# Questions tagged [queuing-theory]

Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.

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### How to estimate the number of expired orders in a factory?

I have this Operations Research problem : Suppose there is a factory that on day 1 has 100 boxes New boxes arrive according to some random rate (e.g. Poisson Distribution) There are 5 employees at ...
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### Multiclass arrivals with different service rates but equal priority

I have a 3 class arrival, each having arrival rate $\lambda_i$ and service rate $\mu_i$. I want to know this queue's expected queue length ($L_q$) and queue waiting time ($W_q$). Assume $M/M/1$ ...
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1 vote
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### Expected queue length in various queueing models

Is there a resource, or could someone list out the expected queue length ($L_q$) in each type of queue model with a server capacity: M/M/c; M/D/c; G/G/c; G/D/c; G/M/c
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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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### Queuing theory question [closed]

At a computerized Rail Reservation window, the customer arrivals are considered to be Poisson with an average inter-arrival time of ten minutes. The railway clerk's time for serving the customer (...
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### Circular queue modeling

Let $P$ be a set of discretely interruptible processes/tasks; $T_i \in \mathbb{N}$ be the running time of process $i \in P$; And $\tau \in \mathbb{N}$ be the maximum amount of time a process can use ...
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### Confusion with Expected Queue Length (Lq) Formulas for M/M/s Model in Queuing theory

I have found two formulas for Expected Queue Length $L_q$ for the M/M/s model regarding Queuing Theory, namely: Found inside the "Introduction to the Operations Research" book made by ...
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### Queueing system with 2 heterogeneous servers with prioritizing customers

This is a special case of a $M/M/c$ queuing system with $c=2$. Here, there is a single customer queue that feeds into two servers, one of which has a higher rate of service than the other. Call them ...
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### How does one model weather in Simio and have it change how vehicles operate within the model?

For context, I am using the Simio modeling software for an OR class, and for fun I am making a simulation model of the traffic outside my dorm. I have recreated the layout and distance of the streets, ...
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### Service probability for M/M/c queue for reneging where reneging time is a function of service time

There is an M/M/1 (getting a result for M/M/c is ideal) queue with arrival rate 𝜆 and service rate 𝜇 and participants can renege. However, the difference between normal reneging settings (constant ...
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### Understanding queueing theory used to model the vehicle routing problem

I am trying to understand some journal articles on the vehicle routing problem, specifically Vehicle routing with dynamic travel times: A queueing approach and An M/M/c queue model for vehicle routing ...
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### m/m/1/k=1 variance

Is there a nice formula for the finite time variance of the m/m/1/k=1 queue in steady state? (Exponential arrivals $\lambda$, exponential service time $\mu$, 1 server and no queue, so if a job arrives ...
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### Modeling an assembly line as a batch processing $M/D^{(b,b)}/r$ queue

Consider an assembly line where some parts are produced in a station following a Poisson process with a rate of $\lambda$. These parts are put directly in a bin (transfer time to the bin is negligible)...
1 vote
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### The impact of utilization rate of a queueing system on its average queue time

For an $M/M/c$ queue where arrivals follow a Poisson distribution with rate $\lambda$ and are iid, service follows a Poisson process with rate $\mu$ and there are $c$ parallel servers, we can estimate ...
1 vote
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### Model or State Uncertainty in Queueing Model due to uncertain arrival rate

Introduction I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy via Value or ...
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### Queuing models in R, $\lambda$ Little
It's noted that the number of folks in a stationary system will maintain an average equal to the rate of arrival multiplied by the mean of the service distribution. The formula $L = \lambda w$ is ...