Questions tagged [queueing-theory]
Queueing theory is the mathematical study of waiting lines, or queues.
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Queueing model with two arrival rates
Suppose I have a process that has poisson arrival rate for some fixed time span $T$ and zero arrival rate for the next time span $T$ alternatively while being processed throughout with service times ...
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M/M/2 with 1 type of customer, 2 types of servers, and customer cannot choose server [closed]
I am new to queuing theory--is there a type of model where M/M/2 involves 1 type of customer but 2 types of servers (e.g., one fast and one slow)? Would it follow the same logic for a M/M/3 with 3 ...
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Modelling a queueing system with equal processing speed across n workflows
Hey all need some help on a real world queuing system. Apologies if we are a little loose with some terminology.
Let a workflow $w_i$ consist of steps $s_k$. A workflow can have n steps, which are ...
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Queuing theory - Probability of servers being busy when packets are discarded if all servers are busy
Here are some simple twists on a queuing question that I cannot seem to get my head around.
a) Suppose that a server $S$ receives packets at rate $\lambda$. Call this arrival process $A$. The time ...
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Independence assumption for interarrival time [closed]
I am new to Queuing systems. There is an independent assumption made for the interarrival time. Can someone please explain to me why this assumption is true, can you provide me with an example?
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Distribution of the longest queue's length in parallel queues
Considering $n$ people line up at $q$ queues.
Let's say all people choose which queue to line up randomly, so each people has probability $1/q$ to choose a particular queue. Then the length of any ...
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Queues wait for other queues: A communication problem
I am working on a problem which involves a single server that requires multiple inputs to do a computation. Each of these inputs arrive as a Poisson process with rate $\lambda$. Hence, a situation ...
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Calculating Variance in Waiting Time for a Queueing Network
I'm working on a queueing network model that incorporates blocking and features two states. After defining the global balance equations, I solved them for my parameters arrival rates (λ), service ...
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Let $W_t$ be the standard Wiener process, find probability $P_t(u)=P(|W(s)|\leq u,0\leq s\leq t)$.
For an one-dimensional standard Wiener process $W_t$, find $P_t(u)=P(|W(s)|\leq u,0\leq s\leq t)$.
This arises from the problem to find the first time a random walk has travelled a given distance, or ...
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Queueing theory - connected queues stability condition
hey everyone, given a system with poissonian process split with probabilities p and q to queues with exponential serving times, notice you can move from being assigned to queue 1 to instead being ...
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M/M/c Queue Model Solutions for Average Waiting Time and Queue Length
I am seeking assistance with a queueing theory problem involving the M/M/c queue model from my textbook. I have attempted to solve the problem and would greatly appreciate it if someone could review ...
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Number of ways arrival and departure events happen in a FIFO queue.
Consider a FIFO queue with an upper bound of queue size $U$. $N$ people already in the queue when this person A arrives at time $t_0$. Now there are $N+1$ people in the queue ($N+1\leq U$). Suppose A ...
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How to calculate the response time with M/M/c/PS(Processor Sharing) models in queueing theory?
I'm trying to model the process scheduling mechanism in Linux using queueing theory models.
Assuming that both the arrival and processing times of processes in the system follow a Poisson distribution ...
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M/M/1 Queues : Exclusive Queue Length is not Markov
For a M/M/1 queue let $N_q(t) = (Q(t)-1)^{+}$ be the number of customers in the queue except the one being served. We have to show that $N_q(t)$ is not a continuous-time Markov chain. [src: Sidney ...
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Interpreting $\displaystyle\frac{\lambda}{c\mu}<1$ in steady-state solution of M/M/c model
In this video, the professor embarks on finding the equilibrium solution to an M/M/c queueing model, with the condition that $\displaystyle\frac{\lambda}{c\mu}<1$, where:
Customers arrive into the ...
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