/G/1 queues with detailed Discrete Time Markov Chain drawn and how to get the steady state distribution, the average number of ...
0
votes
2answers
42 views

Continuous Markov chains, arriving pairs

I have been trying to sort out this exercise but really stuck on this. Preparing myself for exams and found many exercise on continuous Markov chains but I am always stuck when it comes to transition ...
2
votes
0answers
56 views

What does a customer see when it begins to be served in $M/M/1$ queue?

In queueing theory, the PASTA (Poisson Arrivals See Time Averages) principle [wiki] justifies $a_n = P_n$ where $$a_n = \text{proportion of customers that find } n \text{ in the system when they ...
0
votes
1answer
51 views

M/M/1 Queuing Theory Question

Lets say I have packets arrive to a terminal at Poisson rate $\lambda$ per hour and my terminal has an exponential service rate $\mu$ per hour (so the mean service time is $\frac{1}{\mu}$). So this is ...
1
vote
1answer
29 views

Strict proof of markovity of queing system of type $M/M/n/\infty$

I have a queing system of type $M/M/n/\infty$. The service time is exponential, and the arrival process is poisson. I do understand that because of these two facts the future of the system in ...
0
votes
1answer
49 views

M/M/1 queue with probability of new client leaving

I'm looking at a M/M/1 queue system and trying to show that $\{M_t\}_{t\geq}0$, the number of clients in the system, is a birth-death process. In the simplest of cases this is true if $\lambda_i = ...
0
votes
1answer
50 views

What is the Deterministic Traffic Generation Model?

I am studying Markov chains and queuing theory. I was curious about traffic generation models and actually happened to see the Deterministic Traffic Model, referred to as $D$ in Kendall's notation. ...
0
votes
1answer
29 views

Queue system with queue-triggered input process

I have a queue system, a classic system with an input generator, a queue and a servant. The servant is a $M$-servant with a certain serving rate $\mu$. The queue can contain an infinite number of ...
1
vote
1answer
64 views

Application of queueing theory

Jake's Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now be made on the speed at which to set the grinder. The grinding time required by a machine operator ...
0
votes
2answers
71 views

Calculate average time to empty the router

Consider a buffer, in which every second the number of packets increases by 1 with probability. Currently there are n packets in the router. Calculate the required to empty. Any help?
0
votes
0answers
43 views

Is this two dimensional Markov chain correct for this queueing system?

The problem that I have two single server station with no queuing space a customer goes to station 1 if it is available else it goes to station 2 if it is available or it will be lost output from ...
0
votes
1answer
114 views

m/m/2 question in queueing theory

Customers arrive at a serving-system according to a Poisson process with rate 1. In the system there are two serving stations, A and B, which only take care of one customer at a time. If a customer ...
-1
votes
1answer
206 views

markov chain application

Two workers handle three machines(i.e. we can at most repair two machines at a time). The time until the machine breaks down is exponentially distributed with expectation value 1/2 and independent of ...
1
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1answer
199 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 ...
1
vote
1answer
50 views

Mean number of particle present in the system: birth-death process, $E(X_t|X_0=i)$, $b_i=\frac{b}{i+1}$, $d_i=d$

Let $\{X_t\}$ be a birth–and–death process with birth rate $$ b_i = \frac{b}{i+1}, $$ when $i$ particle are in the system, and a constant death rate $$ d_i=d. $$ Find the expected number of particle ...
1
vote
0answers
222 views

Modified M/M/1/2 with 2 possible arrival rates and M/M/1/5 queue

I've been stuck on this question for hours, and could use some help :) "An M/M/1/2 queue has service rate $\mu$ and arrival rate of either $\lambda_1$ or $\lambda_2$. The rate can change only when ...
2
votes
1answer
199 views

Question on M/M/2 queue variation

I have the following question: Two workers handle three machines(i.e. we can at most repair two machines at a time). The time until the machine breaks down is exponential distributed with expectation ...
2
votes
0answers
158 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). ...
1
vote
2answers
461 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). ...
1
vote
1answer
233 views

Queueing model with two servers

I have a two-server queue with Poisson arrival rate and $\lambda$ exponential services with $\mu$ ( first server service rate) and 2$\mu$ ( 2nd server service rate). Capacity is infinite. Then why is ...
1
vote
1answer
151 views

Chernoff bound for Geometric RVs compared to exact tail bound

I keep getting a result I can't interpret. X is a Geometric RV with distribution ($0<\rho<1$) $$ \pi_k = \rho^k(1- \rho) $$ so directly applying Geometric series the tail bound is $$ B_1 = ...
2
votes
1answer
223 views

Comparing two Markov chains

I am interested in the question of the positive recurrence of a Markov chain that (in some sense) converges to another Markov chain known to be positive recurrent. The following is a concrete example ...